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1 EFFECT OF CATHODE MICROSTRUCTUR E ON CATHODE POLARIZATION IN SINTERED STRONTIUM-DOPED LANTHAN UM MANGANITE/YTTRIA STABILIZED ZIRCONIA SOLID OXIDE FUEL CELLS By AIJIE CHEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2008
2 2008 Aijie Chen
3 To my father, the single most in fluential person in my life. He has come to mean more to me than I ever thought possible. No one will ever begin to compare to him.
4 ACKNOWLEDGMENTS I acknowledge the Alliance for Graduate Educat ion and the P rofessoriate, the Alumni of the College of Engineering, and the Department of Energy for all financial support associated with the completion of this wo rk. I also would like to tha nk my committee members, Profs. Robert DeHoff, Eric Wachsman, Mark Orazem, and Dr.Gerald Bourne, for their support. I extend gratitude to Prof. Kevin S. Jones, my supervising committee chair, for his encouragement and support, for ongoing profe ssional and personal discussions, and for guiding me through this challenging yet rewarding learning experience at UF. I am also very grateful to Prof. Robert T. DeHoff, who provi ded a great deal of insight regarding this research. Very few graduate students have the opportunity to have a committee member who truly treats them as one of their own students. I will always regret not fully exploiting the luxury of having a professor as devoted to the intellectual growth of students as he. I am also very grateful to Prof. Eric Wachsman, for providing intellectual ideas and fi nancial support for this research. Without his help on demand, I would not have completed this work. I would like to acknowledge Dr. Gerald Bourne for his assistance in developing the TEM sample preparation technique. Furthermore, I recognize, and am grateful to, several people in the Major Analytical Instrumentation Center (MAIC) w ho contributed to the success of this work. Specifically, I thank Kerry Siebein for the effective crash course in TEM analysis; Dr. Luisa Dempere for valuable advice and discussions on instrument use. I am thankful to the member s of the UF-DOE HiTEC and Software and Analysis of Advanced Materials Processing (SWAMP) groups, for providing an atmosphere of camaraderie and friendship. In particular, I would like to tha nk Dr. Jeremiah R. Smith for discussions on the fundamentals of impedance spectroscopy; I would also like to thank Danijel Gostovic, Diane Hickey, Sam Moore, and Nicholas Rudawski for invaluable disc ussions on FIB operation; Lucia
5 Romano, David Jaeger, and Sherry Huo for a dvice on writing my Ph D dissertation; and Sean Bishop and Martin Van Assche for discussions on electrochemical principles. Last but not least, I would like to acknowledge my family who has supported me in all my endeavors. I will forever be indebted to my moth er for her endless support and encouragement. I would like to extend my deepest gratitude and lo ve to my husband and best friend, Yuming Niu, for supporting me, for taking care of our son, and for brightening my life. Without his support and encouragement, I would not have completed this work.
6 TABLE OF CONTENTS Figure page ACKNOWLEDGMENTS ............................................................................................................... 4LIST OF TABLES ...........................................................................................................................9LIST OF FIGURES .......................................................................................................................10ABSTRACT ...................................................................................................................... .............13 CHAP TER 1 INTRODUCTION .................................................................................................................. 151.1Motivation .....................................................................................................................151.1.1Importance of Solid Oxide Fuel Cells (SOFCs) ............................................... 151.1.2Open Questions .................................................................................................151.2Literature Review ..........................................................................................................171.2.1Fundamentals of SOFCs ...................................................................................171.2.2Cathode Polarization .........................................................................................191.2.4Lanthanum Strontium Manganite/Yttr ia Stabilized Zirconia Materials Property ............................................................................................................. 2184.108.40.206Lanthanum strontium manganite (LSM) ............................................ 2220.127.116.11Yttria stabilized zirconia (YSZ) .......................................................... 218.104.22.168Chemical reactivity with the YSZ ......................................................301.2.4.4SOFCs processing ...............................................................................311.2.5Microstructure Properties ..................................................................................322.214.171.124Topological properties ........................................................................ 3126.96.36.199Metric properties .................................................................................3188.8.131.52Materials characterization techniques ................................................. 341.2.6Three-Link Paradigm ........................................................................................361.3Hypothesis .....................................................................................................................381.4Summary of Focused Topics .........................................................................................392 ANALYTICAL TECHNIQUES ............................................................................................452.1Focused Ion Beam/ Scanning Electron Microscopy (FIB/SEM) .................................. 452.2Stereology .................................................................................................................... .482.2.1Classical Quantitative Stereology .....................................................................482.2.2New Quantitative Stereology ............................................................................ 5184.108.40.206Serial-section probe ............................................................................5220.127.116.11Disector probe .....................................................................................542.3Transmission Electron Microscopy (TEM) .................................................................. 542.4Electrochemical Impedance Spectroscopy (EIS) .......................................................... 572.4.1Fundamentals of EIS .........................................................................................572.4.2Error Analysis of EIS ........................................................................................59
7 3 FIB/SEM TECHNIQUE DEVELOPMENT .......................................................................... 643.1Metric Property Analysis of the Composite Electrode ................................................. 643.1.1Introduction to the Composite Cathode ............................................................643.1.2Quantification of Vv,Sv and Pore Size ............................................................. 653.1.3Experimental Design ......................................................................................... 653.1.4Results and Discussions .................................................................................... 673.1.5Conclusions .......................................................................................................683.2Interfacial Analysis of the Lant hanum Calcium Manganite (LCM)/YSZ Composite Electrode ..................................................................................................... 683.2.1Objective ........................................................................................................... 683.2.2Experimental Design ......................................................................................... 683.2.3Results and Discussions .................................................................................... 703.2.4Conclusions .......................................................................................................713.3Homogeneity Analysis .................................................................................................. 713.3.1Objective ........................................................................................................... 713.3.2Disector Analysis ..............................................................................................723.3.3Experimental Design ......................................................................................... 733.3.4Results and Discussions .................................................................................... 743.3.5Conclusions .......................................................................................................764 ISOCHRONAL SINTERING STUDY ..................................................................................874.1Effect of Metric Properties on Activation Polarization.................................................874.1.1Literature Review ..............................................................................................874.1.2Quantification of LTPB and SV ...........................................................................884.1.3Experimental Design ......................................................................................... 894.1.4Results and Discussions .................................................................................... 904.1.4.1Effect of sintering on the cathode microstructure ...............................904.1.4.2Effect of metric propertie s on the reaction impedance .......................904.1.5Conclusions .......................................................................................................934.2Tertiary Phase Formation Mechanism .......................................................................... 944.2.1Literature Review ..............................................................................................918.104.22.168 Lanthanum zirconate (LZO)formation mechanism ........................... 922.214.171.124Open questions ....................................................................................974.2.2Experimental Design ......................................................................................... 974.2.3Results ...............................................................................................................9126.96.36.199LZO composition profile .................................................................... 9188.8.131.52Epitaxial relationships ........................................................................9184.108.40.206Kinetics of the tertiary phase formation ........................................... 1014.2.4Discussion ....................................................................................................... 1014.2.4.1Tertiary phase formation mechanism ............................................... 1014.2.4.2Delay of the tertiary phase formation ...............................................1034.2.4.3Change in the interfacial resistance .................................................. 1044.2.5Conclusions .....................................................................................................106
8 5 ISOTHERMAL SINTERING STUDY ................................................................................ 1155.1Effect of Metric Properties on Activation Polarization...............................................1155.1.1Literature Review ............................................................................................1155.1.2Experimental Design ....................................................................................... 1185.1.3Results and Discussion .................................................................................... 1195.1.4Conclusions .....................................................................................................1255.2Tertiary Phase Growth Kinetics ..................................................................................1275.2.1Literature Review ............................................................................................1275.2.2Experimental Design ....................................................................................... 1315.2.3Results and Discussion .................................................................................... 13220.127.116.11Epitaxial relationship ........................................................................ 1318.104.22.168LZO growth kinetics .........................................................................1322.214.171.124Contributions of LZO formati on to activation polarization .............13126.96.36.199Effect of LZO phase formation on ohmic polarization .................... 1385.2.4Conclusions .....................................................................................................1415.3Effect of the Topology Properties on Concentration Polarization .............................. 1425.3.1Literature Review ............................................................................................14188.8.131.52Skeletonization model ...................................................................... 14184.108.40.206Pore-network models ........................................................................ 14220.127.116.11Impact of gas transport on concentration polarization ..................... 1485.3.2Experimental Design ....................................................................................... 1485.3.3Results and Discussion .................................................................................... 1505.3.4Conclusions .....................................................................................................1556 SUMMARY AND FUTURE WORK .................................................................................. 1696.1Summary ..................................................................................................................... 1696.1.1FIB Technique Developments.........................................................................1696.1.2Dependence of the Activation Polari zation on the Metric Properties ............. 1706.1.3Tertiary Phase ................................................................................................. 1736.1.4Dependence of the Concentration Pola rization on Topological Properties .... 1756.2Future Work ................................................................................................................176APPENDIX A FIB MANUAL ......................................................................................................................180B ELECTROCHEMICAL PROPERTIES AND SCANNING TRANS MISSION ELECTRON MICROSCOPY-ENERGY-DISP ERSIVE X-RAY SPECTROMETRY (STEM-EDS) CONCENTRATION PROFILES ..................................................................188C GEOMETRIC PROPERTIES OF THE ISOTHERMAL SINTERED SAMPLES ............. 194LIST OF REFERENCES .............................................................................................................195BIOGRAPHICAL SKETCH .......................................................................................................205
9 LIST OF TABLES Table page 3-1 Summary of porosity an d pore size m easurement .............................................................863-2 The R and d spacing of LCM a nd YSZ on TEM diffraction patterns ............................... 865-1 Calculation of the LZO oh mic polarization (resistance) ..................................................168C-1 Geometric properties of the isothermal sintered samples ................................................ 194
10 LIST OF FIGURES Figure page 1-1 Projected energy consumption (1980~2030) .....................................................................421-2 Schematic of SOFC.......................................................................................................... ..421-3 I-V curve of SOFC ......................................................................................................... ....421-4 Pervoskite structure. ..................................................................................................... ......431-5 Fluorite structure. ....................................................................................................... ........431-6 Three-link paradigm ....................................................................................................... ....442-1 FIB geometry .............................................................................................................. .......612-2 Sampling a curve with a line probe. ................................................................................... 612-3 The calculation of net spherical image .............................................................................. 622-4 Interaction of a high-energy electron beam with a sample ................................................ 622-5 Individual resistance measurement using a modified Voigt equivalent circuit. ................ 633-1 FIB flexible geometries. .................................................................................................. ...783-2 FIB/SEM cross section of cathode supporte d SOFC sample imaged with ion beam ........ 783-3 Pore migration on the dense electrolyte. ............................................................................ 793-4 Pore size and porosity of the cross-section sample ............................................................ 803-5 Schematic of Omniprobe-mad e TEM cross-section sample .............................................. 803-6 High magnification bright field im age of LCM/YSZ and the corresponding diffraction patterns. ............................................................................................................813-7 Comparison of diffraction patterns. ................................................................................... 823-8 High resolution phase contrast im age at the LCM/YSZ interface. .................................... 833-9 Homogeneity test of the is othermally sintered samples .................................................... 843-10 Homogeneity test within a sample. .................................................................................... 843-11 Open porosity gradient of one isothermally sintered sample ............................................. 85
11 4-1 Top view of the LSM/YSZ interface.. ............................................................................. 1074-2 Cross-section images of the isochronal sintered samples ................................................1074-3 LZO formation by Mitterdorfer et al. ..............................................................................1084-4 Metric properties of the isochronal sintered samples. .....................................................1094-5 Dependence of the charge transfter re sistance on the triplephase-boundary length ....... 1094-6 Dependence of the dissociative adsorption resistance on pore surface area of the isochronal one hour sintered samples .............................................................................. 1104-7 LSM/YSZ interface after 1200 C one hour sintering. .....................................................1104-8 YSZ/LZO interface and LZO/LSM interface. ................................................................. 1114-9 LSM/YSZ interface after 1100C one hour sintering. ..................................................... 1124-10 YSZ/ /LSM interface for 1100C one hour sintering. ......................................................1134-11 LZO thickness of one hour sinter ing at different temperatures ....................................... 1144-12 Comparison of rate consta nts of the LZO formation. ...................................................... 1145-1 Three paths of oxygen reduction ...................................................................................... 1565-2 Cross-section images of the isothermal sintered samples. ............................................... 1575-3 Effect of the LTPB on the activation polarization. ............................................................. 1595-4 Effect of the SV on the activation polarization of th e isothermal sintered samples ......... 1605-5 Nyquist plot of the interfacial resistance .........................................................................1605-6 Epitaxial relationship between the LZO and the polycrystalline YSZ. ........................... 1615-7 Effect of the LZO on th e activation polarization. ............................................................1625-8 Effect of metric propertie s on Ohmic polarization of the isothermal sintered samples. .. 1645-9 Skeleton of pore networks for th e isothermal sintered samples. ..................................... 1655-10 Microstructure properties for th e isothermal sintered samples. ....................................... 1665-11 Effect of microstructure properties on concentration polarization by Kim's model. ....... 1665-12 Effect of microstructure properties on concentration polarization by Koponen's model................................................................................................................................167
12 B-1 Charge transfer resistance of the isochronal sintered sam ples ......................................... 188B-2 Dissociative adsorption resistance of the isochronal sintered samples ............................ 188B-3 Nyquist plot of the isothermal sintered sample ................................................................ 189B-4 Bode plot of the isot hermal sintered sample ....................................................................189B-5 Interfacial resistance of the isothermal sintered samples ................................................. 189B-6 Charge transfer resistance of the isothermal sintered samples ........................................ 190B-7 Dissociative adsorption resistance of the isothermal sintered samples ........................... 190B-8 STEM-EDS of 12002h .....................................................................................................191B-9 STEM-EDS of 12004h .....................................................................................................191B-10 STEM-EDS of 12008h .....................................................................................................192B-11 STEM-EDS of 120015h ...................................................................................................192B-12 STEM-EDS of 120020h ...................................................................................................193
13 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy EFFECT OF CATHODE MICROSTRUCTUR E ON CATHODE POLARIZATION IN SINTERED STRONTIUM-DOPED LANTHAN UM MANGANITE/YTTRIA STABIILIZED ZIRCONIA SOLID OXIDE FUEL CELLS By Aijie Chen May 2008 Chair: Kevin S. Jones Major: Materials Scie nce and Engineering Cathode polarization in stront ium-doped lanthanum manganite (LSM)/ yttria stabilized zirconia (YSZ) Solid Oxide Fuel Cells (SOFCs) was compared to cathode microstructure under 1h isochronal sintering between 950 and1400C, a nd under isothermal sintering at 1200C for 225h. My study investigated comprehensively the effects of two-dimensional (metric), threedimensional (topological) microstructure pr operties on cathode activ ation, ohmic, and concentration polarizations. In the study of the activati on polarization, the developed focused ion beam/ scanning electron microscopy (FIB/SEM) serial-sectioning t echniques were combined with the disector homogeneity analysis. Investigation of the topological homogene ity ensured unbiased quantification of me tric properties by applyi ng classical stereology. A new method of preparing transmission electron microscopy (TEM) cross-sec tional sample of the LSM/YSZ interface using a FIB and a micromanipulator was applied to the TEM study of the initial stages of La2Zr2O7 ( LZO) formation at the A-site deficient LSM/YS Z interface. The effect of LZO formation on activation polarization was underlined with respect of previous works that attached no relevance to it. It was found that LZO phase modifies the metric properties and rapidly degrades the
14 activation polarization, thus makes difference in the relationship between the metric properties and the activation polarization, suggested in previous SOFC models. During the investigation of the ohmic polariz ation, Ohms law was applied to relate LZO thickness (one of the geometric factors) with high-frequency im pedance (ohmic resistance). It was found that LZO phase dominated ohmic polar ization by modifying geometry factors and physics of the oxygen reduction mechanism. During analysis of the concentration polarization, a new way of quantification of the geometric tortuosity of the porous cathode was performed using an elementary skeletonziation model. In conjunction with two pore-network models under different flux domains, the elementary skeletonization model was effectiv e to study transport properties of the oxygen. It was found that the faster kinetics of the gas transport through th e porous cathode, the less resistance to the gas transport, thus the smaller concentration polarization.
15 CHAPTER 1 INTRODUCTION 1.1 Motivation 1.1.1 Importance of Solid Ox ide Fuel Cells (SOFCs) Departm ent of Energy projected that the primary energy use (including electricity generation losses) will increase by 31 percent over next 25 years. Figure 1-1 shows that energy consum ption in the commercial sector grows much more rapidly than in other sectors . The desire for high-efficient, fuel-versatile and cl ean energy has led to the development of Solid Oxide Fuel Cells (SOFC) programs in both stationary and mobile power generation systems. Basically, SOFC consists of cathode, anode and electrolyte, and it dire ctly converts hydrogen and air by chemical reactions into electrical energy, heat, and wate r without the intermediate of thermal energy, its conversion efficiency can be up to 70% for some pressurized SOFC/gasturbine power systems [2, 3]. In addition, SOFC s can be directly opera ted on a full range of practical hydrocarbon fuels such as natural gas, methanol, waste bi ogas, diesel, and gasoline, etc. due to its high operating temperatures and tolera nce to CO . Furthermore, SOFCs reduce high levels of NOx and SOx emission associated with traditi onal energy-conversi on systems . 1.1.2 Open Questions Because of potentials of SOFC, many people have worked on elucidating microstructurechemical reaction-performance relationship to understand how and w hy SOFC performance changes with time and temperature under different sintering processes, especially for the cathode, which actually contributes to the major performance of the SOFCs. Many advances in electrochemical performance measurements and mi crostructure characterization have allowed a deep understanding of this important relationship. Some groups focused on how 2D metric properties of the cathode microstructure a ffect the chemical reaction rate at the
16 cathode/electrolyte interface and subsequently, ch ange in cathode polarization (the loss in voltage on the cathode side) [4, 5]. Later, kinetics of the tertiary phases formation as a result of the chemical reaction at the cathode/electrolyte interface was further studied to explain degradation of the catho de performance at high thermal budget [6-8]. However, various conclusions on the relations hip between the cathode microstructure and its performance are ascribed to the complex microstructure of the cathode and the complex chemical reaction mechanism. In addition, there is a lack of statistical quantification of the metric properties and effective sample prep aration techniques for performing advanced microstructure characterization. Furthermore, few researches have been focused on the effect of the topology of the cathode mi crostructure on the kinetics of chemical reaction within the cathode bulk, although this critical microstructure property domina tes the major performance of the cathode. An effective technique to quantif y 3D internal microstructure needs to be developed. Therefore, an important remaining issu e is to obtain unbiased quantification of 2D and 3D microstructure properties in order to interpret the effect of the cathode microstructure on the performance. The cathode performance is c ontrolled by effectivene ss of chemical reaction mechanisms that happen at specific geom etry locations of the microstructure. In this work, a new technique that gives rise to statistical quantification of 2D microstructure properties using FIB/SEM has be en developed and applie d together with the classical stereology analysis. A method of buildi ng 3D cathode microstructure and a strategy of conducting the stereolgy analysis as well as 3D skeletonization model have been performed for the quantification of th e 3D topological features. Moreover, a sample preparation technique of the cross-section TEM has been developed usi ng a dual-beam FIB and an in-situ Omniprobe manipulator. These experimental t echniques that have been origin ally developed in this work
17 will be described in details. HRTEM-EDS char acterization of the cathode /electrolyte interface will be related to growth and kinetics of the tertiary phase formation. Critical microstructure properties will be associated with cathode polar ization. Understanding of how microstructure properties affect cathode polar ization will engineer design and fabrication of SOFCs. 1.2 Literature Review Because th is research is focused on interpretation of the relationshi p between the cathode microstructure and the SOFC performance, th e fundamentals of SOFCs and chemical reaction mechanism are first reviewed in this chapter. The general aspects of critical microstructure properties and the cathode pe rformance are described. The three-link paradigm among microstructure properties, chemical reaction mechanisms, and cathode polarization are fully addressed. This three-link paradigm indicates how microstructure properties affect the effectiveness of the chemical reactions, how ch emical reactions contro l cathode polarization, and subsequently, how microstructure prope rties dominate cath ode polarization. 1.2.1 Fundamentals of SOFCs The first Solid Oxide Fuel Cell (SOFC) was operated by Baur and Pr eis in 1937 at 1000C  a fter Nernst discovered solid-oxide elec trolytes in 1899 . Since then it has been considered to be a potential candidate for envi ronmentally friendly, fuel-flexible, and efficient energy. The environmental benefits of SOFCs f it better with the energy market trend towards combined heat and power generation than fossil power plants; mobile applications are predicted in ships, locomotives, and auxiliary power units fo r automobiles, trucks a nd recreational vehicles due to its fuel flexibility; high conversion effi ciency makes SOFCs a potential candidate for the fuel cell/turbine hybrid systems compared to the conventional combustion systems. The SOFC has many advantages over conventional fuel ce lls due to the high operating temperature of around 1000 C. On the other hand, high operating temperature causes a slow start-up time and
18 degradation of SOFCs performan ce. The latter can be controlled by engineering microstructure evolution or retarding isolat ing phases formed by thermal reactions. In order to understand chemical reaction mechanism, general information of SOFCs is introduced. The SOFCs mainly consists of an anode, a cat hode, an electrolyte and interconnect. There are four types of SOFCs desi gns: sealless tubular design, se gmented-cell-in-series design, monolithic design and flat-plate design. Of them, the most advanced one out of the four is based on an oxygen-ion-conducting stabili zed zirconia electrolyte . Figure 1-2  gives a schem atic of a single unit of the purely elec tronic conductive SOFCs: a porous electronic conductive ceramic behaves as the electrode, fo r example, LSM, and a dense ionic conducting ceramic behaves as the electrolyte, for instance, YSZ. Both interfaces between the cathode and the electrolyte and between the a node and the electrolyte are exposed to oxygen or hydrogen gas. Two chemical reactions occur. The oxygen gas travels through porous cathode and reacts with electrons to form oxygen ions. This oxygen re duction happens at th e cathode/electrolyte interface. The oxygen ions are conducted through the el ectrolyte toward the electrolyte/anode interface. These ions react w ith hydrogen gas and produce electrons, water and heat. This reaction is hydrogen oxidation. Th e cathodic half-cell r eaction and the anodic half-cell reaction are 2 21 2 2 eOO and2 222HOHOe respectively. The produced free electrons on the anode side will travel to the cathode along th e external circuit. The free electrons and oxygen gas will start the cathodic reaction for the next cycle. In this manner, the SOFC converts electrochemical energy into elec trical power. The conversion efficiency is determined by these chemical reactions, whose primary limiting fact or is the oxygen reductio n mechanism . The energy loss (polarization) on the cathode side is a major contribu tion to polarization loss of the whole SOFC.
19 1.2.2 Cathode Polarization Polarization is overpotential or voltage loss as a function of curren t density in SOFCs. Three major polarizations are: 1) ohmic polarizati on; 2) concentration pola rization; 3) activation polarization. The I-V curve  in Figure 1-3 shows that cathode concentration polarization and activation polarization are dom inant at high current density and low current density, respectively. At high current density, the chemical reactions ar e limited by the diffusion of the oxidizer or the reducer from the bulk, at low cu rrent density, the reaction pro cess is activation-controlled. Ohmic polarization includes voltage lo ss from electrolyte, electrode, and electrode/electrolyte in terface. Electrolyte ohmic polarization and electrode ohmic polarization are associated with the conduction of oxygen ions through the electrolyte and the conduction of electrons through the purely elect ronic conductive electrode, resp ectively. Interfacial ohmic polarization is contribu ted to interruption of conduction m echanism and/or reaction mechanism at contacts between electrodes and the electrolyte. Microstructure defects in cluding tertiary phase affect conduction mechanism and/or reaction mech anism at the electrodes and the electrolyte interfaces. For electrolyte-s upported SOFC, ohmic polarizatio n mainly results from the electrolyte. In order to decrease it, the thickness of the electrolyte is re duced and an alternative electrolyte with higher ion conduc tivity is selected during SOFCs fabrication. Cathode ohmic polarization can be reduced by using thin cathode layer and ma terials with high electronic conductivity. The physical resistance to the transport of gaseous species through the anode and cathode at a given current density is treated as an electr ical voltage loss. Therefore, it is called concentration polarization. Cat hode concentration polarization is the major component of the SOFC concentration polarization due to lower binary diffusivity of O2-N2,22OND, on the cathode side than that of H2-H2O on the anode side and sma ller partial oxyge n pressure (2OP) than partial
20 hydrogen pressure (2HP). In order to reduce cathod e concentration polarization,c conc the cathode limiting current density,csi, must be increased by increasing effective cathode diffusivity,() ceffD,and reducing cathode thickness,cl . Loss in voltage due to thermally activated reactions contributes to activation polarization. Cath ode activation polarization is controlled by the slowest surface chemical reacti on of the oxygen reduction. In order to decrease activation polarization, both possible rate-limiti ng steps of the surface reaction need to be identified. If the whole oxygen reduction mechan ism including individu al reaction step is understood, then cathode polarization can be re duced by adjusting kinetics of the individual reaction step under operating conditions [1-3]. 1.2.3 Oxygen Reduction Mechanism Krger-Vink notation of the oxyge n reduction is written as 2()1 2' 2 x g OOOeVO The oxygen reduction mechanism is complicated. Several variables affect processes occurring in and on the various geometric components of the mi crostructure. These involve three different species: ions, electrons and gas molecules. Th e proposed generic steps for the oxygen reduction are as following : 1. Oxygen gas transport through pores within the cathode 2. Surface adsorption of oxygen mole cules on the porous electrode 3. Dissociation of adsorbed oxygen molecules ( Oads) on the porous electrode or dense electrolyte 4. Surface diffusion of adsorbed oxygen atom to the Triple-Phase-Boundary (TPB ) 5. Charge transfer between Oads and eat the TPB These steps can be interpreted in terms of cons ervation of oxygen reacta nt species in serial reactions. Several assumptions in clude:1) In gas transport st ep, oxygen gas transports through
21 pores within the cathode under a steady-state and constant oxygen pressure gradient. Here, oxygen pressure gradient is independent of wher e oxygen molecules are in contact with the LSM surface. In addition, oxygen gas transport is assu med to be the rate-controlling step in the oxygen reduction in the low current density region; 2) Oxygen being absorbed on the LSM/Pore surface area is concerned in surface adsorption step. Th e area of the YSZ/Pore surface is a smaller interfacial area compared to th e LSM/Pore surface; 3) In dissociative adsorption step, only LSM/Pore surface is considered to be the place in which the di ssociative adsorption occurs. The reason is the same as in surface adsorption step; 4) In surface diffusion step, the position of the surface diffusion is located as close as possible to the TPB; 5) In charge transfer step, charge transfer reaction is not limite d by the amount of electrons. For purely electronic conducting electrodes, interfacial chem ical reactions at the TPB dominate polarization loss of th e cathode , therefore, a description of how the kinetics of these serial steps is related to cathode polarization losses starts fr om the charge transfer reaction in the last charge transfer st ep. The amount of reactants: electrons and dissociative adsorbed oxygen, Oads, affects the kinetics of the charge transfer reaction at the TPB. Based on the relationship between the exchange current and the number of electrons, in the low current density regime, the amount of active electrons involved in the charge transfer reaction, ne, TPB can be calculated as [15, 16] 0 eTPB CT R T n FRI [1-1] Provided that charge transfer resistance RCT in a unit of m2 and exchange current density I0 in a unit of A/m2 can be measured. R, F and T are ga s constant, Faradays constant, and temperature, respectively. Here, the number of electrons involved in the ch arge transfer reaction ,ne,TPB, per unit time, is another term of a rate consta nt of the charge transf er reaction according to
22 Faradays law. On the other ha nd, exchange current density, I0, and charge transfer resistance, RCT, determine energy barriers that this reaction has to overcome in order to occur at the TPB. This relationship is defined by 0TPBc act CT LRI A [1-2] In the low current-density region, c act is one component of activ ation polarization of the cathode (charge transfer resistance), and TPBLAis the contact area for three phases: LSM,YSZ and gas phases. It means that the kinetics of the charge transfer reaction (ne,TPB) will be affected by the metric properties of the microstructure (TPBL A ) and subsequently contributes to a component of the activation polarization. Since surface adsorption and dissociative ad sorption steps happen in a series with the charge transfer reaction, thei r kinetics and contributions to components of the activation polarization can be explained by th e amount of active electrons in the charge transfer reaction, ne,TPB. The minimum amount of Oads at the TPB,,adOTPBn, is one half of the number of electrons, 02adOTPB CT R T n FRI which is the integration of the flux of Oads,O s J going into the TPB sites within a fixed time along a length of the TPB, LTPB. In other words, the total number of O atoms needs to be 00 02TPB adtL O OTPBsTPB CT R T nJdLdt FRI [1-3] After the dissociative adsorbed oxygen, ,adODAn is diffused along some distance, LDA, either on YSZ/pore surface or LSM/pore surface. In this case, the magnitude of the LDA is comparable
23 to LTPB. Therefore, the number of the Oads diffused into TPB sites,,adOTPBn is equal to the amount of the dissociatively ad sorbed oxygen being diffused eith er on YSZ/pore surface or on LSM/pore surface,adODAn thus ,, 00DA adadtL O ODAsDAOTPBnJd Ld tn [1-4] where ,adODAn is formed by dissociation of the surface adsorption of oxygen molecules,2, OSAn and is a half of amount of,adODAn Therefore, 2,, 02adOSAODA CT R T nn FRI [1-5] where 2, OSAn is calculated by the integration of the flux of O2, 2 cpO s J being adsorbed on a unit area of the LSM/Pore surface, SCP, within a finite time, t, 2 2, 00CP cptS O OSAsCPn JdSdt [1-6] Equation 1-2 ( 0TPBc act CT LRI A the relationship between the activation polarization and the exchange current density at the TPB), is related to the amount of the disso ciation of the adsorbed oxygen (,adODAn ) by 0,,ad adODAODAIrn (Faradays relationship betw een the rate constant and the dissociation of the adsorbed oxygen, ,adODAr to the amount of its reactant, ,adODAn ). The same equation is associated with the amount of the surface adsorption of oxygen molecules (2, OSAn ) by 220,, OSAOSAIrn (Faradays relationship between the rate constant and the surface adsorption of O2 2, OSAr to the amount of the surface adsorption of oxygen molecules 2, OSAn ). Both kinetics of the dissociative adsorption (in dissociative adsorp tion) and the kinetics of the surface adsorption
24 of oxygen molecules (in surface ad sorption ) are associated with one metric property of the microstructure (area of the LSM/Pore surface) an d thus are related to one kind of the activation polarization loss (dissociative adsorpti on resistance). Note that flux of O2 being adsorbed on a unit area of the YSZ/pore surface is also pos sible in surface adsorption and dissociative adsorption. Because gas transport in gas transpor t step is strongly affected by the morphology of the LSM bulk, which dominates the amount of O2 transporting through connected pores within the LSM bulk. LSM/pore surface is emphasized for simplification. Here2 2,cpO V sO CPJJ, 2, V O CPJ is the maximum flux of O2 being supplied by forcing oxygen molecules to penetrate from outsi de of atmosphere to the LSM/Pore surface. Since Darcys law states that this flux is proportional to the gradient of the phase av eraged oxygen pressure ( 2ocp O cPP P l ) by 22, V OO CPK JP [1-7] where2OPis proportional to the difference in partia l oxygen pressure between the top surface of the cathode, oP and the LSM/Pore interface, cpP which is close to the TPB sites. In addition, (the averaged dynamic viscosit y) and K (the averaged permeability of oxygen flux through the LSM layer) are constant. In surface adso rption step, the total number of O2 being adsorbed on a unit area of the LSM/Pore surface, 2, OCPn is equal to that of O2 penetrating into the LSM bulk under the oxygen pressure, and subseque ntly, is the twice the amount of Oad participating in charge transfer reactions at the TPB sites. 22,, 00 02CP adtS OCP OCPOTPB CTKR T n PdSdtn FRI [1-8]
25 Of the interest is the permeability, K. It states the effect of the microstructure terms on the flow rate of O2 into connected pores w ithin the cathode bulk. Th e relationship between the permeability and the geometry of pores within LSM bulk (tortuosity, open porosity and pore surface area) is discussed within a simple capillary theory by Kozeny  and further developed by Koponen  (see section 5.3). According to this theory, the materi als topology is closely related to the activation pol arization of the cathode by 200CP TPBtS L OCP c act R TA K PdSdt F [1-9] Additionally, since2, V O CPJ a term of the rate of gas transport, is associated with the interfacial reaction rate in orde r to obey mass conservation of the oxygen, which is defined as ,201 22CP TPB OTPB adS L nO C P c actRTA K rPdS Ft [1-10] It is clear that cathode activ ation polarization can be contro lled by gas transport kinetics and material properties. In order to describe the effect of the gas transport kinetics on the cathode polarization, Kim has established a model  by assuming that the binary diffusion mechanism, the only factor of the maximum flux, 2, V O CPJ is under a constant concentration gradient (see section 2.2). The flux 2, V O CPJ is related to the current density, i, by 2,4V A O CPiN J F [1-11] The tie between gas transport kinetics and concentration polariza tion is as following: ln(1) 4c conc cs R Ti Fi [1-12]
26 where the cathode limiting current density, 2()(,,)ceff c cs O cD ifpTp l, is a function of oxygen partial pressure on the cathode side,2c O p operation temperatures, T, and the topology of the cathode defined by () ceffD (see section 5.3). An alternative model developed by Koponen et al. assumes the viscous flow as the major contribution of the 2,V O CPJ . This model can cooperate with the Kims model to explain how concentration polarization is attributed to kinetics of the gas transport under a constant oxyg en pressure gradient. Kims m odel exhibits that the total number of O2 being adsorbed on a unit area of the LSM/pore surface with a finite time, 2,V O CPJ can be related to a exchange curr ent density, i, as a function of c conc In this case, geometric microstructure properties control exchange curren t density by introducing permeability to the gas transport flux: 22,4V A OO CPKiN JP F [1-13] Additionally, the cathode limiting current density,csi can be affected by the permeability, since it is proportional to the effective binary diffusivity of an mixture gas, in this case,22ONDaccording to the Ideal gas law. It is cl ear that three-link tie remains among the kinetics of the gas transport, the topology of the microstructure and the concentration polarization,c conc (gas transport resistance). In order to reduce energy loss in the SOFC system, each component of SOFCs must meet certain requirements. From the long-term stability point of view, each component not only needs to have chemical compatibility and similar thermal expansion coefficients with other
27 components during cell operation and fabrication, but also, individual chem ical stability, phase stability, and morphological stab ility in both reducing and/or oxi dizing environments. From the chemical reaction point of view, the electroly te and interconnect must be dense enough to prevent gas mixing, and the cathode and the anod e must be porous enough to allow gas transport to the reaction sites instead . Because this research mainly focuses on the symmetric and purely electronic conductive SOFC s, materials properties of the strontium doped lanthanum manganite cathode and the yttria stabilized zircon ia electrolyte are desc ribed in details. 1.2.4 Lanthanum Strontium Manganite / Yttria Stabilized Zirconia Materials Property LSM and YSZ are state-of-art cathode materi al and electrolyte material, respectively. 18.104.22.168 Lanthanum strontium manganite (LSM) LSM meets critical requirements such as 1) high electronic conductivity to offer sufficient electrons for oxygen reduction by facilitating ki netics of electrons conduction, 2) sufficient porosity to enhance kinetics of oxygen transport to the cathode/electrolyte interface for better oxygen reduction, 3) minimum reactivity and interdiffusion between the electrolyte and the interconnections to reduce degr adation of the cathode performa nce by retarding or avoiding isolating tertiary phase formation, 4) compatibil ity with other cell components and so on. These advantages of the LSM over other cathode material s are attributed to mate rials properties of the lanthanum manganite (LMO). LMO is a p-type perovskite oxide with a space group of Pm 3m, with twelve-coordinate cations for A-site of La3+ six-coordinate catio ns for B-site of Mn3+ and six-coordinate anions for C-site of O2as shown in Figure 1-4. In the unit cell, A-site (La3+) and B-site cations (Mn3+ ) occupy corners of the lattice site s and the body-center of the latt ice sites, respectively. Oxygen anions are located at C-site, the face-center lattice sites. LMO shows reversible oxidation-
28 reduction behavior, therefore change s in the Mn valence in LMO, which contributes to intrinsic p-type conductivity, must be controlled. At high temperature, LMO experiences the oxygen nonstoichiometry depending on oxygen partial pressu re and La nonstoichiometry. In order to increase electronic conductivity a nd reduce reactivity with the YSZ, these variations in chemical composition need to be noted. Substituting with lower valence states of cations such as Sr or Ca in A-site will enhance electrical conductiv ity of the LMO by increasing the Mn4+ content  according to the following Krger-Vink notation: 3234 3113 xxxxSrOLaMnOLaSrMnMnO [1-14] Sr-doped LMO is the preferred cathode material because of its high electronic conductivity in the oxidizing environment [19-21]. Electronic conductivity is affected by the concentration of Sr, partial oxygen pressure, and operating temperat ures, which modifies defect chemistry in the materials. Changes in Sr level alter the electron ic conductivity of LSM at different temperatures . It appears that 20mol% Sr causes the ma ximum electronic conductivity. This dependence will vary with different sample fabrication methods, processing conditions, and measuring techniques. In addition, electr onic conductivity of the LSM is st rongly affected by oxygen partial pressure at different operating temperatures. It has a stronger dependence of the partial oxygen pressure at lower 2OP than the critical value than high2OP At low 2OP (oxygen-deficient), mobility of the major carriers (holes) is reduced due to low concentration. The electronic conductivity is reduced by decrea sing operating temperatures, a nd the extent of reduction in electronic conductivity is varied at different operation atmospheres.
29 22.214.171.124 Yttria stabilized zirconia (YSZ) SOFCs are defined by types of the electrolyte, through whic h oxygen ions migrate from the air cathode side to the fuel anode side. Of those electrolyte ma terials such as rare-earth-doped ceria, bismuth oxide, and doped lanthanum gallates, YSZ is the most commonly used electrolyte. It meets similar criteria as th e cathode except :1) high ion con ductivity to increase kinetics of oxygen ion transport to the anode side; 2) neglig ible electronic conductivity to prevent shortcircuiting of the reactive gases; 3) reasonable ge ometry to reduce Ohmic loss. Yttria-stabilized zirconia is formed by doping ZrO2 with Y2O3. Zirconia has the fluorite structure with a space group of Fm 3m at high temperatures, with eight-coordinate cations for A-site of Zr4+ and 4-coordinate anions for B-site of O2-. In the unit cell as shown in Figure 1-5 the cations occupy the face-cen ter lattice sites, while oxyg en atoms are located at eight tetrahedral sites. Zirconia is not a competitive electrolyte candidate due to low ion conductivity and low phase st ability under opera ting conditions. Substituting Y3+ for the A-site of Zr4+, not only increases ionic conductivity but also stability of zirconia in oxidizing and reducing atmospheres. The ionic conductivity is increased by creating a large concen tration of oxygen vacancies due to charge balance as shown in the following Krger-Vink notation: 23223 x Z rooZrOYOYVO [1-15] Mobility of oxygen ion is increased and s ubsequently increases oxygen ion conductivity. Oxygen ion conductivity varies as dopant concentration changes. It initially is increased and then decreased at higher dopant concentr ation due to defect ordering or electrostatic interaction . The maximum ion conductivity corresponds to the minimum amount of dopant needed to fully stabilize zirconia, whic h will be addressed late r. For yttria, the dopant is around 10mol% [22,
30 23]. Operating temperature is attributed to i on conductivity of the YSZ as well, which follows Arrhenius-type relationship. Oxygen partial pressu re does not have the effect as strong on ion conductivity of YSZ as on elec tronic conductivity of LSM due to small change in oxygen vacancy concentration at th e practical partial oxygen pr essure range (0.21 atm-25 atm) [24, 25]. If YSZ is compared to zirconia, YSZ is stabilized over a larger range of 2OP In other words, zirconia is stabilized by doping yttria. The pure zirconia has monoclinic crystal structure under the operating conditions. Zr4+ cations have seven coordinates of oxygen anions and one more coordinate of oxygen vacancy after doping with Y3+, because the formed oxygen vacancy preferentially sits around the Zr4+ cations . Therefore, cubic yttria-stabilized-zirconia is stable. This stability is determined by temperature and pressure c onditions. Within this temperature range (room temperature to its meltin g point), cubic yttria-stabilized-zirconia is stable . This is one of the advantag es of using YSZ as the electrolyte. 126.96.36.199 Chemical reactivity with the yttr ia stabilized zi rconia electrolyte YSZ has good chemical compatibility with LSM, however, some interfacial reactions between YSZ and LSM still remain when the fabricating temperatures above 1200oC. Reaction products, including La2Zr2O7 (LZO) and SrZrO3, depend on composition of Sr in the LSM, the latter will be avoided with a Sr composition less than 30 mol% [27, 28]. LZO will be focused in this research due to the use of (La0.8Sr02)0.98MnO3as the cathode. The concern of LZO formation at the LSM/YSZ interface results from the degradation of the cathode performance, because LZO has two and a half order of magni tude lower ion conductivity than the YSZ . Interfacial reactions can be predicted using the chemical potential diagram for the La-MnZr-O system [26, 34] with different compositions of reactants. It shows that stoichiometric LMO
31 reacts with ZrO2 to form the three-phase combination among ZrO2, La2Zr2O7, and A-sitedeficient La1-xMnO3 as shown in the following equation: 32222713(0.75)0.5xLaMnOxZrOOxLaZrOLaMnO [1-16] This equation indicates that Mn cation ch anges its valence state by oxidizing and has important impacts on LZO formation. Much ef fort has been made to study interdiffusion between LSM and YSZ in order to understand the chemical nature of the LZO formation during high-temperature treatment. It is found that manganese is the mo st mobile species , its high mobility increases the probability of LZO formation and needs to be reduced due to its effect on electrical characteristics and the structure of the cathode . Furthermore, La1-xMnO3 does not react with YSZ showed in above equation. Many gr oups have investigated that the effect of Asite-deficient LSM on LZO formation and cathode performance [7, 27, 28, 35, 36]. LZO formation is minimized or retarded by decreasing the ratio of A-site to B-site in LSM cathode, thus reducing activity of La. The corresponding cathode perfor mance is improved after a heat treatment below 1200oC . Finally, above equation indi cates that LZO formed at the LSM/YSZ interface will disappear from the TPB due to the shift of the oxi dizing to the reducing atmosphere [36-38]. In order to minimize interfacial reactions between the LSM cathode and the YSZ electrolyte and subsequently re duce cathode polarization, other e fforts including fabrication of a composite cathode of LSM and YSZ layer at th e LSM/YSZ interface [39, 40] and different dopants such as Ca and Co and low fabri cation temperatures have been made. 188.8.131.52 SOFC processing How SOFCs components are fabricated determin es the microstructure properties of the electrolyte and the electrodes. Singhal summarizes different fa brication processes for three
32 designs of SOFCs . Here, fabrication processes of the most common tubular SOFC are described. In the tubular design, thin layers of the cell components are deposited on the porous tubular support. It is formed by an extr usion of a mixture of CaO-stabilized-ZrO2 powder, followed by sintering at 1550C in air. The cathode, mainly doped LMO, is fabricated by depositing slurry of the doped LMO on the suppo rt tube and sintering in air at about 1400C. The interconnect, LaCrO3 and the electrolyte, YSZ, are made by the electrochemical vapor deposition (EVD) process. The electrolyte is depo sited over the entire active area of the cell on all sides of the interconnect befo re the interconnect is protected by a masking material and after the interconnect is electrical contacted . Th e last part, anode, applied by dipping the cell in nickel slurry covers the entire electrol yte surface and fixed by EVD of doped ZrO2 in the nickel matrix, which functions as a sintering inhibito r and maintains a porous and stable anode. The procedures in fabrication step are tailored to produce sintered cathode layer having the desired properties such as microstructure pr operties  discussed in next. 1.2.5 Microstructure Properties Microstructure parameters characterize topol ogy of the LSM bulk and metric properties of the LSM bulk and the LSM/YSZ interface. These w ill be discussed in the following section. 184.108.40.206 Topological properties To understand transport of oxygen molecules through open pores within the LSM bulk up to the LSM/YSZ interface, the topology of pore networks, including porosity VV, tortuosity and connectivity CV have to be characterized. Furthermore, connectivity of LSM grains is helpful to study the ease of electrons conducting through the LSM bulk to the LSM/YSZ interface. Porosity, volume fraction of open pores within the volume of the LSM bulk, is a parameter related to the amount of oxygen molecule being offered for o xygen reduction. Tortuosity of
33 connected pores in the LSM bulk, is a key topological parameter of a pore network, which is essential in terms of transport in porous media , si nce it is related to the distance that oxygen molecules must travel within the cathode bulk. It has two physical meanings: 1) averaged flow length distribution over a given le ngth, a weighted averaging flux in a flow field [18, 42, 43]. Tortuosity is numerically equal to the average of th e relative lengths of the flow lines of all fluid elements within a fixed volume, V, passing thro ugh a given cross section, A, during a given period of time; 2) a anticosine relationship betw een the normal of a flow field and the flow direction. Tortuosity is the relative flow length ratio of the path that oxygen gas travels through connected pores to the thickness of the cathode. In this work, the first alternative is used for quantifying tortuosity in a por ous media. Connectivity, CV, measures how branched the structure is, or more specifically, the number of connectio ns per unit volume or possible paths that are present between connections. Connectivity is closely related to tortuos ity in terms of gas transport through the pore network. It represen ts possibility for the gas transport through the porous cathode. In another word, gas transport prefers to follow the less tortuous path through interconnected channels if the connectivity is high. All parameters will affect kinetics of gas transport within the LSM bulk. 220.127.116.11 Metric properties Metric properties will affect the rest of steps after gas is filled into pore space within the LSM bulk. It consists of pore surface area, SV (SCP), the diffusion distance at the LSM/pore interface, LDA, and triple-phase-boundary length, LTPB. Pore surface area, SV, is defined as the exposed area at the LSM/Pore interface, and is associated with the amount of oxygen entering in to porous cathode that can be adsorbed at the surface of the electrode. Diffusion dist ance along the LSM/Pore interface, LDA, is closely related to how fast adsorbed oxygen arrives at the TP B site. The triple-phase -boundary length is
34 calculated as the perimeter of LSM electrode in contact with both gas and the YSZ electrolyte, and is a crucial microstructure parameter to ch aracterize the LSM/YSZ interface. It affects the completeness of the charge transfer reaction a nd the degradation of the cathode performance [4, 28]. 18.104.22.168 Materials characterization techniques Different experimental methods have been used to measure metric properties of pore structure [44, 45]. The method of mercur y injection determines open porosity, VV, and pore surface area, SV. The pore radii can be calculated by the Washburn equation .The cumulative pore volume can be measured by forcing mercury into interconnected pores under high pressure . Mercury, however, never perfectly fills al l the edges and corners of the pores, and high pressure may cause damage to the pore struct ure. Archimedes method measures open porosity in a safe way. In this method, the differen ce in weight between the dried sample and the completely saturated sample imbibed into a wettin g fluid is divided by the density of the fluid. The volume of open pores is then calculated. This method also calculates the bulk volume by measuring the difference in weight between the completely saturated sample exposed to air and the saturated sample suspended in water. Compar ed to other measurements used to obtain open porosity, Archimedes method will be the most accu rate measurement with the proper care . One limitation of this method is that it ca nnot calculate pore surf ace area and pore size. Brunauer-Emmett-Teller (BET) method can be used to measure these parameters. This technique measures pore surface area based on adsorption isotherms , however, BET has limited useage because sample preparation is challengi ng for a porous and fragile ceramic with a distribution in pore size. The op tic method (combining with classi cal quantitative stereology) is not affected by sample preparation techniques and it qua ntifies areal porosity pore size and pore surface area based on two-dimensional polished sections of the sample. Applying three
35 fundamental relationships in the classical stereology analysis, 3D microstructural features and two dimensional microstructural features can be simply quantified by a one dimensional line probe technique. However, this quantification technique must be applied to count open pores. More specifically, the optical images must diffe rentiate closed pores from open pores before applying classical stereology anal ysis [47, 49]. Ruud et.al., (2004) and Song et.al., (2005) have calculated areal porosity [50,51] and pore size by applying classical stereology analysis based on field emission scanning auger autoprobe images  and SEM images [50, 51], however, they have not mentioned how to discount closed porosity which could affect the accuracy of their results. To get accurate measurement of the TPB lengt h, correctly applying classical quantitative stereology is as crucial as identifying open por es. Although Mizusaki et al (1991), Fukunaga et al. (1996) and Kuznecov et al. (2003) peeled off or etched away electrodes from electrolyte to expose the electrode/electrolyte interface, and they calculated normalized TPB (length of the particle multiplying by number of particles pe r area) as shown in SEM images . Their estimations may be biased because regions of study are not random-selected. Both quantifications of TPB length and pores need identification of open pores and require a new technique to meet the conditions of the classical st ereolgy analysis (isotropic microstructure, uniform spacing and random orientation) (IUR) [49, 53, 54]. 3D geometric properties can be obtained from a well-established method using serialsection tomography experiments . It incl udes physical sections, optical sections and sequential sections [56-58]. One ol d way of making physical sections is to polish flat planes of an impregnated sample. In an impregnated sample, Woods metal, epoxy or wax, is used to fill in interconnected pores. The first laye r of the material is polished and then SEM images are taken,
36 then the second layer of the materials is polishe d and SEM images are taken and so on. Another physical sectioning approach is to use diamond kni fe to cut thin sections of an impregnated sample (Microtome), and use light micros copy to take the corresponding images. Both techniques offer information of the pore evolution, however, it is hard to reproduce the same spacing for each section. Whats more, these te chniques might cause distortion of volume of interest, therefore, these types of serial sections may not be su itable for 3D reconstruction . The popular optical sectioning tech nique uses a confocal scanning light microscope. It avoids physical distortion of the sample due to comp ression. However, it is not suitable for opaque media. In addition, change in resolution increases difficulties of the 3D image processing. Since the dual beam systems-FIB/SEM has a deeper dept h of field than the confocal scanning light microscope does, it is a new developed technique to fulfill collecting volume of several microns of the internal microstructure layer by la yer for 3-D reconstruc tions [60-62, 86]. FIB tomographic experiments have been used to study 3D feature morp hology of nickel base superalloys , fuel cells  ceramics , biological materi als  and 3D X-ray spectral analysis of precipitates and corrosive products in metallic alloys . 1.2.6 Three-Link Paradigm It is clear that fabrication processes that optimize microstructure properties can improve cathode performance by affecting kinetics of the oxygen reduction mechanism occurred on the cathode side. Since cathode ohmic polarization is a minor part of the cathode overpotential, concentration polarization and activ ation polarization are emphasized in this research. There are three possible rate limiting steps in series em phasized in the oxygen reduction in the purely electronic conductive cathode . Each is associated with components of cathode polarization. The magnitude of the cathode polarization is de termined by voltage losse s due to the slowest reaction step. The first one affect s concentration polari zation, and is related to topology of the
37 microstructure (see section 22.214.171.124). The second and third contribute to activation polarization and are affected by metric properties of the cathode (see section 126.96.36.199). The first step is gas trans port through the porous cathode ( Figure 1-6). It influences the lim iting current density by impacting gas tran sport properties including effective cathode diffusivity,()ceffD. The cathode thickness, cl is fixed. The effective cathode diffusivity,()ceffD is a function of the binary diffusivity of O2-N2, 22OND, volume fraction of O2 entering the cathode bulk, VV, tortuosity of pore channels, connectivity, CV, and the pore surface area, (SCP=SV). These geometric properties control the kinetics of gas transport by affecting effective diffusivity and then the exchange current density. Because the exchange current density is associated with the concentration polarization, concentration polarization can be optimized by controlling geometric properties of the cathode microstructure. The second step is dissociative adsorption reaction ( Figure 1-6). How big the area between the open pore and the cathode, SV, and open porosity, Vv, determines the amount of oxygen molecule can be dissociated to oxygen atom s at the electrode/por e interface after oxygen molecules are adsorbed at the electrode/pore interf ace. Vv represents the probability of the actual amount of oxygen molecules in the reaction. The third step is charge transfer reaction. For the purely electronic conductive cathode under normal operational situations, charge transf er reaction only happens on the triple-phaseboundary, where oxygen, cathode and electrolyte meet together. The perimeter of the electrode in contact with gas and the electrolyte, LTPB, affects the number of active sites there will be for the charge transfer reaction between Oads and e-. The corresponding compone nt of the activation polarization (charge transfer re sistance and dissociative adsorption resistance) and specific
38 microstructure properties (LTPB, VV, and SV) were discussed in section 1.2.6 by bridging kinetics of each serial step with the charge transfer reaction. However, ties among them are only effective fo r the charge transfer reaction in an ideal case. If the microstructure change s affect gas transport and dissociative adsorption; if the tertiary phase is formed at the cathode/electrolyte inte rface due to high sintering temperatures; if the connection between cathode grains as well as between the cathode and the electrolyte is not complete enough, then conduction of eand OV is interrupted from the source (electrode for electrons and electrolyte for oxyge n ions) to the sink (TPB site s). These conduction barriers of the reactant species cause insufficient amount of reactants for the charge transfer reaction, and LTPB will not represent active sites for charge transfer between LSM and YSZ. In summary, the concentration polarization du e to gas transport resistance depends on cathode effective diffusivity, specifica lly, a combination of the open porosity,VV, tortuosity, and pore surface area, SV. The activation polarization consis ts of the dissociative adsorption resistance and the charge transfer resistance. Two resistances are associated with the energy barrier that needs to be overcom e for the thermal active reactions to occur, and they are mainly affected by metric properties of the porous cathode such as pore surface area, Sv, and LTPB, as shown in Figure 1-6. Cathode pol arization can be influenced by a combination of changes in these geometry parameters of the cathode. Change s in these geometry properties are ascribed to kinetics of the three possible rate-limiti ng steps in the oxygen reduction mechanism. 1.3 Hypothesis Under two different sintering conditions: isochronal sinterin g and isothermal sintering, concentration polarization (gas transport resistan ce) will be reduced by less tortuous path, high open porosity and fully connected pores. Additionly, dissociative adsorption resistance, one
39 component of the activation polarization, will be increased by small pore surface area, SV. Furthermore, another component of the activation polarization, char ge transfer resistance, will be decreased by long LTPB provided that the amount of reactan ts is sufficient and conduction of reactants is not inhibited. In order to analyze the impact of microstructure properties on the cathode polarization, anal ytical techniques are de veloped as followings: 1. Plane-serial sectioning techniques using FIB/SEM and 3D skel etonization model are applied to quantify topology of the pore space. 2. Cross-serial sectioning techniques using FIB/SEM and classical stereology model are used to statistically quantify metric properties of the porous cathode and the cathode/electrolyte interface. 3. Cross-section TEM sample preparation technique using FIB/SEM, an in-situ micromanipulator, and HRTEM are fulfilled to study tertiary phase formation at the cathode/electrolyte interface. 1.4 Summary of Focused Topics As explained in the introduction, characterization of the metric and topologic properties of the cathode microstructure is an important area of study to im prove the understanding of the three-link paradigm among the cathode microstructure, oxygen reduction mechanism, and the cathode polarization. This research will seek to understand this important three-link paradigm first under isochronal sintering study (one hour sintering in th e temperature range between 950 and 1400C) and then focus on degradation of th e cathode performance under the isothermal sintering (1200C in the time range between 2 and 25hrs). After a brief description of the main charac terization techniques (FIB, Stereology, and TEM-EDS) used in this work (see Chapter 2), the original experimental topic of this research consists of three parts: 1) Chapter 3 explores new applications of FIB/ SEM coupled with other advanced analyses. In particular, the comb ination of FIB/SEM and stereology limit the disadvantages of FIB/SEM technique. Statistical quantification of the metric properties of the
40 Siemens-Westinghouse cathode-supported solid oxide fuel cell (SOFC) sample becomes feasible using FIB/SEM and classical stereology. The hom ogeneity study of the topology of the state-ofart SOFC samples is likely to combine FIB/SEM with advanced stereology. Interfacial characterization of the Siemens-Westinghouse cathode-supported SOFC sample is accomplished by using HRTEM, since a new methodology of preparing TEM cross-section sample has been developed. These new applications of the FIB/SEM are successfully applied to several materials system (see Chapter 4 and 5). 2) The impact of th e metric properties of the state-of-art SOFC samples on the cathode activation polarization is described unde r the isochronal sintering in Chapter 4. The isochronal sintering study provides a big picture of the evolution of the microstructure as well as the electrochemical pr operties. The individual reaction is affected by the specific metric property t hus the corresponding activation polarizatio n is changed. The tertiary phase formation mechanism is discussed as well. The formation of the tertiary phase is affected by changing the stoichiometry of the ca thode. The tertiary phase formation mechanism contributes to dramatic changes in the microstructure and elec trochemical properties under the isochronal sintering condition. 3) Chapter5 fo cuses on a systematic study of the effects of geometric properties on the cathode polarizati on (concentration polar ization, activation polarization and ohmic polarizat ion). How topology of the cathode microstructure affects the concentration polarization is a ddressed at the two flux dominant domains. The isothermal sintering study provides the first picture of how tertiary phase fo rmation interrupts the chemical reaction and physical conduction mechanism, thus electrochemical properties are degraded. Kinetics of the tertiary phase formation in this stoichiometry of LSM has been systematically studied for the first time. The study of the tertia ry phase formation bri ngs a new angle to the
41 understanding of the dependence of the cat hode activation polarization and cathode ohmic polarization on the metric pr operties of the cathode.
42 Figure 1-1. Projected ener gy consumption (1980~2030) Figure 1-2. Schematic of SOFC Figure 1-3. I-V curve of SOFC 
43 Figure 1-4. Pervos kite structure: La3+ sits in A-site (gray circles); O2sits in C-site (white circles); Mn3+ sits in B-site (black circles). Figure 1-5. Fluorite structure: Zr4+-site in blue circles; O2--site in red circles.
44 Figure 1-6. Three-link paradigm: oxygen reduc tion kinetics; microstructure properties (topological and metric properties); elect rochemical propertie s (activation and concentration polarizations). Picture on the left shows that gas transports through the porous cathode, picture on th e right shows occurrence of three possible ratedetermining-step in details.
45 CHAPTER 2 ANALYTICAL TECHNIQUES This chapter will des cribe four analytical methods, which have been used in this work: Focused Ion Beam/ Scanning Electron Microscopy (FIB/SEM), Stereology, Transmission Electron Microscopy (TEM) and Electrochemical Im pedance Spectroscopy (EIS). The goal is to help readers better understand the results and disc ussions presented in the subsequent chapters. 2.1 Focused Ion Beam/ Scanning Electron Microscopy (FIB/SEM) A dual-beam FIB/SEM system combines a fo cused ion beam with a scanning electron beam, E-beam. FIB has experienced an intensive period of maturation over past 20 years. It is rather a tool of preparing samp les for numerous other analytical techniques than an expensive TEM sample preparation tool, which is used in the semiconductor industry. In addition, new applications of FIB are being developed for 3D materials characteri zation and nanotechnology, for applications in ceramics  metallurgy [65, 67], polymer a nd biology . Its contribution to this work is that it allows for characterization of the metric properties of microstructure (two dimensional) and topology of microstructure (three dimensional) for porous SOFC ceramics via automated serial sectioning. A dual-beam FIB/SEM system consists of a vacuum system, liquid metal ion source (LMIS), electron and ion-column systems, stage, computer systems and detectors. The LMIS allows for the finely focused ion beam milling with high lateral resolution. Ga+ is the most common liquid source due to its materials pr operties described in . Usage of Ga+ leads to high resolution milling because of following reas ons. Its emission characteristics enable high angular intensity with a small energy spread, and its super-coo ling properties allow for formation of a Taylor cone shape of a point source with a 2-5nm diameter, afte r the tungsten tip is applied to an electrical field. Therefore, this LMIS provides an ample amount of the evaporated
46 ions by applying low voltage. Whats more, the lo w energy spread of the beam yields a stable beam under low emission currents. These advantag es are attractive for hi gh-resolution electronbeam imaging. In order to achieve this, the problem of charging for low conductivity ceramic materials needs solving. As the SEM characterizes a poorly c onducting specimen, the specimen becomes electrically charged when the num ber of electrons received is off balance with the number of emitted electrons . As a consequence, the negative charge built up on the surface of the specimen generates a negative electrical field [69, 70]. This electrical field will interfere with the collection of secondary electrons and, even worse, deflect the incident beam and damage the specimen [70-72]. In low voltage SEM, although surface potential was reduced by decreasing the number of incident electrons on the surface, a high conductivity coating should be applied on the specimen. High quality images are achieved by in creasing secondary electron yield. The regular C and Au-Pd coatings will not meet these stringent requirements and may introduce image artifacts [70, 71]. In the recently developed va riable pressure SEM, charge at surface is neutralized by positive ions introduced by gas. This gas, however, reduces the efficiency of collecting secondary electrons [70, 73]. In the FIB/SEM, Ga ions introduced by the scanning ion beam (SI) neutralize the negative charge on the surface or within the bu lk and reduces the charging effect  T he electrical field between the surface and the subsurface becomes less negative than the corresponding field at normal incidence. Because the specimen is tilted with respect to the incident electron beam in the FIB/SEM, the number of electrons which are escaped from the bulk of the specimen is increased. In addition, several options of FIB operation such as low beam current, small scanned region and quick scanning rate and SI imaging will suppress charging.
47 The integration of the FIB/SEM system is cap able of performing serial sectioning due to the relatively low damage to the sample; this is compared to mechanical serial sectioning. Both beams can operate independently, and they can be coincided at the same focused point of the specimen. The angle between the ion b eam and the electron beam is 52 ( Figure 2-1). In FIB/SEM, the Ga+ scan ning ion beam gradually m ills material through the bulk of the interested region. The non-destructive secondary electron b eam (SE) takes high quality images with the atomic resolution. Like the tr aditional single ion b eam, channeling contrast allows to study microstructure features, which ha ve different crystal or ientations. One main advantage of the ion beam in FIB/SEM over the traditional single ion beam is that SI, reduces the damage to the sample and decreases the alterati on of the crystal struct ure . Furthermore, the cooperation of the ion beam assisted chemical vapor deposition with the gas sour ces system produces Pt layers, deposited on the specific sites, these layers prot ect the region of interest from further ion milling. Therefore, compared to physical sectioning, ion beam serial-sect ioning minimizes the distortion of the interested feature . In addition, shape of pore-network is not changed because ion beam current can be adjusted to control the damage extent for pores as low as possible. Microstructure characterization of 3D requires that evolution of the microstructure feature of interest is recorded with re solution from 1 to 10 microns. Like traditional SEM, the secondary electron beam in FIB/SEM has a large depth of fi eld. Using a small spot size increases the depth of focus in the secondary electron mode in FIB/SEM. The large depth of field gives FIB/SEM the capability of imaging deep structural formation through several microns [74, 75]. In addition, the secondary electron beam in FIB/SEM takes hi gh resolution images with a large depth of field. Therefore, the difficulty of image processing due to the change in resolution as seen in the
48 confocal scanning light microscope is avoided. Furthermore, FIB has a relatively large working distance of ~2cm, it is capable of imaging t opology of the sample w ithout varying fields. Image alignment of the serial sectioning must be performed before image processing. To properly align several microns of materials, reproducible spac ing, fiduciary mark and high resolution image must be adequate [76, 77]. The ion beam slices materials with the spacing of several tens of nanometers, addi tionally, fiduciary marks are produced as reference points of the image alignment, and the sectioned image taken by the e-beam has a submicron scale of lateral spatial resolution [78, 62]. Therefore, the integration of electron a nd ion beams provides a useful tool for 3D inspection of pore structure, bur ied defects or metrology [79, 80], whereas, the conventional SEM is restrict ed to 2D surface analysis. Position-flexibility of the FIB/SEM system permits statistic characterization of microstructure features in 2-D (metric prope rties) combined with stereology. Five-axis movement and automatic precise-positioning are also offered in the FIB/SEM system. In summary, the FIB/SEM system provides fo cused ion-beam milling with a high lateral resolution of a few nanometers, low damage to th e specific sites on the sample and large depth of field (~ ten microns). These ar e important criteria to quantify co mplete microstructure properties like pore surface area, triple-phase-boundary length, volume fraction of pores, how pores connected with each other, connectivity and how straight pore channel is, tortuosity, for porous SOFC materials. 2.2 Stereology 2.2.1 Classical Quantitative Stereology Classical stereology provides a set of tools to quantify properties of the 3D microstructure by analyzing two-dimensional optical images. It is effective not only because it solves the problems of quantificatio n of microstructures when informa tion on 3D microstructure features
49 can not be achieved by experiment, but also beca use it simplifies the quantification process when the microstructure is complicat ed. It requires an unbiased sampling strategy, systematic sampling probe, and statistical analysis to get ac curate estimates [53, 54]. It appears important when the microstructure is not uniform and not isotropic in terms of the distribution of microstructural features. Classi cal stereology requires three f undamental relationships for the quantification of metric properties of pores . The traditional rule in stereology is that the vo lume fraction of a phase within the structure can be measured by the area fraction of this phase on the image, that is, volumetric porosity (Vv) can be simplified by calculating areal porosity (AA), Vv= AA . The length of lines per unit area can be measured by counting the number of in tersections at the line probe and the pore solid interface per unit length (LA). Line probes are required to be pa rallel to each other, uniformly distributed and randomly oriented. In this work, TPB length density (LTPB) is numerically equal to LA as discussed in the following paragraph, and can be calculated by counting number of intersections (PL) of line probes that sweep through th e interface. The surface area per unit volume can be quantified in a similar way of calculating LTPB. The difference is that for the pore network in ceramics, pore surface area density (Sv) can be calculated by counting the number of intersections that line probes sw eep through the spherical image. All metric properties above are estimated by two dimensional or one dimension probes [49, 82, 83]. This is one of the main attractions of classical quan titative stereology analysis. The perimeter of the triple-phase-boundary per unit area, a two dimensional feature, can be calculated by integrating the number of intersections formed per unit length of the test line, which is randomly orientated in two dimens ions. Positional probability and orientational probability are taken into account for quantifica tion. Imagining a randomly oriented curve is
50 contained in a square of length L as shown in Figure 2-2, the position probab ility (X) of a pair of line probes shown in Figure 2-2a, parallel to y axis, intersecting the curve is numerically equal to the ra tio between the projection length(() dx ) and the length (L) of the square: () dx L The projection length represents the distance between two intersecti ons being projected on the x dimension. The number of intersected points by N line probes intersecting the curve is the product of N and X. In addition, the orientati on probability of intersections (Y) by a pair of randomly oriented line probes is shown in Figure 2-2b. Y can be calculated by angle fraction of the curv e ( /2 d ). The total number of intersections by the randomly oriented line probe per unit length (LP) is defined by () 2 2 00 00 2Ldx d N NXY L P NLNL [2-1] where is the length of the curve, () dx is the projection length of a finite element component of (d ), therefore, ()cos dxd is defined as the angle between the tangent line of d and the x axis, and d is the angle between two line probes. The right side in equation 2-1 is equal to 2 2 L where 2 L is called normalized curve length per area. As a consequence, the normalized TPB length per area AL is calculated by the line intersect count,LP and is defined as [82, 83] 2ALLP [2-2] In the case of deriving SV, based on the previous description, the position probability for a pair of line probes (X) intersecting the surface element is the ratio of the projected area ((,) dA ) to the square area (L2).
51 (,) 2 dA X L [2-3] Therefore, the projected surface area per vol ume can be calculated by integrating number of intersections per unit lengt h of N test line probes (PL) in space. 2 3(,) (,) (,)LNdA dA L dP NLL [2-4] In spherical coordinates, is the angle between normal of the surface element and the line probe in y-z plane, and is the angle between normal of th e surface element and the projection of the test line probe in x-y plane. The orientation probability (Y) of the line probe sweeping the surface element in all orientati ons is the enclosed area ((sin) dd divided by the total sphere area (4 )). Taking into account all the positions and the orientations, the number of intersections with a uni t of surface element by th e unit length of a line probe is defined as 22 33 0000(,)cos()1 sin 4 2LNd sd s dd dP XY NL L L [2-5] Finally, 322v LL ss ds Pdp L [2-6] where Sv is the surface area per unit volume. The metric properties of the cathode can be quantified by the line probe technique. The probe can be randomly oriented in regular two dimensional imag es and can be uniformly spaced to get unbiased estimations of the TPB length and the pore surface area. The topological properties of the cathode can not be measured by one layer of regular optic images, because keeping track of the open pores changing to th e closed pores, and observing one pore splitting up to several pores, require three dimensional reconstruction of the microstructure. A technique that
52 can take serial sections of the microstructure and can record fingerprints of the pores from the start to the end is necessary. A volume of about several microns is needed to see the internal microstructure. 2.2.2 New Quantitative Stereology New quantitative stereology is recently develo ped comparing to the classical stereology. 188.8.131.52 Serial-section probe A new stereology analysis tec hnique, serial-section probe, is used to measure the topology of pore space. The topology of pore space aff ects diffusion and viscous flow of oxygen gas through the bulk of the cathode. It determines how many oxygen molecules are available at the interface [13, 84, 85]. In serial -section probe, a set of closed spaced sections sweep through the 3D structure. It surveys details of the entire f eature of interest in the milled volume provided that the spacing of the two consecutive images is close enough. It allows calculation of the net spherical image (whole surface area that binds the 3D structure)Vnet which is the basic parameter for calculating connectiv ity of the pore space . ConnectivityVC is a key topological para meter of a pore network, which is essential in terms of transport in porous media . It m easures how branched the structure is, or more specifically, the number of conn ections per unit volume or paths that are present between locations. The basic theorem of topol ogy confirms that the connectivity VC of a closed surface is equal to the corresponding genus G, which is th e largest number of cuts that are made through parts of the shape without totally isolating any pa rt from the rest. In this work, connectivity is calculated by relating number of the area tangent count of convex, VT number of the area tangent count of concave, VT, and number of the area tangent count of saddles, VT, to the Euler characteristic, ()VVNC .VC is the connectivity of the pore and VN is the number of pores,
53 respectively. A 3-D structure can be reproduced by building a net spherical image (the area of the unit sphere element in 3D microstructure). The area of the unit sphere is 4 steradians. The net spherical image consists of convexes, concaves and saddles as shown in Figure 2-3 . This im age is a function of number of the tangent vect ors of the convex, concave and saddle as Eq 2-7 shows. 2( )Vnet VVVTTT [2-7] where Vnet is the net spherical image, VT ,VT and VT are the number of the tangent vector count for convexes, concaves and saddles, respectiv ely. In addition, the net spherical image is numerically equal to the Eu ler characteristic. 4()Vnet VVNC [2-8] In the case of V N << VC and VVTT <
54 184.108.40.206 Disector probe The disector probe technique characterizes the volume contained between two closely spaced plane sections (a small thin volume elem ent). Compared to the serial-sections probe, the disector probe is not so stringent to orientational isotropy bu t emphasizes design of probes and sampling strategies . One disadvantage of the serial-section probe versus the disector probe is a strong dependence on a computer processing. Therefore, the disector is very useful for dealing with a pore network in ceramics. By examining the changes that occur between successive sections at random sampling spot s, the disector probe provides homogeneous topological information for a distributed feature in the 3D microstructure. 2.3 Transmission Electron Microscopy (TEM) Transmission electron microscopy (TEM) uses a high-energy electron beam to image the microstructure of a material . This technique permits high-reso lution imaging, with point-topoint resolution of better than 2 nm. Therefore, it reduces measurement errors of the tertiary phase at the cathode/electrolyte interface as compar ed with the SEM due to the difference in the interaction volume, which is discussed in the foll owing paragraph. Combining with the analytical TEM, it allows for recording interdiffusion between the cathode and the electrolyte by collecting the characteristic X-rays from the interaction volume. Furthermore, it provides information of present phases, crystal orientation and atom arrangement due to elastically transmitted electrons scattering within the interaction volume. A variety of reactions occur wh en the high-energy electron beam interacts with the sample. Figure 2-4 shows the various byproducts due to these electron-sam p le reactions . The shape and size of the interaction volume inside the sample depends on a number of factors, such as the atomic number of the components being imaged, the accelerating voltage being applied, and the incident angle for the electron beam. Higher atom ic number materials absorb more electrons and
55 therefore have smaller interaction volume; higher accelerating voltages penetrate father into the sample and generate larger inte raction volumes; and the greater th e incident angle, the smaller the interaction volume. Regardless of the interac tion volume, these electron-sample interactions can be used to study various as pects of the material being im aged. Inelastically scattered electrons are incident electrons losing energy during the interac tion. These electrons are then transmitted through the rest of the specimen. Th e inelastic loss of energy by the incident electrons produces characteristic x-rays or a uger electrons, which are characteristic of the elements that the beam interacted with. These energies are unique to the energy state of each shell of the atom and thus can be used to extract compositional information on the specimen region being examined. Therefore, these signals c ontributing to analytical TEM are collected to identify extra phases. It is well known that a portion of the electrons within the beam are transmitted through the sample without any intera ction occurring inside the sample. These are commonly referred to as unscattered electrons. The transmission of unscattered electrons is inversely proportional to the specimen thickness. Areas of the specimen that are thicker will have fewer transmitted unscattered electrons and so will appear darker, conversely the thinner areas will have more transmitted and thus will appear lighter. Elastically scattered electrons are incident electrons that are deflected from their or iginal path by atoms in the sample without loss of energy. These scattered electrons are then transmitted through the remaining portion of the sample. Since the electrons that follow Bragg's Law are scattered according to =2dsin [2-10] where d and are the interplanar spacing for a particular set of planes and the angle between the incident beam and the lattice plane of interest, respectively. All incident electrons scattered by the same atomic spacing will be scattered by the same angle. These scattered electrons can be
56 collected using magnetic lenses to form a diffraction pattern; an array of spots each of which corresponds to a specific interplanar spacing (i.e., an atomic plane). The interplanar spacing can be calculated by use of Rd= L [2-11] where R is the measured distance between the transmitted beam and the diffracted spot of interest, is the wavelength of the electron beam, a nd L is the camera length being used. Since both and L are measured constants, the interpla nar spacing can be calculated by measuring R. In the case of the cubic crystal struct ure, the corresponding d is compared to 222a d hkl [2-12] where a is the lattice pa rameter of the material being examin ed, and h, k, and l correspond to the Miller indices of the atomic plane . If a is known, then the correct combination of Miller indices can be calculated. It should be noted that since the L product is constant for a particular micrograph, the R1/d2 = R2/d1 comparison can be used to conv eniently calculate neighboring lattice planes. Since the diffraction obey s the Braggs law, the angle between R1 and R2 is an important parameter to rule out atomic planes which has the same ratio of d1 to d2. Therefore, the diffraction pattern can be used to yield informa tion about the orientation, atomic arrangements, and phases present in the area being examined. Scanning and transmission electron micr oscopy (STEM) will be used to study interdiffusion between the cathode and the electrolyte High resolution transmission electron microscopy (HRTEM) will be used to monitor the tertiary phase growth as a function of both sintering temperature and sint ering time. In addition, crys tal structure and orientation
57 relationship between the tertiary phase and two parent phases are identified by the HRTEM under both the isochronal and the is othermal sintering conditions. 2.4 Electrochemical Impedance Spectroscopy (EIS) Electrochemical impedance spec troscopy (EIS) has been widely used in the fields of aqueous corrosion science and solid state ionics for probing the nature of electrochemical mechanisms . It is a powerful tool to measure impedance of the SOFC components, Z(), as a function of a wide range of the characteristic frequency, from 1mHZ to 1MHZ. This represents the kinetics of each elect rochemical reaction in the SOFCs. 2.4.1 Fundamentals of EIS The impedance of a device can be calc ulated as an alternating voltage, is applied between two electrodes a nd the resulting current,, is measured, according to the following equation : )sin( )sin( )( tI t I Z [2-13] where () Z is a time-dependent variable, and consists of real impedance, Zreal, and imaginary impedance, Zimag, which are plot as x-axis and y-axis in the Nyquist plot ( Figure 2-5a), respectively. For a single electr ochem ical process, the Nyquist plot has a semicircle with a diameter coinciding with the xaxis. This simple Nyquist plot can be simulated with some equivalent circuit models, which consists of resistors and capacitors The magnitude of the diameter, Rp, multiplied by the corresponding capacitance, Cp, indicates the time constant of the electrochemical reaction, therefore the characteristic frequency, for the specific chemical step as shown in equation 2-14, 11pp R C [2-14]
58 where Cp can be calculated based on Zimag. Zimag corresponds to the peak magnitude of the semicircle in the Nyquist plot, as described in the following equation: 1imagZ j c [2-15] Therefore, several steps in the oxygen reduction are identifiable if they have distinctive time constants. The transport of O2ions through solid electrolytes is generally the fastest process so it is observed at the highest frequencies ( Figure 2-5a). This will change if the isolating phase on the electrolyte su rface slows down transport of O2ions. If the charge-transfer is a fast electrode process but not as fast as O2ions conducting through the elect rolyte so its contribution to the sample impedance is observed at intermediate frequencies ( Figure 2-5a). Gas transport and adsorption/desorption of ga s are both slow processes so they are obs erved at low frequencies, for the A.C., EIS case ( Figure 2-5a). A time-constant for each of these processes has its own dependency on tem perature, reactant concentration, materials, and microstructure. As a result, it is possible to diffe rentiate serial reaction steps in the oxygen reduction by measuring the impedance as a function of the dependent vari ables (temperature, gas concentration, etc.), and by developing an equivalent circuit which fits the experimental data. A modified Voigt equivalent ci rcuit, which consists of a c onstant-phase element (CPE) in series ( a resistor in parallel with a capacitor ) ( Figure 2-5b), is applied to deconvolute individual rate -limiting electrode reaction in this work. The assumption is that these individual rate-limiting electrode reactions (cha rge transfer reaction, dissociative adsorption reaction and gas transport reaction) are in serial within the whole oxygen reduction mechanism. Each rate-limiting electrode reaction has its own charac teristic time constant. A nested equivalent circuit, which is composed of a double layer capacitor in parallel with a series connecti on of a resistor and a Voigt element, and then the double layer capacitor is in serial with a Voigt element, which
59 describes the electrical response of an elec trochemical reaction with a strongly adsorbed intermediate, and includes components whic h contain the contribution of the surface concentration (coverage) of the adsorbed interm ediate (mass transport, GT), the rate of adsorption or desorption (DA), and charge transfer reaction (CT) ( Figure 2-5c) . This circu it is applied in this work, because LS M is a major electronic conductive electrode, adsorption and/or surface diffusion can replace mass transport . An accurate understanding of the cathode polarization depends on the determ ination of the sequence and the mechanisms of the electrochemical steps contributin g to the oxygen re duction mechanism. 2.4.2 Error Analysis of EIS There are many uncertainties on the sequence an d the individual mechanism of the oxygen reduction mechanism, the big concern is about de convolution of the impedance spectra, which is often hindered by the presence of a high-frequency (>5*104 Hz) artifact. The influence of this artifact on the quality of the impe dance data is described in deta ils . In that work, author attempts to use the Kramers-Kronig relations to examine the validity of impedance data. The objective is to study kinetics of chemical reac tion happen within the frequency range of 6*103 to 8*104 Hz using valid high-frequency impedance data. Since many of the electrochemical steps of interest happen within the frequency range of 6*103 to 8*104 Hz presence of a high-frequencyartifact can complicate data anal ysis. For ideal data, which is consistent with the Kramers-Kronig relations, Zreal and Zimag share the same information. Failure of this consistency between the Zreal and the Zimag corresponds to a failure of the experiment to comply with one or more of the constraints of linearity, stability and causality [ 90]. Therefore, utilizati on of the Kramers-Kronig relations enables one to identify and/or reduce error in the acquire d data . Smith et al. have found that the high-frequency can significantly a lter electrochemical para meters attained when modeling the raw data. A high frequency correct ion process is proposed which significantly
60 increases the KK consistency of the high-frequency data, thus ma king high-frequency data more reliable. A modified Voigt equivalent circuit ( resistance-constant phase element, R-CPE ) can be used to simulate the impedance response of many elec trochemical phenomena as seen in Figure 2-5 For a single Voigt elem ent in Figure 2-5 a, th e characteristic frequency of the individual process (the peak of the arc) in Figure 2-5 d (Bode plot) is given by 11 ()RQ [2-16] where Q and are parameters of the constant phase el ement. R represents individual reaction resistance. Each constant phase element in th e modified Voigt element equivalent circuit represents a single electrochemical proce ss seen as an arc in the Bode plot ( Figure 2-5d). In the end, the ind ividual reaction is di fferentiated from each other due to the distinct characteristic frequency of the various processes.
61 Figure 2-1. FIB geometry A B Figure 2-2. Sampling a curve w ith a line probe. A) Position pr obability. B) Rotation probability. E-beam Imaging Ion-beam Cutting 52 LSM YSZ Stage E-beam Imaging Ion-beam Cutting 52 LSM YSZ Stage
62 Figure 2-3. The calculation of net spherical image by counting number of concaves, convexes and saddles . Figure 2-4. Interaction of a high-ener gy electron beam with a sample 
63 A B C D Figure 2-5. Individual resistan ce measurement using a modified Voigt equivalent circuit. A) Nyquist plot. B) Modified Voig t equivalent circuit. C) Nest ed equivalent circuit. D) Bode plot of impedance data. R CTCPEDA R DA CPEDL Z hf CPEGT R GT
64 CHAPTER 3 FIB/SEM TECHNIQUE DEVELOPMENT The investig ation of new FIB applications is a crucial point of this research. The focus of this chapter will be on FIB techniques for these a dvanced analyses, in particular, the statistical quantification of the metric properties of the SiemensWestinghouse cathode-supported solid oxide fuel cell (SWCSSOFC) sample, the interfac ial characterization of the SWCSSOFC sample, and the homogeneity study of the to pology of the isothermally sintered samples will be reported. 3.1 Metric Property Analysis of the Composite Electrode 3.1.1 Introduction to the Composite Cathode Ca-doped pervoskite-type LaMnO3 cathode (LCM) is an alternat ive to LSM. The electrical conductivity of the LaMnO3 has been improved since Ca2+ has lower valence levels than La3+. LCM also shows good compatibility of the thermal expansion and chemical properties with other SOFC component materials. Furthermore, LCM has the same per voskite-type crystal structure. However, differences in elemental properties mi ght cause variations in lattice stability and thermal reactivity with the YSZ. It has been re ported that zirconate formation can be easily avoided in LCM than in LSM  based on thermodynamic analysis. Composite electrodes are commonly made by sintering simultaneously two kinds of powder. One is mainly electronic-conductive po wder, another is mainly ionic-conductive powder. One of the main advantages of the composite cathode over a purely electronic conductive electrode is that in the composite cathode, the trip le-phase-boundary active sites spread over the composite cathode bulk, wher eas in a purely electr onic conductive electrode, triple-phase-boundary active sites exist only at the pur ely electronic conductive electrode/electrolyte in terface thus reducing SOFC performance. Since this chapter is mainly focused on the description of the developm ent of FIB techniques by using the LCM/YSZ
65 composite cathode as a demonstration, oxygen reduc tion mechanism for this materials system is beyond the scope of this work. The objective of this section is to demonstrate FIB/SEMs capability of statistical quantification of the porosity and pore size of the composite LCM/YSZ cathode. 3.1.2 Quantification of Vv,Sv and Pore Size Porosity (VV) and pore surface area (SV) can be quantified by area-probe and line-probe, respectively, which were introduced in section 2.2.1. The pore size (dp) can be calculated by applying a geometric idea, mean line interception ( ) , which is defined as 4V VV S [3-1] The nature of the classical stereology can be displayed by FIB random serial sectioning. 3.1.3 Experimental Design SWCSSOFC samples were made by SiemensWestinghouse. Samples were prepared by the traditional manually polishing and by the low energy ion milling. The final thickness of the electrolyte was reduced from 50m to 10m. Before taking pictures from these samples, FIB serial sectioning geometries we re decided based on how the speci fic microstructure properties affect the possible rate limiting steps. Metric properties (SV and dp) influence gas adsorption and dissociative adsorption occurring on the cathode surface, variation of metric properties (SV and dp) with height was captured in the cross-section images. The normal of the cross-section is parallel to the YSZ/LSM interface. Microstruc ture properties are related to gas transport gradually through the volume (on the top of th e cathode surface to the LSM/YSZ interface), therefore, Cv, VV, and are characterized by plane serial sectioning. Plane serial sectioning records continuously microstructure changes al ong the gas transport pa th. The normal of the plane-view section is perpendicular to the LSM/ YSZ interface. Therefore, one geometry is the
66 milling perpendicular to the surface to collect cros s-sections, and the other is the imaging on the top down (plane-view) while milling simultaneously parallel to the surface. The sample was mounted on the 45 SEM holder for easy changes in FIB geometry. Before FIB cross-section imaging, a region which c onsisted of a thin layer of the electrolyte and a thick layer of the cathode was selected The top of the elec trolyte was tilted 7 toward the ion beam column. In this way, the FIB was perpendi cular to the region of in terest (ROI) during the milling of the electrolyte. The SEM (electron beam column) 52 away on the FIB (ion beam column), was applied automatically to collect a cross-section image of the smooth surface of the sample as shown in Figure 3-1a. The cross-section im age shows the position of the cathode/electroly te interface, therefore, the thickness of the electrolyte as well as the pore size of the cathode can be identified. The thickness of the electrolyte that is milled away up to the cathode/electrolyte interface decides the work volume of the plane-view imaging. In addition, the spacing of ~1/5 of the pore size between serial-s ections during milling on the cathode/electrolyte interface to the top of the cathode will be verified to help keep track of the changes in the pores. The plane-view serial-section images of the cathode were collected on the same ROI where cross-section images were collected. A series of fiduciary marks were patterned beside the ROI for accurate alignment. In this case, the side of the sample was tilted 7 toward the ion beam column ( Figure 3-1b). FIB first milled away the w hole laye r of the electrolyte and left cathode/electrolyte interface as well as the cathod e layer, then consequently milled into serial layers of the cathode with a repeatable sp acing of about one fifth of the pore size (~1m). Before line probes were randomly oriented a nd placed across the whole cross-section or area probes were performed on the plane-section of the LCM/YSZ, the stacks of the plane or cross-section images were loaded into a ResolveR T software. After serial sections were aligned
67 and plane-view images were segmented, the number of interceptions of the line probe with the pore as well as area fraction of the pore in the segmented imaged were measured. 3.1.4 Results and Discussions LCM/YSZ cross section was obt ained using the FIB/SEM ( Figure 3-2). A 30 m wide by 60 m deep trench was created to image and quan tify the microstructure. Since electrolyte and the electrode have different crystal structures, ch anneling contrast of the ion beam was used to distinguish interfaces between the electrolyte a nd cathode phases. The microstructure on the top (region A) represents the dense microstructure of the YSZ electrolyte. Below the electrolyte (region B) lies a ~20 m thick composite cathode (LCM-YSZ) with pores size on the order of 12m. The cathode support (LCM) below the com posite cathode (region C) consists of coarser grains and larger pores >2 m. The one m thick series of slices was analyzed for porosity and pore size. Figure 33 shows the progression of the pores on the el ectrolyte up to the com posite cathode. The corresponding quantification of por e size as a function of depth on the electrolyte surface to the porous cathode layer is shown in Figure 3-4. The x-axis represents the investigated depth away on the electr olyte layer ( Figure 3-3a). The fluctuation of pore size and porosity is attributed to the la rge 8 m slice thickness between each image. Table 3-1 shows that the composite cathode region (8m -16m above the electrolyte) has finer, more closely spaced pores ( Figure 3-3b), compared to the cathode support pores found at the 16 m to 48 m depth. Region A at Table 3-1 represents the elec trolyte layer where no pores were observed. There exists a distribution of poros ity and pore size in region B and C, which was observed in Figure 3-3b-f. Table 3-1 shows that the av erag ed pore size with in regions of A and B is ~2 m.
68 3.1.5 Conclusions The FIB automated serial se ctioning technique has been successfully developed to statistically characterize microstr ucture feature in 2-D combined with stereology. This technique can be expanded to other materials characteriza tion. The FIB/SEM serially sectioned samples showed that the composite ca thode region (LCM/YSZ) was ~20 m thick with average pore diameter on the order of 1-2m. The cathode su pport above the composite cathode consisted of coarser grains and larger pores with the size of >2 m. Porosity within these cathode regions ranged from 5% to 28%. 3.2 Interfacial Analysis of the Lanthanum Calcium Manganite (LCM)/Y SZ Composite Electrode 3.2.1 Objective It is well-known that TPB has been expande d into the LCM/YSZ interface within the bulk of the composite cathode. It has been recognized that the deleterious La2Zr2O7 ( LZO) phase is formed at the LSM cathode/YSZ electrolyte inte rface in co-sintering samples at high sintering temperatures [93-96]. The LZO formation drama tically degrades the cathode electrochemical properties [97-101]. It is crucial to characterize the formation of th e tertiary phase at the interface of the LCM/YSZ composite cathode on atomic scale, for this purpose, HRTEM was used. However, it is always challenging to make an electron-transparent TEM cross-section sample on such porous and complicated oxides. Additionally, it is not easy to find the right position of the interface of the LCM/YSZ composite cathode. 3.2.2 Experimental Design The LCM/YSZ cross-section was prepared by ion milling and then was polished by FIB ion beam. An ion-beam image was taken to find the position of the LCM/YSZ interface ( Figure 3-2). SEM-EDS line-sc ans confirmed the pos ition of the LCM/YSZ interface by composition
69 analysis. The in-situ TEM cross-section foil was prepared using a dual-beam FIB system and an in-situ Omniprobe manipulator at the LCM/YSZ interface ( Figure 3-5a~d). The detailed descriptions of experim ental procedures are shown in Appendix A Part one and two. A planarized region of interest was protected by Pt deposition on the top at the cross-section of the LSM/YSZ interface, then it was isolated by tren ching surrounded areas with a Ga ion-beam milling current of 3nA, followed by ion polishing to a sample size of 32m perpendicular to the LSM/YSZ interface 9m parallel to the LS M/YSZ interface 1.5m thick ( Figure 3-5a). The TEM cross-section sample was released by und ercutting on the LSM/YS Z interface after being atta ched to the in-situ Omniprobe-manipulator ( Figure 3-5b). After the sample was transferred on the Om niprobe-manipulator to the Omniprobe Cu-grid, it was further thinned to 150nm by milling with the Ga ion beam current of 300pA ( Figure 3-5c). A Ga ion beam current (50pA100pA) was used for the final thinning ( Figure 3-5d). The final sample thickness was <50nm thick to ena ble high resolution phas e contrast imaging in the TEM. High-resolution TEM was applied to char acterize the LCM/YSZ interface. Several scanning transmission electron microscopyenergy-dispersive X-ray spectrometry (STEM-EDS) line scans were performed to more precise de termine the LCM/YSZ interface position. These scans collected the characteristic X-rays on the LCM/YSZ interface with a tilt of ~10 to a X-ray detector. Selected area diffraction patterns were taken with a camera length of 25cm at different regions: LCM and YSZ far away from the LC M/YSZ interface, and LCM and YSZ at the LCM/YSZ interface. Diffraction patterns taken at the LCM at the LCM/ YSZ interface covers larger area of the LCM than diffraction pattern s taken at the YSZ at the LCM/YSZ interface. Vice visa. The aperture size of the selected area di ffraction is 120nm. In order to observe details at the LCM/YSZ interface, in the presence of a tertiary phase, a bright field TEM (HRTEM)
70 image at high magnification was taken at the LC M/YSZ interface, when the electron beam was parallel to one of the major zone axis of YSZ. 3.2.3 Results and Discussions This is a new sample preparation technique of the TEM cross-section foil that has never been attempted before but appears to work well for this type of structure. The advantage of using the Omniprobe grid is that the sample does not need to sit on a carbon film, which can interfere with the EDS analysis in the TEM. Also, by atta ching the sample to an Omniprobe Cu grid, we were able to examine the sample in the TEM and subsequently thin it until the sample was sufficiently thin for high resolution phase contrast imaging. This technique allowed for STEMEDS involving phase identification and lattice study at the atomic LCM/YSZ interface. A high resolution TEM (HRTEM) image of the LCM/YSZ interface is shown in Figure 36a. The corresponding single phase diffraction patterns are shown in Figure 3-6b-c. The results are listed at Table 3-2. The diffraction pattern ta ken at the LCM region is shown in Figure 3-7a far from LCM/YSZ interface, and diffraction pa ttern taken at the YSZ region is shown in Figure 3-7d far from LCM/YSZ interface. Figure 3-7b covers larger area of the LCM than Figure 3-7c, and Figure 3-7c covers larger area of the YSZ than Figure 3-7b. YSZ diffrac tion spots are circled and the other diffraction spots are LC M. Most of the diffraction spots in Figure 3-7b and Figure 3-7c are LCM. W hereas diffraction patterns were taken with different emphases, structure information is the same. A high resolution phase contrast image of th e LCM/YSZ interface is shown in Figure 3-8. Diffraction patter ns taken at the LCM and YSZ bulk ( Figure 3-7a and Figure 3-7d ) were compared to thos e taken at the LCM/YSZ interface ( Figure 3-7b and Figure 3-7c), no extra diffraction spots were observed at the LCM/YSZ interface ( Figure 3-7a and Figure 3-7d).This indicates that there is no tert iary phase formation at the LCM/YSZ interface. Table 3-2 summarizes the indexe d diffraction patterns of the LCM and the YSZ far fr om the
71 LCM/YSZ interface as shown in Figure 3-7a and Figure 3-7d. The difference in d-spacing between the reference v alues (d8YSZ) and the calculated ones (dcalc ) is a variation of mole percentage of Y2O3 dopant on the 8 mol%, in standard YSZ. The d-spacing of LaMnO3 (LMO) should be different on the measured d-spacing (dcalc) after the addition of strontium. The R and dspacing of LCM and YSZ are also summarized in Table 3-2. With the assumption that LCM and LMO have sim ilar d-spacing, Table 3-2 shows that the LCM and YSZ are essentially phase pure. The high resolution phase contrast im age is fo rmed by interference effects of direct and diffracted beams (Figure 3-8). Periodic fringes within the LCM and the YSZ region displays high crystallinity of the LCM and YSZ, and th e smooth interface betwee n the LCM and the YSZ was observed everywhere except in a small transi tion region < 6 thick. Phase contrast HRTEM indicates that a tertiary phase is unlikely to ha ve formed at the observed LCM/YSZ interface. If a tertiary phase exists within this transition region, it is too thin to allow for diffraction collection. 3.2.4 Conclusions This FIB sample preparation technique worked well for this type of the SOFC material. The STEM-EDS, diffraction patterns, and the HR TEM phase contrast was used to characterize the LCM/YSZ interface. All results show there was no tertiary phase formed at the LCM/YSZ interface. 3.3 Homogeneity Analysis 3.3.1 Objective Disector probe enables investigations of th e homogeneity of the distribution of the pore space within the cathode bulk by comparing the c onnectivity of each regi on of interest (ROI) with other ROIs. This provides a unique opportunity to identify th e effectiveness and limits of the classical stereology for qua ntifying complicated pore-network and also to estimate the
72 number of the ROIs that should be analyzed by the classical stereology to get unbiased results before serial-sectional images are collected. Homogeneity is one of the important assumpti ons for classical stereology quantification [49, 81, 83]. Homogenous in spatial statistics means stationary in physics. In other words, homogenous means that the distri bution of the structur e analyzed is translation invariant. Knowledge of the homogeneity of the pore-networ k is crucial to deciding effective usage of either classical stereology or 3D reconstruction analysis based on serial -sectioning in this work. Classical stereology is ec onomical and effective for quantifying volume fraction (VV ) and interface densities (SV) as well as line densities (LTPB) [102, 103]. Additionally, the design of the classical stereology analysis determines the a ccuracy of the quantification of the metric properties. If 3D feature parameters (CV and ) are needed, 3D reconstruction analysis based on serial sectioning with simplified assumptions is required. Hence, homogeneity investigations provide further insight into the nature of the por e space. The nature of the pore space decides the operation of the classical stereo logy analysis and the 3D recons truction analysis This section examines the homogeneity of the distribution of the pore-network for the isothermally sintered samples using disector analysis. The experimental design that en ables unbiased quantification of 2-D and 3-D geometric properties of the cathode is discussed. 3.3.2 Disector Analysis The basic formula to perform the disector anal ysis has been introduced in section 220.127.116.11, connectivity density (CV) can be quantified by calculating ch anges in number of connections (VT) among pore networks per volume as written by 1 2V VC VT [3-2]
73 3.3.3 Experimental Design Because this section is focused on FIB t echniques, the sample preparation of the isothermal sintered La0.78Sr0.20MnO3/YSZ is described in section 4.1.3. In order to track changes in connections of a big volume of pore netw ork, the cross-serial sections were collected with a spacing of ~1/5 of the pore size between two consecutive sl ides. This critical spacing was determined after several adjustments in spaci ng between two consecutive slides. There are not obvious changes in connections if th e spacing is less than th is critical spacing. It is too hard to track continuous changes in connections if the spacing is larger than this critical spacing. The disector analysis was performed on three pairs of the cross-serial sections on three random ROIs in all isothermally sintered samples. It covered an area of 15m (the distance away from the YSZ/LSM interface toward the top of the cathode) by 15m (the distance parallel to the YSZ/LSM interface). Connectivity density was qua ntified on twenty pairs of the plane-view sections and twenty pairs of th e cross-section in one isotherma lly sintered sample. These planeview disectors covered a distance ranging from 11m to 20m away from the LSM/YSZ interface. The cross-section dise ctors covered a distance of 10m away from the LSM/YSZ interface. Twenty pairs of the cross-serial sections were taken on twenty random ROIs in the same sample. Each ROI is not related to one another. The area of the cross-section was 15m by 15m. Another twenty pairs of the plane-view se ctions were taken on twenty ROIs for this isothermally sintered sample. Each ROI of the plane-view sections followed the same track along the same normal of the YSZ/LSM interface. Each ROI was randomly taken on a distance ranging from 11m to 20m away from the LSM/YSZ interface. Th e area of the plane-view section was 15m by 15m. Changes in morphology of the sectio ned features (saddles, concaves, and convexs) were compared with in a finite volume of 15m by 15m by ~1/5 of the pore size, the
74 area sectioned by FIB was determined by the resolution of the FIB image and the time spent on disector analysis. The total distance being milled away along the normal of the LSM/YSZ interface (depth) was determined by a compromise between the resolution of FIB images and the depth of field of the FIB. ~5m was the total depth (5m away from the LSM/YSZ interface) for plane-view serial images to quant ify 3D microstructure property. It is the critical distance that ensures accurate alignment of the serial-secti on images using the Amira software. It is not necessary to pre-process images artifacts before image analysis. These image artifacts are caused by corrections of the stage shifts. 3.3.4 Results and Discussions The connectivity density was calculated on images with a pixel size of 0.019m by 0.024m on x and y dimensions, respectively. The pi xel size in the z direction depends on the pore size of all isothermally sint ered samples. It ranges from 0.044m to 0.064m. Figure 3-9 shows the c hange in connectivity density as a function of th e sintering time. It appears that the c onnectivity density changes from one sample to another. Connectivity density for the sample sintered from 1h to 25h is initially increased th en decreased. It is consistent with DeHoffs paper . Initial incr ease of the connectivity density occurs because the number of contacts between particles within a given volume increases when volume shrinks. Decreasing in connectivity density occurs becaus e pore channels close as the sintering time increases, thus reducing open porosity. Figure 3-10 shows the connectiv ity density calc ulated on the serial-section images taken on 40 random cross-section and 40 random plane-section images. A gradient in open porosity is shown in Figure 3-11 as a function of the height of the sam ple. Connectivity density calculated on forty ROIs (twenty pairs of cross-section images and twenty pairs of plane-view images) was
75 compared within one sintered sample, and the re sults were statistically analyzed. T-test shows that the connectivity density is distinct within a confidence level of 95% between plane-view images and cross-section images. This might indicate nonhomogeneity of the sample on the micron scale. The plane-view disectors covered the region further away from the YSZ/LSM interface than the cross-view disectors. C onnectivity density quan tified by plane-section disectors is high within the distance ranging from 11m to 20m away from the LSM/YSZ interface. Connectivity density qu antified by cross-section disect ors is low within a distance 10m away from the LSM/YSZ inte rface. The connectivity of pore network is reduced when the pores are closer to the LSM/YSZ interface. The c onnectivity density is hi gher on the top half of the sample ( Figure 3-10) because open porosity is higher ( Figure 3-11). Disectors taken on the bottom half of the LSM give lower connectivity density ( Figure 3-10) because open porosity is lower ( Figure 3-11). Difference in connectivity density at different heights of the sample reflects the gradient of open porosity (the gr adient in density of the cathode) ( Figure 3-11). Error bar of the connectivity density based on plane-view sections is less than a half of that on crosssection images. Of twenty sets of the plan e-view disectors (first ten pairs taken from the top of one seventh of the LSM, from 17m to 20m away from the LSM/YSZ interface, and second ten pairs taken from the middle one qua rter of the LSM (a distance from 16.3m to 11m away from the LSM/YSZ interface). T-test show s that connectivity dens ity is 66% the same between twenty sets of the plane-view disector s. Whereas, only 20% of connectivity density is statistically identical between the twenty sets of cross-section images (taken at the bottom half of LSM, a distance of 10m away from the LSM/YSZ interface) with a confiden ce level of 95%. The connectivity does change less from the top half of the LSM (from 11m to 20m away from
76 the LSM/YSZ interface) than the bo ttom half of the LSM (from 0m to 10m away from the LSM/YSZ interface). Connectivity based on cross-secti on disectors is so di fferent that the twenty ROIs on crosssection are enough to differentiate geometric properties of different ROIs. These ROIs were taken within a distance of 10m away from the LSM/YSZ interf ace. Additionally, more than 40 pairs of plane-section image are needed for diffe rentiating topological properties. In this work, 25 ROIs will be studied for characterizing the metric properties. This means that precision of the measurements of the metric properties will be increased by 80% if ~25 ROIs have cross-section images taken for each sample. ~5m (~100 plane-section images) away from the LSM/YSZ interface of one sample will be characterized for the topological properties. This number allows an increase in the precision of the measuremen ts by 90% with the confidence level of 95%. The mean value of the topological properties will be two times closer to its averaged value of the topological properties. This conclusion is based on a comparison of an in vestigation of the 100 plane-section images to an investigation of the 40 plane-section images. It is a sufficient number to meet the requirement of the classical stereology. 3.3.5 Conclusions The homogeneity of one sample was explored by the disector analysis of the connectivity density coupled with a T-test. C onnectivity density appears to cha nge as the distance away from the LSM/YSZ interface changes. Connectivity dens ity for the isothermally sintered samples initially increased and gradually decreased with incr easing sintering time. 20 sites were enough to identify significant differences in geometric pr operties of the cross-section. The number of cross-section images for metric property analysis and plane-view images for quantification of the
77 topology were decided to be 25 and 100, respec tively. These optimized numbers enable unbiased quantification of geometric properties.
78 A B Figure 3-1. FIB flexible geomet ries. A) Cross-serial sectioni ng. B) Plane-serial sectioning Figure 3-2. FIB/SEM cross sect ion of cathode supported SOFC sa mple imaged with ion beam. Interfaces between LCM and YSZ are visible. E-beam Imaging-Ion-beam Cutting 52d LSM 5 m YSZ E-beam Imaging-Ion-beam Cutting 52d LSM 5 m YSZRegion A YSZ Region B Active cathode Region C Cathode su pp ort E-beam: Imaging Ion-beam: Cutting 52d 5mLSM Pt layer E-beam: Imaging Ion-beam: Cutting 52d d 5mLSM Pt layer
79 Figure 3-3. Pore migration on the dense electr olyte. A) Up through the composite cathode. B) Composite cathode. C-F) Cathode support. 5 m A 5 m 5 m 5 m 5 m 5 m electrolyte composite cathode cathode support cathode support cathode support cathode support cathode C E B D F
80 Figure 3-4. Pore size and porosity of the cross-section sample in Figure 3-3 Figure 3-5. Schem atic of Omnipr obe-made TEM cross-section sample LSM YSZ LSM YSZCu gridAB D C 10 m 5 m 12 m 20 m LCM YSZ LCM YSZCu grid A C 10 m 5 m 12 m 20 m B D
81 Figure 3-6. High magnificati on bright field image of LCM/YSZ and the corresponding diffraction patterns. Beam direction for LCM is , and  for YSZ A) Bright field image at the LCM/YSZ interface. B) Diffraction patterns of the LCM. C) Diffraction patterns of the YSZ.
82 Figure 3-7. Comparison of diffraction patterns. A) Was take n at the LCM bulk (B=). B-C) Were taken at the LCM/YSZ interface. D) Was taken at theYSZ bulk (B=. Index as Figure 3-6). B C A
83 Figure 3-8. High resolution phase contrast image at the LCM/YSZ interface. LCM on the left and YSZ on the right have di fferent crystallographic or ientations, which correspond to different oriented periodic fringes. It is apparent that the LCM/YSZ interface is not rough.
84 Figure 3-9. Homogeneity test of the isothermally sintered samples Figure 3-10. Homogeneity test within a sample. First two sets of data represent connectivity density based on plane-view serial stacks, wh ich were taken from the top half of the cathode; last two show changes in connectiv ity density of the cross-section serial images, which were taken from the bottom half of the cathode.
85 Figure 3-11. Open porosity gradient of one isothermally sintered sample
86 Table 3-1. Summary of poros ity and pore size measurement Region Pore size (m) Porosity (%) Depth of the region of interest (m) A-electrolyte 0 0 0~8 B-composite cathode 0.19~1.79 4.6 8~16 1.07~5.81 27.84 16~24 C-cathode support 2.48~4.07 17.05 24~32 0.7~3.87 22.9 32~40 1.63~3.2 25.3 40~48 0 0 0~8 Table 3-2. The R and d spacing of LCM and YSZ on TEM diffraction patterns LCM ]101[ B YSZ ]011[ B R(mm) (hkl) d LMO (0A) dcalc(0A) R(mm) (hkl) d YSZ (0A) dcalc(0A) R1=21.3 010 3.96 3.7 R1=41 022 1.82 1.9 R2=30.3 10 1 2.80 2.6 R2=28.5 200 2.58 2.8 R3=37.5 11 1 2.29 2.1 R3=25.5 11 1 2.97 3.1 R1=21.3 010 3.96 3.7 R1=41 02 2 1.82 1.9
87 CHAPTER 4 ISOCHRONAL SINTERING STUDY This chapter will attempt to apply FIB techniques that were described in the previous chapter to study effect of the metric prope rties of the LSM/YSZ materials on activation polarization. In addition, this chapter will point out tertiary phase formation mechanism, which is ascribed to dramatic changes in metric propert ies and activation polarization under the isochronal sintering. 4.1 Effect of Metric Properties on Activation Polarization 4.1.1 Literature Review Electrochemical impedance spec troscopy (EIS) are used to ch aracterize the overall reaction resistance or interfacial react ion resistance (Rp) by studying changes in reaction kinetics [4, 105107]. These reactions either occur within the electrode bulk or o ccur at the electr ode/electrolyte interface. Previous work suggested that the interfacial electrochemical properties dominate SOFC performance [27, 93, 108]. It becomes important to study how the interfacial electrochemical polarizations are ascribed to interfacial reactions kinetics. It is necessary to understand the effect of the specific metric prope rties of the microstructure on the interfacial reactions kinetics. There have been many studi es on the impact of the triple-phase-boundary length (LTPB) on the interfacial reaction resistance (Rp) [4,109-111,107]. LTPB affects efficiency of the charge transfer reaction occurring at th e electrode/electrolyte in terface. There exists a relationship between the charge transfer resistance and the LTPB. This relationship varies if charge transfer resistance and LTPB are quantified in different ways In other words, if an overall interfacial resistance is assumed to be the charge transfer resistance , or if the shape factor of the triple-phaseboundary is neglected ( Figure 4-1), (triple-phaseboundary is assumed to be
88 an ideal circle)[4, 109], then diffe rent dependences of the charge transfer resistance are obtained on the TPB length. In my study of such an important relationshi p, the charge transfer resistance and the dissociative adsorption resistance will be separated from the overa ll resistance by using EIS . FIB coupled with classical stereo logy enable us to quantify specific microstructure parameters. Microstructure parameters incl ude triple-phase-boundary length,TPBL, surface area of the pore/LSM interface, cpS, as well as open porosity, VV. Since my study is focused on the low current-density region, a linear proportionality law can be applied to describe the activation polarization of the cathode to the exchange current density, which is a function of microstructure parameters . In my study, individual charge transfer resistance a nd dissociative adsorption resistance will be compared to TPB L andcpS. 4.1.2 Quantification of LTPB and SV Three fundamental relationships are applied in the classical ster eology analysis, two dimensional microstructural features can be si mply quantified by a one dimensional line probe technique (see section 3.1.2). However, this quantification tec hnique must be applied to open pores. More specifically, closed pores in the optical images mu st be differentiated with open pores before classical stereology analysis [49, 47] Additionally, to get accurate measurement of the TPB length and pores, correct ly applying classical quantitativ e stereology is as crucial as identifying open pores to achieve un biased estimations. Equation 2-2 ( 2TPBLLP ) and Equation 2-6 ( 2VLSP ) can be applied to quantification of the me tric properties of the microstructure.
89 4.1.3 Experimental Design A set of nine symmetric SOFC samples was made by screen-printing LSM on both sides of the YSZ samples. The electrolyte used in the work contained 8 mol % yttria, the thickness of the YSZ is 150 m, a 10mm 20mm sample was prepar ed from it by a tape cast method by Marketech International, Inc.. LS M ink, with a composition of La0.78Sr0.20MnO3, was provided by Nextech Materials, Ltd.. The LSM ink was screen-printed on both sides of the YSZ with a square area of 64 mm2. A drying step was performed in a Fisher Isotemp drying oven at 120 C for two hours. After drying, a set of nine isoc hronal samples was sintered at temperatures ranging from 950 C to 1400 C for one hour in Lindberg/Blue hi gh-temperature box furnace. The resulting symmetrical samples ha d a cathode thickness of about 43 m and YSZ thickness of 180 m. FIB/SEM experimental design in this section is referred from FIB techniques described in section 3.1.3 and section 3.3.3. FIB/SEM was operated at electr on-beam energy of 5kV and a Ga ion beam current of 300pA. Thirty stacks of five cross-serial sect ions with a spacing of ~1/5 of the pore size were taken first from an area of 15m m. The magnification of the crosssection image was 15kX. Open pores at the LSM/YSZ interface were identified by observing pore evolutions in consequent slices. Then 25 cr oss-section images with the spacing of the pore size were taken randomly from this set of 150 cross-section images to quantify LTPB and SV. A line probe was applied right across the LSM/YSZ interface to quantify LTPB, and two line probes were placed on the 25 cross-section with random angles to quantify SV. Charge transfer resistance and dissociative adsorption resistance were obtained using el ectrochemical impedance spectroscopy .
90 4.1.4 Results and Discussions The changes in the microstructure and the reaction impedance will be discussed as a function of the sintering temperature. 18.104.22.168 Effect of sintering on the cathode microstructure The cross-section images of the LSM/YSZ in the isochronal sintering study are shown in Figure 4-2. Microstructure evolutions of LSM grains and pores, which w ere observed at these stages: (950-1200 C, 1200-1300 C and 1300-1400 C) in my study are common in the sintered ceramic materials . Figure 4-2 shows that mi crostructure of the 1000 C sintered sample is similar to 1100 C in terms of grain size, but contact areas between LSM grains are slightly increased by neck growth of LSM grains . Up to 1200 C, rapid grain growth and coarsening of LSM grains enclose continuous pore channels at LSM grain edge. On the other hand, rapid growth of pores continues and reduces the contact area between the cathode and the electrolyte . Up to 1300 C, continuous pores are eventually pinche d off. Closed pores are present at the LSM/YSZ interface ( Figure 4-2 at the temperature of 1400 C). Densification of the LSM grains becom es evident. At such high temperatures, de nsification of cathode microstructure is likely caused by bulk diffusion of atoms to the grai n boundary or by vacancy diffusion along grain boundary from pore channels . 22.214.171.124 Effect of metric properties on the reaction impedance Figure 4-4a shows the TPB lengt h as a function of the sinter ing temperature. It is found that TPB length is reduced from 1.41.07 m/m2 to 0.210.01 m/m2 as the sintering temperature increases from 950C to 1350C. This reduction is due to an increase in the grain size from sintering. Figure 4-4b shows the pore surface area as a function of the sintering temperature. Pore surface area decreases from 5 to 0.5m2/m3 as the sintering temperature increases. Pore surface area at 1350 C is ei ght times smaller than that of 950 C (Figure 4-4b).
91 Decreasing of the pore surface area is caused by growth of pore fr om sintering . The charge transfer resistance increases from 1 to 300 as a function of the sintering temperature (see Appendix B Figure B-7). The comparison of the TP B length to the charge transfer resistance is showed in Figure 4-5. The charge transfer resistance increas es as the TPB length decreases. The rapid increase of the charge tran sfer resistance correlates strongl y with the abrupt reduction in the TPB length upon sintering above 1200 C. Reduction in TPB length contributes to a loss of the number of active sites for the charge transfer reaction, thus increasi ng the charge transfer resistance. The dissociative adsorption resistance is quadrupled from 100 to 400 as a function of the sintering temperature (see Appendix B Figure B-8). The dissociative adsorption resistance increases by a factor of 4 as the pore surface area decreases by a factor of 3 ( Figure 46). The decreasing trend of th e dissociative adso rption resistance slows down when the pore surface area is larg er than 3.3m2/m3. The increasing of the pore surface area in creases the active area for the dissociative adsorption reaction, this appears to lead to a decrease in the dissociative adsorption resistance. The microstructure evolution of the sintered sa mple is consistent with the effect of the sintering temperature on TPB length and pore surface area. The TPB length is decreased by 23% starting from 1000 C to 1200 C ( Figure 4-4a) and the correspondi ng po re surface area slowly decreased ( Figure 4-4b). Both TPB length and pore su rface area are reduced gradually as a function of the sintering tem perature. Neck growth of the LSM grains competes with pore growth at the LSM/YSZ interface, contact areas between LSM grains and por es at the LSM/YSZ interface are decreased slightly thus reducing slightly TPB length. Consistent with Figure 4-5, it shows that the charge transfer res istance increases only by one time as TPB length decreases gradually. This phenomenon was previous observed by other studi es of interfacial resistance
92 around the sintering condition of the 1200 C [95, 114-116]. Slight pore gr owth leads to the slight decrease of the pore surface area. The pore surfa ce area was decreased by 27% in the range of 1000-1200 C and results in the decrease of the ac tive area for the dissociative adsorption reactions. The growth of pores re sults in the slight decreasing of the pore surface area , as a consequence, the dissociative adsorp tion resistance was increased by 6% ( Figure 4-6). This can be explained by the fact that por e area determ ines the area expose d for dissociative adsorption of oxygen and therefore affects the cathode activation polarization. The pore surface area falls sharply between 1200 C and 1300 C ( Figure 4-4b). As a result, the dramatic decrease of TPB length by 57 % causes a dramatic increase of the ch arge transfer resistance by four times, as shown in Figure 4-5. The rapid decrease of pore su rface area by 63% resu lts in the dramatic increase of the dissociative adsorption resistance more than 188% ( Figure 4-6). It is noted that the dissociative adsorption resistan ce was increased suddenly and ra pidly within this tem perature range. It might indicate that connected pores st art to close channels thus reducing pore surface area rapidly . From 1300 C to 1400 C, microstructure images in Figure 4-2 show a com bination of grain densification and formation of closed pores. Up to 1400 C, TPB length and pore surface area are reduced to ~0  due to complete densification of the LSM microstructure. Unfortunately, resistance valu es are too high to be determined by EIS measurement within this temperature range. De nsification of the microstructure reduces tremendously the available TPB boundary area, which is close to zero, for the charge transfer reaction. In addition, isolated pores inhibit transp ort of oxygen molecules or diffusion of the oxygen intermediates to reaction s ites at the LSM/YSZ interface. It is apparent that microstr ucture evolution above 1200 C degrades the electrochemical properties of the sintered samples . Th e study of this dramatic evolution of the
93 microstructure and its effect on the observed increase of the cathode polarization upon the isothermal sintering at 1200 C will be discussed in section 5.1. 4.1.5 Conclusions In summary, the cathode activation polarizat ion, which consists of charge transfer resistance and dissociative resist ance, depends on two aspects of the microstructure: TPB length and pore surface area. Consistent with common sintering behavior of the ceramics material, the isochronal sintering study di splays three stages of the sintering as following: 1) First stage (950 C -1200 C): Neck growth of the LSM grains competes with pore growth at the LSM/YSZ interf ace, the gentle reduction in contact areas at the LSM/YSZ interface reduces gradually TPB length. This appears to be correlated with a slight increase in the charge transfer resistance. Slight reduction in the pore surface area due to gradual increasing of the pore size causes the gradual rise of the di ssociative adsorption resistance. Both TPB length and pore surface area are not reduced abruptly as a function of the sintering temperature. This is consistent with gradual reduction trends in both the charge transfer and the dissociative adsorption resistances at this temperature range. 2) Second stage (1200 C -1300 C): Rapid grain coar sening of cathode microstructure leads to abrupt decreases of the grain/pore co ntact area  at the LSM/YSZ interface thus reducing dramatically TPB length. Th is appears to be correlated with a dramatic increase of the charge transfer resistance. Ra pid growth of pores and continuous pore channels enclose at LSM grain edge cause the dramatic reduction in the pore surface area . This appears to increase dramatically the dissociative adsorption resi stance. Reduction slopes in both metric properties (TPB length and pore surface area ) at this temperature range are at least two times as steep as the slopes in the temperat ure range of 950-1200 C. Re duction in the activation
94 polarizations (charge transfer and dissociative ad sorption resistances) are more rapidly at this temperature range than the te mperature range of 950-1200 C. 3) Final stage (1300 C -1400 C): Densification due to grain growth decreases abruptly TPB length, and formation of closed pores reduces dramatically pore surface area . As a result, TPB length and pore surface area are close to zero at 1400 C. Therefore, both charge transfer resistance and dissociative adsorption resistance increases trem endously. It should be noted that the magnitude of the charge transfer resistance being increased at this stage is seven times larger than increase in the LTPB at the second stage. It does not follow a linear proportional law. TEM results of tertiary phase formation at the LSM/YSZ interface will explain this dramatic change in the activation polari zation (see section 126.96.36.199). 4.2 Tertiary Phase Formation Mechanism 4.2.1 Literature Review Tertiary phases, lanthanum zirconate (LZO) an d/or strontium zircona te (SZO), increase cathode polarization due to their lower ionic conductivity than YSZ . For cathode materials with Sr<30mol%, La2Zr2O7 ( LZO) is the only tertiary phase [93, 28]. The deleterious LZO phase was observed at the LSM/YSZ interface for co-sin tering at high temperatur es [36, 93-96]. LZO phase degrades the cathode electrochemical prope rties [97-101]. Therefore, the focus of some work are on how to avoid or c ontrol formation and growth of zirconate phases by adjusting composition of La , modifying fabrication method of the cathode, and sinter ing processing . Specifically, how LZO formation depends on La activity is the popular topic. Yokokawa et al. predicted the possible reac tions between LSM and YSZ to form LZO by thermodynamic study. LZO can be avoided if La composition is less than ~86mol% . Chen et al. studied LZO phase diag ram and showed that LZO formation could not be avoided by substituting a LSM cathode with a La deficient LSM. LZO formation is rather dependent on Y
95 composition in YSZ than dependent on La insufficiency in LSM . Absence or retarded formation of the LZO has been confirmed by XRD  and SEM analyses  at the A-site (La, Sr) deficient LSM/YSZ interface. LZO can be avoi ded or minimized due to low cation activity of the LSM [27, 28, 35]. However, previous studi es of LZO formation were limited by the poor detection limits of XRD and SEM or by the challenge of making TEM cr oss-sections of the interface, numerous studies of LZO formation focused on either very long time anneals (>100h) at low temperature (<1473K ) or shorter anneals (<10h) at high temperature (>1473K ). In order to identify factors of the initial stages of LZO formation, a few studies of the LZO formation by TEM were performed. 188.8.131.52 Lanthanum zirconate (LZO) formation mechanism Tricker et al. reported the morphology evolut ion of the LZO phase nucleation at the LSM/YSZ interface by HRTEM  LZO nucleates on the YSZ su rface, forming bridge-like connections [121, 36] and LZO gr ows primarily into the LSM phase. Loss of contrast in the bright field image near the LZO/L SM interface contributes to the presence of a new Mn-deficient LSM phase at the LZO/LSM interface. Misfit dislocations were observed at the LZO/YSZ interface. Loss of Mn appears to be the primary cause of LZO formation. Mn diffusion alters the LSM stoichiometry beyond the solubility limit of La This rejected La reacts with YSZ to form LZO [121, 122]. Mitterdorfer et al. further analyzed the nucle ation mechanism for the initial stages of LZO by using HRTEM, atomic force microscopy (AFM) a nd EIS . Of particul ar interest is the comprehensive analysis of the effect of th e A-site (La, Sr) nonstoichiometry on the LZO formation and the detailed kinetics study of the LZO formation at the A-site rich La0.85Sr0.15Mn0.98O3 /YSZ interface. AFM experiments showed that cube-like LZO embryos were initially formed and grown in diameter and height, and then LZO islands were formed by
96 combining LZO embryo with one another. Mitter dorfer et al. suggested that LZO islands grow between the cathode grains and the YSZ surface towards the cathode, although cathode layer was etched before TEM sample preparation. Surface di ffusion of Zr cations along the side of the LZO island to the top of the LZO island controls the growth of the LZO islands. As soon as the YSZ surface is entirely covered by LZO further growth is limited by bulk diffusion or grain boundary diffusion of Zr cations . LZO phase was formed in a distinct way at the A-site deficient La0.85Sr0.15Mn1.02O3 /YSZ interface. Mn-rich YSZ rings were detected initially on top of the YSZ surface by HRTEM and AFM (Figure 4-3a). They were formed after sintering for two hours at 1100C. LZO grains start to nuc leate on the top of the Mn-rich YSZ rings until La2O3 forms ( Figure 4-3a and Figure 4-3c). After a sintering time of twelve hours at 1100C, ring-shaped LZO islands were observed on top of the Mn-ZrO2 rings by HRTEM ( Figure 4-3b). LZO is precip itated after La2O3 reacts with ZrO2 at the TPB ( Figure 4-3c). LZO growth in this Mn excess LSM is controlled by the reductive decom position of the LSM, which supplies La cations for the LZO reaction . Tricker et al. and Mitter dorfer et al. showed th at LZO insolating layer starts to nucleate at the TPB. Structure analysis was performed by Trickers and Mitterdo rfers groups. An epitaxial relationship between the LZO and the YSZ wa s reported by both groups [6, 36] based on diffraction patterns taken at the YSZ/LZO interface  ( Figure 4-3d). The epitaxial growth of LZO occurs because it consum es a low energy. This epitaxial relationship depends on the crystal orientations of the YSZ . The splitting of the LZO reflections represents a slight misorientation (~1 tilt) of the diffraction patterns existing betw een LZO and YSZ. In order to quantify the probability of the LZO phase formation, many groups calculated activation energy for various stoichiometries of LSM under differe nt sintering conditions [6-8,
97 123]. An Arrenhius law was applied to extract the slope of the rate constant vs. the reciprocal temperature (the activation ener gy of the LZO phase formation). The rate constants of the LZO formation were determined using an establishe d method [7, 123, 124]. Th is method assumes that the LZO thickness increases linearly with the square root of time. 184.108.40.206 Open questions Among the few studies of LZO formation at the initial stage, Mitterdo rfer et al. mainly focused on the kinetics of the LZO formation in various stoichiometric A-site rich LSM, especially in the A-site rich La0.85Sr0.15Mn0.98O3 /YSZ interface . However, the ability to measure the thickness of the LZO layer by AFM is compromised if the acid etching process removes any of the LZO layers  or if the samp le is too thick to accura tely measure the initial stages of LZO formation by TEM . There are no in -depth kinetics studies of the initial stages of LZO formation at the A-site deficient LSM/ YSZ interface in the lite rature at present. The following section reports on a study of the initial stages of LZO formation using the TEM/EDS analysis. TEM enables to monitor the fo rmation of the LZO at the A-site deficient LSM/YSZ interface at an early stage. Based on TEM measurements of the LZO thickness, the formation mechanism of the LZO and the kinetics of the interfacial reactions to form LZO will be discussed. The effect of the LZO formation on the charge transfer resistance will be briefly addressed. 4.2.2 Experimental Design A set of nine SOFC sample s with a composition of La0.78Sr0.20MnO3/8 mol % Y2O3-92 mol % ZrO2 was prepared ( section 4.1.3). This set of nine isochronal samples was sintered at temperatures ranging from 950C to 1400C for one hour. TEM cross-section foils of four samples were prepared with a Dual-beam FIB system and an in-situ Omniprobe manipulator.
98 The details were described in section 3.2.2. The TEM analysis was performed on this set of four isochronally sintered samples. High-resolution TEM was applied to charac terize the LSM/YSZ interface. The diffusion profile was characterized by scanning transmi ssion electron microscopyenergy-dispersive Xray spectrometry (STEM-EDS). The structure orientation relationship was determined by selected area diffraction with an aperture size of 1200 Diffrac tion patterns were taken with a camera length of 25cm in the YSZ bulk far away from the LSM/YSZ interface, and at the YSZ/ LSM interface. Fixed position EDS of the LSM bulk, LSM/YSZ interface and YSZ bulk were performed to determine the tertiary phase compos ition. In addition, adja cent fixed spots were placed at the region of interest 15nm-40nm apart. These scans collect the characteristic X-rays from the LSM/YSZ interf ace with a tilt of ~10 to an X-ray detector. Diffusion profiles of the different species at the LSM/YSZ interface we re constructed. EDS line scans were also collected. Thickness of the tertiary phase was measured based on the co rresponding bright field image, which was taken when the electron beam was parallel to one of the major zone axe of the YSZ. This procedure was repeated for four isochronally sintered samples (1100 C, 1200 C, 1300 C, and 1400 C). The rate constant (r) for tertiary phase formation was estimated by using the Wagner equation of 2 x r t where x is the LZO thickness determined by TEM and t is the annealing time. 4.2.3 Results 220.127.116.11 LZO composition profile Figure 4-7 and Figure 4-8 show TEM results of the 1200 C one hour sintered sam ple. Figure 4-7a shows a bright fiel d im age taken at a high magnificat ion. The LZO layer is present between the LSM grains and the YSZ surface ( Figure 4-7a) on three samples sintered at 1200C,
99 1300C and 1400C. A sharp boundary was observed in the bright field im age of the LSM/LZO interface. A tertiary phase wa s present at the LSM/YSZ inte rface analyzed by STEM-EDS on each of three samples (1200C, 1300C and 1400C). Figure 4-7b represents the typical EDS concentration profiles of this tertiary phase. The tertiary phase contains La and Zr ( Figure 4-7b). Vertical lines have been placed on th e EDS line scan to indicate the approximate location of the interfaces between phases. It should be noted that no Mn was found in the LZO and the YSZ regions. No ZrO2 was observed between the YSZ and LZO region. The Zr concentration decreases in the YSZ region. Figure 4-9 shows TEM results of the 1100 C one hour sintered sam ple. Figure 4-9a shows a sharp bounda ry at the LSM/YSZ interface, Figure 4-9b represents the corresponding STEM-EDS profile. A transition region with high concentration of La and Zr was not observed in the 1100C sintered sample. The change in concentration of Mn and La appears the same at the LSM/YSZ interface. 18.104.22.168 Epitaxial relationships Diffraction patterns were obtai ned both from the YSZ bulk and the LSM/YSZ interface for each of three samples (1200C, 1300C and 1400C). Structural results are the same. Diffraction patterns taken in the YSZ bulk and at th e YSZ/ LSM interface are showed in Figure 4-8a and Figure 4-8b, respectively. The corresponding high re solution phase contrast im ages are shown in Figure 4-8c and Figure 4-8d, respectively. Figure 4-8a shows the cubicfluorite structu re of the YSZ with the zone axis of ]011[. The tertiary La and Zr-rich pha se appears to form coherent interface with the YSZ ( Figure 4-8c). The diffraction pattern s for the two phases appear very sim ilar and well aligned. It is known that the te rtiary phase has a diffe rent pyrochlore crystal structure. The more intense diffraction spots in Figure 4-8b came from the tertiary phase matrix, these a re identified as La2Zr2O7 (LZO) based on d-spacing. The small spots in an array
100 correspond to double diffraction . Several pair s of diffraction spots, each consisting of two spots in close proximity to one another, are identified from both LZO and YSZ. LZO]011 [//YSZ]011 [ LZO)222(// YSZ)111( Therefore, LZO shows the epitaxial relationship to the YSZ, which is confirmed by lattice image at the YSZ/LZO interface ( Figure 4-8c), in which <111> in YSZ extends into LZO, and overlaps with <222> LZO. No pa rallel re lationship was observed from a lattice image at the LZO/LSM interface ( Figure 4-8d). In addition, so m e misfit dislocations were observed at the YSZ/LZO interface both in the corresponding lattice image ( Figure 4-8c) and in the b right field image shown in Figure 4-7a. There remains ~1 tilt between the epitaxial relationship between LZO and YSZ. Figure 4-9 and Figure 4-10 show TEM results of the 1100 C one hour sintered sam ple There exists a sharp boundary in both bright field image ( Figure 4-9a) and lattice image ( Figure 4-10c) between the LS M and YSZ phase in the 1100C sintered sample. Figure 4-10b shows that YSZ has a cubic-fluorite structure w ith the major zone axis of . The more intense diffraction spots in an array in Figure 4-10b came from the YSZ matrix. The small spots correspond to the LSM phase. The angle of ~ 18 between the YSZ (200) plane and the diffraction plane of the LSM in diffraction pattern s is consistent with the plane orientation between the YSZ and the LSM in the lattice image as shown in Figure 4-10c. Extra diffraction spots were n ot observed at the LSM/YSZ interface. It is consistent with the absence of the tertiary phase region in STEM-EDS profile of the LS M/YSZ interface ( Figure 4-9b).
101 22.214.171.124 Kinetics of the tertiary phase formation The LZO thickness of the isoc hronal sintered samples in creases as the sintering temperature increases ( Figure 4-11). The rate constant of the LZO for mation at 1200C in La0.78Sr0.20MnO<3 is lower than LZO rate constant at 1100C in La0.85Sr0.15Mn<0.98O3  ( Figure 4-12). 4.2.4 Discussion 126.96.36.199 Tertiary phase formation mechanism Mn is the most mobile species . EDS s uggests that Mn diffuses further into the LSM bulk and reduces the ratio of the B-site (Mn) to A-site (La,Sr) in the LS M lattice, and then the La-rich LZO region causes the tertiary phase to form in the LZO region ( Figure 4-7b). In addition, M n diffusion causes such a La-rich LSM that La3+ is able to react with Zr4+ in the YSZ lattice to form a LZO layer at the LSM/YSZ interface [6, 121, 122] Therefore, formation of the La and Zr-rich layer is mainly controlled by Mn diffusion [6, 7, 95]. LZ O formation cannot be avoided with a La composition less than 86mol % [6, 120]. STEM-EDS results of the LSM/YSZ interface suggest there are no Mn in the YSZ a nd the LZO regions, and suggest an absence of ZrO2 near the YSZ/LZO interface. Th e detection limit of the STEM -EDS is ~1 mol%. If there were 1 mol% Mn, the Mn composition (at mo st 1 mol%) is much lower than the 7.4 1.0 mol% Mn in the Mn-rich YSZ ring and the 7 mol% Mn in the ZrO2 islands detected by TEM-EDS in Mitterdorfers study . In a ddition, EDS results support abse nce of Mn near the LSM/LZO interface ( Figure 4-7b). The sharp boundary of the bright field im ag e suggests that a new phase was not observed near the LZO/LSM interface ( Figure 4-7a). It contra dicts w ith Trickers observation. Tricker mentioned that a Mn-depleted LSM phase contri butes to the contrast loss of a LSM region near the LSM/LZO interface in a TEM bright field image  It is possible that
102 changing the chemistry of the catho de and varying sinter ing conditions contribu te to differences in Mn diffusion. The epitaxial relationship between the LZO a nd the polycrystalline YSZ was observed as discussed in all samples sinter ed above 1100C. These samples have LZO phase. This epitaxial relationship is independent of the different crystalline or ientations of the polycrystalline YSZ. It does not change as a function of the sint ering temperature (1200 C -1400C for one hour sintering), and the sintering time (1h-25h at 1200C), which will be describe in section 5.1. The inconsistency with the Trickers structural analysis is attributed to the wider range of sintering conditions being studied in this work. Misf it dislocations at th e YSZ/LZO interface ( Figure 4-7a ) are responsible for the sm all misorientation of ~1 of the diffraction patterns at the YSZ/LZO interface as shown in Figure 4-8b [6, 36]. A roughly 1 tilt between the epitaxial relationship between LZO and YSZ corresponds to the small misfit strain of ~4.88% between the LZO and YSZ . It is not clear where the initial interface of the LSM/YSZ is located. Structural information of the sample sintered at 1200 C suggests that the initial interf ace of the LSM/YSZ is located at the YSZ/LZO interface, and misfit dislocations at the YSZ/LZO in terface support that the initial interface of the LSM/YSZ has low mobility. The epitaxial LZO star ts to grow at the LSM/YSZ interface and grows toward LSM [6, 36]. However, if the initia l interface of th e LSM/YSZ is located at the YSZ/LZO in terface, then it is not clear where th e Zr comes from in the LZO layer. No mass balance is observed between Zr in YS Z and Zr in LZO. If the initial LSM/YSZ interface is located in the middle of the LZO , then EDS concen tration results explain that Zr comes from YSZ and La comes from LSM in th e LZO layer. However, the epitaxial growth usually grows perpendicular to the YSZ/LSM interface. Further study of the surface morphology
103 is needed to determine where the LSM/YSZ initial interface is located. Appa rent slopes of the La at the YSZ/LZO interface and Zr at the LZO/LSM interface may be artifacts of the EDS scans. La has at most 1.5mol% solubi lity in the YSZ [119, 120]. It has been proposed that th ere are two stages for the LZO formation at the LZO/YSZ interface [6, 36]. During the first stage, the interf ace reaction is mainly controlled by diffusion of Mn out of the LSM lattice. As a result, the La in LSM reacts with the Zr in YSZ to form a LZO layer. During the second stage, LZO is epitaxiall y grown away from the parent phase, YSZ, into the LSM grain . 188.8.131.52 Delay of the tertiary phase formation The established method [7, 123, 124] of dete rmining the rate constants at different sintering temperatures will be confirmed in th e isothermal sintering study. The isothermal sintering study shows that the LZO thickness increases linearly with the square root of time from 1h to 25h ( section 5.2.4). In my study, no LZO was observed after 1100 C sintering for one hour ( Figure 4-10). The minimum thickness detect ed by HRTEM is ~10, thus the LZO thickne ss was assumed to be less than or equal to 10 to calculate the maximum rate constant of the LZO formation at 1100C. Figure 4-12 compares the rate constant of LZO formation as a function of sintering te mperature, determined by the TEM measurements in my study with the rate constants of LZO formation from the study of Mitterdorfer, which were calculated by AFM measurements . Mitterdorfer et al. reported that increasing the ratio of A-site to B-site from 1:0.95 to 1: 1.02 retards the form ation of LZO. In my study, no te rtiary phase wa s observed after one hour sintering at 1100C with th e ratio of A-site to B-site,1:1. 02. This is consistent with the report of Mitterdorfer: af ter four hours sintering at 1100C with th e same ratio of A-site to B-site (1:1.02 ). The rate constant of the LZO forma tion at 1200C in my study is lower than the result in the study of Mitterdorfer at 1100C ( Figure 4-12). The ratio of A-site to B -site (1:1.02) in my
104 study is at least 4% lower than the ratio of A-site to B-site (1:0 .98 and 1:0.95) in Mitterdorfers study. As the sintering temperature is incr eased above 1100C, LZO formation increases dramatically despite the lower A-site to B-site ratio. Therefore, changing in the ratio of A-site to B-site will not prevent LZO formation [6, 28, 120] but appears to delay its formation [6, 120]. It is possible that the decrease in A-site to B-si te ratio stabilizes the LSM thus retarding LZO formation. In other words, LZO formation is retarded by excess amount of Mn and insufficient supply of La . The activation energy calculated based on my study (170KJ/mol) is comparable to other stoichiometric LS M: 168 (KJ/mol) for La0.85Sr0.15MnO3 [7, 124] and 167 (KJ/mol) for La0.65Sr0.3MnO3 (although this paper reported both SZO and LZO formation) . There does not appear to be a significant effect of the ratio of A-site to B-site on the activation energy for LZO formation. However, this is difficult to confirm given that many variables involved in these various studies including characte rization techniques, variation in sample composition, different sintering histories etc. If the activation energy at higher temperatures is not significantly affected by the stoichiometry of the LSM materials, then th e effect of varying the A-site to B-site ratio discussed by Mitterdorfer is pr obably related to a change in the attempt frequency of the reactions. 184.108.40.206 Change in the interfacial resistance The relationship between the charge transf er resistance and the triple-phase-boundary length ( Figure 4-4) shows that the decrease of TP B length b y 57% causes an increase of the charge transfer resistance by four times above 1200 C. On the other hand, the charge transfer resistance is only increased by 52% as decreasing TPB length by 22% below 1100 C. TEM study showed that LZO phase was observed above 1200 C. LZO formation at the LSM/YSZ
105 interface inhibits oxygen ion conduction to the LS M/YSZ interface, thus LZO phase blocks the supply of the oxygen vacancies from the YSZ to the TPB . Oxygen v acancies are one type of reactant species for the charge transfer r eaction. A reduction in concentration of the oxygen vacancies directly decreases the exchange curren t density at the LSM/YSZ interface as described in the Faradays law, as a result, charge transfer resistance increases. Therefore, this effect can account for the dramatic increasing in charge transfer resistance between 1200 C and 1300 C. Both reduction in TPB length and LZO formation are attributed to the Mn diffusion at the LSM/YSZ interface. LZO formation at the LSM/YSZ interface is controlled by Mn diffusion. Excess Mn stabilizes LSM thus retarding LZO formation. The reduction in the amount of the active sites is caused by Mn diffusing away the LSM/YSZ interface. Absence of Mn in the LZO region in STEM-EDS profile ( Figure 4-7) suggests Mn diffusi on away th e LSM/YSZ interface. STEM-EDS profile shows vacancy evolution on the nanometer scale. Mn diffusion enhances vacancy concentration at the LS M/YSZ interface . Increasing in vacancies concentration at the LSM/YSZ interface on the scale of the nanomet er is consistent with pore growth at the LSM/YSZ interface as showed in cross-section FIB/SEM image ( Figure 4-2). Cross-section FIB/SEM im age shows vacancy evolution on the micron scale. Reduction in contact area among LSM/YSZ/Pore (TPB length) is attributed to the pore growth at the LSM/YSZ interface. In the isochronal sintering study, a quantitative study of the c ooperative effects of the LZO formation and triple-phase-boundary length on charge transfer resist ance is not focused on, since many dependent variables are involved at the same time in this isochronal sintering study, such as distinct microstructure evolutions and their different contri butions to the LZO formation. Therefore, an investigation of an isotherm al sintering, under which the effect of the microstructure evolution on the cathode performance is minimized, will show the influence of
106 LZO formation and the effect of reduction in LTPB on the interfacial resistance. This open question will be answered by the isothermal si ntering study described in the Chapter5. 4.2.5 Conclusions FIB in-situ Omniprobe manipulat or has been applied to make electron-transparent TEM cross-section samples from A-site deficient LSM/YSZ material. This sample preparation technique enables the stu dy of the LZO formation kinetics of an initial stage. The kinetics study of the LZO formation clarifies the delay of the LZO formation in previous thermodynamic studies, whether La deficiency avoids or retards the LZO formation. HRTEM, STEM-EDX analysis, diffraction pattern and lattice image at YSZ /LZO interface i ndicate that LZO phase formation is not avoided but is retarded by reducing La co mposition. Comparison of rate constants of LZO reaction in 1100C samples shows that decreasing the ratio of A-site (La, Sr) to B-site (Mn) is necessary for retarding LZO formation. LZO phase formation is controlled by Mn diffusion at the interface. Rate constants fo r the interfacial reacti on were affected by Mn concentration within samples sintered between 1100C and 1400 C for one hour. The different observations of Mn diffusion and of the epitax ial relationship between the LZO and the YSZ were emphasized. The interfacial reaction betw een the LSM and the YSZ does not cause a new Mn-deficient phase formation at the LSM/LZO interface. The structural analysis shows an epitaxial relationship between the LZO phase a nd the YSZ. The epitaxial relationship does not change with different crystallin e orientations of the YSZ. Calc ulated activation energy of the LZO formation for this ratio of A-site to B-site (1:1.02) is similar to those of previous studies with different stoichiometry of LSM. LZO forma tion appears to correlate well with the dramatic increase in the charge transfer resistance above 1200C. Further study of th e isothermal sintering is needed to answer this question.
107 Figure 4-1. Top view of the LSM/YSZ interface The sharp outline is the triple-phase-boundary. Figure 4-2. Cross-section images of the isochronal sintered samples
108 A B C D Figure 4-3. LZO formation by Mitte rdorfer et al . A) On Mn-ri ch YSZ ring detected at the Asite deficient LSM/YSZ interface by AFM. B) On Mn-rich ZrO2 detected at the Asite deficient LSM/YSZ interface by HRTEM. C) Proposed LZO formation mechanism at the A-site defi cient LSM/YSZ interface. D) Ep itaxial relationship at the A-site rich LSM/YSZ interface.
109 A B Figure 4-4. Metric properties of the isochronal sintered sa mples. A) TPB length of the isochronal sintered sample. B) Pore surface area of the isochronal sintered sample. Figure 4-5. Dependence of the charge transfter resistance on the triple-phase-boundary length 1200 C 1300 C 1200 C 1300 C 1200 C 1300 C
110 Figure 4-6. Dependence of the dissociative adsorption resistance on pore surface area of the isochronal one hour sintered samples A B Figure 4-7. LSM/YSZ interface after 1200 C one hour sintering. A) HRTEM image. B) STEMEDS analysis. 1200 C 1300 C
111 A B C D Figure 4-8. YSZ/LZO interface an d LZO/LSM interface. A) Diffrac tion pattern of YSZ from the bulk for 1200 C one hour sintering. B) Diffraction pattern of LZO/YSZ interface for 1200 C one hour sintering. C) Lattice image of YSZ/LZO interface for 1200 C one hour sintering. D) Lattice imag e of LZO/LSM interface for 1200 C one hour sintering. (Note lack of epitaxial relationship).
112 A B Figure 4-9. LSM/YSZ interface after 1100C one hour sintering. A) HRTEM image. B) SETMEDS analysis (a) YSZ LSM (c)
113 A B C Figure 4-10. YSZ/ /LSM interf ace for 1100C one hour sintering. A) Diffraction pattern of YSZ from the bulk. B) Diffraction pattern of LSM/YSZ interface. C) Lattice image of YSZ/LSM interface. (Note 18 between the LSM and YSZ both in B and C) ( c ) 18
114 Figure 4-11. LZO thickness of one hour sintering at different temperatures Figure 4-12. Comparison of rate constants of the LZO formation base d on: TEM-circle; AFMcross, star and triangle .
115 CHAPTER 5 ISOTHERMAL SINTERING STUDY In this chapter, developed FIB techniques are app lied to extend the findings in chapters 3 and 4 in order to clarify the relationship betw een the microstructure properties and the cathode polarization. Furthermore, this ch apter will study the tertiary phase growth kinetics to explain the degradation of the cathode polar ization that has been observed during the isochronal sintering study (see the previous chapter). Isothermal sintering was performed at various times between 2h and 25h at 1200 C. This set of sintering samples was focused on: 1) the impact of the metric pr operties of the cathode microstructure on charge transfer resistance in sec tion 5.1; 2) the kinetics of the LZO growth at the LSM/YSZ interface and the im pact of the LZO phase formation between the LSM and the YSZ on the total ohmic polarization of the SOFC. How LZO growth and LTPB affect the charge transfer reaction will be addressed in the isothermal study (see section 5.2); 3) the role of topology on cathode concentration po larization in section 5.3. Th erefore, the manner in which these parameters impact all components of the cathode polarization will be discussed. 5.1 Effect of Metric Properties on Activation Polarization 5.1.1 Literature Review Previous work reported that interfacial re actions kinetics and geometric properties dominate SOFC performance. There have been many studies on the impact of the geometry of the cathode, electrolyte and the ca thode/electrolyte interface on the interfacial reaction resistance (Rp) [4, 107, 110, 125]. Many researches suggested that the interfacial reaction resistance depends on the diffusion paths for oxygen through th e cathode material as well as on the triple phase boundary [3, 4, 126, 127]. In terms of whic h diffusion path of oxyge n reactants take, the electrode is defined as surface-diffusion and bulk-diffusion types.
116 In the surface diffusion electrode if the electroact ive species are suppl ied to the reaction zones by surface diffusion, then the interfacial impedance (RP) is inversely proportional to the LTPB [4, 105, 107,110, 128]. Mizusaki et al. a ssumed that adsorption of oxygen gas and dissociative adsorption occur at the YSZ/por e interface followed by the surface diffusion of dissociated oxygen atom ( Figure 5-1 P1). Occurring at the TPB site, ch arge transfer reaction is not the rate-limiting-step. The elec trolyte resistance was studied by Fabry and Kleitzs groups as well. The electrolyte resistance is a linear functi on of the reciprocal of the averaged interface radius for a point electrode [129, 130], the averag ed interface radius was defined as a function of LTPB. It is questionable that LTPB is the only factor. St eele et al. concluded that the interfacial resistance is inversely proportional to a surf ace diffusion area of dissociated oxygen atom (Oad) along the LSM/pore interface toward the TPB, the product of the LTPB and the collection length (cl) [109, 125]. The collection length represents the vertical diffusion distance of the dissociated oxygen atom (Oad) from the touching point on cathode/ pore interface to the TPB  ( Figure 5-1). A second reaction path is com e up with, adsorption of oxygen gas and dissociative adsorption occur not at the YSZ/pore in terface but at the LSM/pore interface ( Figure 5-1 P2). A dissociative oxygen adso rption step might be th e rate-limiting-step . In addition, Rp (the interfacial resistance) is affected by the oxygen molar vo lume in the perovskite (2,lsmOV) and surface exchange coefficient ( ) at the TPB as following: 2, 221lsmO p TPBcV RT R zFLl [5-1] In the internal diffusion electrodes, oxygen is supplied to the elec trode interface by bulk diffusion through the electrode material. In this case, the interfacial pot ential resistance was found to be proportional to LTPB-1.3 [106, 111]. Assuming LSM as a mixed electronic and ionic
117 conducting cathode, Kuznecov app lied a bulk-diffusion contro lled oxygen reduction model, which was developed by Adler , and conc luded that the inte rfacial resistance (RP) is affected by TPB length as well as contact area between the cat hode and the electrolyte. Kuznecov assumes that the oxygen transport at the La0.8Sr0.2MnO3/YSZ interface is controlled by bulk diffusion of oxygen vacancies  The relationship is written as 1 2~()PcTPBRSLderived from equation 4-2. A third reaction path was assumed. Whole oxygen redu ction occurs at the same place, the mixed conducting cathode/pore interface, oxygen ion conducts through cathode bulk into the YSZ ( Figure 5-1 P3). It is a special case th at LSM materials f unction as a ionic conductor. Ionic conductivity of the LSM coul d not be negligible when the operational atmosphere changes between oxidizing and reducing conditions. Adler et al. pointed out that the polarization resistance depends not only on the microstructure (LTPB, Sc and VV), but also on the electrocatalytical properties of the cathode material: i onic conductivity (i ), chemical diffusion coefficient of oxygen vacancies (OVD ) and surface exchange coefficient ( ) etc. as following : 1 21 () (1)Oc p V ViTPBS RD VL [5-2] where contact area is approximate to be surface fraction of the cathode grains in the LSM/YSZ interface, defined by ~(1)cVSV The average time of the oxygen vacancy transferring into the electrolyte is defined as 0 c TPBS L and the collection length represents the surface diffusion distance of the oxygen vacancies in Kuznecovs model, and 1/2 0()Oc VlD The surface
118 diffusion distance of the dissociated oxygen atom is also equal to the collection length . Finally, Equation 5-2 can be simplified as: 1/4 c p cil R S [5-3] If collection length is not introduced in this equation, then Equation 5-2 can be expressed as 1/2 1/21 [()] ()OV p cTPBiD R SL [5-4] It is noted that these models question that LTPB is the only geometric factor. If all models had considered a condition under which the interf acial reaction is blocked by a tertiary phase, then these models predicted reliable relationships between the Rp and the LTPB. It is well-known that LSM reacts with YSZ to form a deleterious tertiary phase at the LSM/YSZ interface at the normal operating temperature of 1000 C . In order to reduce the interf acial resistance, it is more credible to investigate the contribution of the interfacial microstructure to the kinetics of the dominant reaction step. At l east resistance of thr ee processes (charge transfer of oxygen ions at the cathode/electrolyte interface, dissociation of adsorbed oxygen molecules and diffusion of oxygen species to the cat hode/electrolyte interface) contribute to the overall resistance, when the La0.85Sr0.15MnO3 cathodes were sintered at 1300C [1 31, 132]. It also was confirmed by EIP characterization of the La0.78Sr0.20MnO<3 cathodes in the isochrona l sintering study . 5.1.2 Experimental Design Symmetric SOFC samples were prepared by sc reen-printing process (see section 4.1.3). This set of eight isothermal samples was sintered at 1200C from 2h to 25h. The resulting cathode thickness is about 43m and YSZ thickness is about 180m. Cross-section image stacks were collected in the same way as described in section 4.1.3. LTPB and SV were quantified by applying the same relationship of the classical stereology ( section 4.1.3). Open porosity was
119 quantified using the area probe on ~100 FI B/SEM images. Area probe assumes that open porosity (VV ) is numerically equal to the area fraction of open pores (AA). The contact area between the LSM and YSZ (Sc) was calculated as a function of the area fraction of open pores. (1)cVSAV where A is determined by the screen-print process. Change transfer resistance and dissociative adsorption resistance were obtained using electrochemical impedance spectroscopy  based on Nyquist plot (see Appendix B Figure B-3) and Bode pl ot (see Appendix B Figure B-4). 5.1.3 Results and Discussion Cross-section FIB/SEM images are shown in Figure 5-2 for samples sintered at 1200C f rom two hours to twenty-five hours. Figure 5-2a shows the cro ss-s ection images of the isothermally sintered samples from two hours to eight hours, the highlighted part represents contact region between the cathode and the electro lyte. It appears that th e contact area between the LSM grains and the YSZ was changed by tw o competitive mechanisms (neck growth of LSM grains and pores growth) at the LSM/YSZ interface. Neck growth of LSM grains causes face to face contact, whereas, point to point co ntact increases by pore growth. At the early sintering process (less than 8 h), contacts among LSM grains and between LSM and YSZ increase, point to point contact ch anges into face to face contact. Figure 5-2b shows that after sintering for 8h, coarsening of the LSM grains co mpetes over the growth of the continuous pore channel, LSM grains densify. Figure 5-3a and Figure 5-3b show changes in the contact area and changes in T PB length as a function of the sintering time. Figure 5-3a shows that the contact area between the LSM and YSZ increas es as the sintering time increases. Increasing contact area arises from changes in contact between the LSM an d the YSZ from point to point contact to face to face contact. Pore growth intends to reduce co ntact area as the sintering time is increased up to
120 8h, whereas, grain growth becomes dominant and in tends to increase contact area. As a result, contact area increases. The TPB length is initially increased to the maximum (0.9m/m2) and then decreased to the minimum (0.4m/m2) as the sintering time increases ( Figure 5-3b). It is consistent w ith changes in TPB length in the samples sintered at 1100C from 10min to 103min based on AFM measurement . Variation of the TPB length is contributed to changes in effective contact area between the LSM grains and the YSZ. After sintering less than 8h, contact between LSM grains and YSZ increases by grain neck growth, at the same time, continuous pore channels are present at the LSM/YSZ interface. Thus, increasing face to f ace contact increases effective contact area, subsequently, increases TPB length. After sintering for 8h, formation of the closed pore channels decreases the effective contact area between the LSM grains and the YSZ. As a result, TPB length is dramatically reduced whereas contac t area is increased. Tw o mechanisms of the interfacial microstructure evolution affect the TPB length. Nyquist plot is shown in Appendix B Figure B-3. At the high fre quency in the Nyquist plot, a slope of the 45 line was observed. Peak frequency from the right to the left in the Bode plot (see Appendix B Figure B-4 1200C 8h) are ~104 Hz (high frequency intercept), ~10 Hz (middle peak) and ~0.1 Hz (low frequency in tercept). As the sintering time increases, two semicircles/peaks are combined into one ~1 Hz (1200C 25h). Interfacial resistance (the math difference between the high-frequency and the lowfrequency intercept in the Nyquist plot) as a function of the square root of the sintering time is shown in Appendix B Figure B-5. The comparison of the interfaci al resistance to the TPB, collection length and contact area is shown in Figure 5-3c, Figure 5-3d and Figure 5-3e. The interfacial re sistance as a function of the sintering tim e is shown in Appendix B Fi gure B-5. It increases from 187 to 565 Figure 5-
121 3c shows that the decrease of LTPB increases the interfacial resistance (Rp), Rp and TPB length do follow the trend (RP~LTPB -1). In Mizusakis impedance data, one depressed semicircle was observed. It arises from the charge transf er process with a peak frequency of ~104 Hz. This relationship was discussed by many groups [105-111]. The deviation (at the shortest sintering time) from the straight line will be explained as the effect of the TPB length on the charge transfer resistance will be discussed (see page 123). The interfacial resistance incr eases as the surface diffusion area (the product of the LTPB and lc) decreases ( Figure 5-3d). The interfacial resistance f ollows the prediction of the Steeles model after sintering up to 8h. However, at the sintering time le ss that 8h, data points are more scattered comparing with the Mizusakis model. One reason arises from the introduction of the collection length, which repres ents the diffusion distance of the oxygen intermediates (oxygen vacancy or oxygen dissociative species) in the cathode to the TPB. In other words, a distance over which oxygen intermediates must be collected to maintain a specified current density at the TPB. Another reason arises from the assumption of the Steeles model, the mass transfer process is not rate-limiting-step. Nyquist plot shows appare nt mass-transfer process, which contributes to a slope of 45 on the left side of the semicircle. The interfacial resistance incr eases as the product of the LTPB and Sc decreases ( Figure 53e). Not all data poin ts follow a power dependen ce of .5 of the interfacial resistance on the product of the LTPB and Sc . Kuznecovs model gives the worst fit with the isothermal sintering sample comparing to Mizusakis and Steeles models. Deviation of the isothermal sintering data from the Kuznecovs model might be contributed to different interfacial reaction mechanisms under different sintering stages an d the various ionic conduc tivity of the LSM. In the Kuznecovs impedance data, one semicircle with a peak frequency of ~2 Hz was observed
122 after sintering for 5h at 1300 C. It indicates that the microstructure was in the late densification process. However, the isothermal sintering micros tructure was in the early densification process. In the Kuznecovs model, LSM was increased its ionic conductivity by three orders of magnitude by mixing with the YSZ powders. YSZ has the ionic conductivity of 0.1 Scm-1 . In the isothermal sintering samples, the regular LSM was used, LSM has an ionic conductivity of 10-710-6 Scm-1 . It should be noted that LSM el ectrodes do not generally exhibit behavior consistent with the bulk diffusion model, sin ce LSM is a poor ionic conductor . It is consistent with the electrochemical impedance study described in Smiths paper . The controversy between the isotherm al sintering study and the Kuznecovs model might arise from the changes in contact area as well. Three models that were discussed above predicte d that the total interfacial resistance at the TPB, however, charge transfer resistance as a function of the sintering time is shown in Appendix B Figure B-6. It corresponds to the process with the peak frequency of ~104 Hz in the Bode plot , which is consistent with the Mizusakis data. It increases from 3 to 9 The comparison of the charge transfer resistance to the TPB, collection length and contact area is shown in Figure 5-3f, Figure 5-3g and Figure 5-3h. The decrease of TPB length increases the charge trans fer resistance. There does rema in a linear relationship between the 1/LTPB and the charge transfer resistance. The linear fit indica tes that charge transfer resistance is ~0 when LTPB goes to infinite. In ideal case, charge transf er resistance should be close to zero because infinite LTPB means that number of the reaction sites is sufficient for the charge transfer reaction. The inconsistency with Mizusakis result (RP~LTPB -1) at the shortest sintering time is ascribed to the sintering microstructure. Mizusaki et al calculated TPB length at the LSM/YSZ interface contacted by face to face contact. TPB length will be larger with face to face contact than with
123 point to point contact. Therefore, the actual point 1/LTPB is smaller than the first point predicted by the model ( Figure 5-3f). In addition, limited amount of SEM im ages was applied to calculate TPB length. The homogeneity study of the micros tructure has showed that the sintered LSM microstructure has some extent of no nhomogeneity (see section 3.3 in details). Therefore, TPB length in Mizusakis study might only repres ents local metric property of the cathode microstructure. The charge transfer resi stance is inversely proportional to the LTPB 1 instead of the LTPB 1.3, which was observed by Kleitz et al ., who assume the bulk-diffusion controlled mechanism, which will be discussed as Kuznecovs model is discussed. The charge transfer resistance increases as the surface diffusion area of the oxygen intermediates (the product of the LTPB and lc ) decreases ( Figure 5-3g). The charge transfer resis tance follows the prediction of the Steele s model. When the surface diffusion area goes to infinite, the charge transfer resistance is ~1.6 It appears that the charge transfer resistance is affected by the collection length, the critical diffusion distance of the oxyge n intermediates in the cathode to the TPB sites, over which the suffici ent current density at the TPB is maintained. Steele et al. concluded that the dissociative adso rption reaction is the po ssible rate-limiting step. The impedance plots for this set of samples (see Appendix B Figure B-3 and Figure B-4) suggest that peak magnitude of the dissociat ive adsorption process (~10Hz in 1200C 8h profile) increases as the sintering time increases. As th e dissociative adsorption resistance increases, the supply rate of the oxygen intermedia te in the cathode to the TPB site is slowed down, as a result, the charge transfer resistance increases as the ox ygen intermediate is one of reactants of the charge transfer reaction. It seems that Mizusakis model ( Figure 5-3f) fits the isothermal sinte ring data better than the Steeles model ( Figure 5-3g). This can be re lated to the effect of a tertiary phase formed at the LSM/YSZ interface on the collection length. If the tertiary phase
124 covers the diffusion distance of the oxygen intermediates to the TPB, the sufficient current density at the TPB should be maintained by adjusting the experimental collection length. In addition, as the collection length increases, diffu sion of the oxygen intermediates in the cathode to the TPB site causes a resistance term in the ch arge transfer reaction, as a result, the intercept of the charge transfer resistance is larg er than zero as the product of the LTPB and lc goes to infinite large. The charge transfer resistance in creases as the product of the LTPB and Sc decreases ( Figure 5-3h). A power dependence of .5 of the ch arge trans fer resistance on the product of the LTPB and Sc  was observed in the isothermal sinter ing study. It suggests that the charge transfer resistance depends on contact area between LSM and YSZ as well as TPB length. Contact area between the LSM and the YSZ as we ll as TPB length both affect the area of the chemical reactive zone for the charge transfer re action . It appears that the manner in which charge transfer resistance is affected by both LTPB and Sc is similar to the manner in which charge transfer resistance is affected by the LTPB ( Figure 5-3h and Figure 5-3f). This model predicts th at charge transfer resistance is ~-8 when LTPB and Sc go to infinite large. It is different from Mizusakis prediction with the infinite large of the LTPB. In reality, charge transfer resistance should be close to zero if the chemi cal reaction zone of the charge transfer reaction goes to infinite. Kuznecovs and Kleitzs mode ls assumed that the oxygen reduction mechanism is controlled by the bulk diffusion mechan ism. The controversy between my study and two models suggests that the bulk-diffusion model is not applicable to explain the relationship between the activation polarization and the metric properties in this material [89, 110]. Varying diffusion paths for oxygen through the cathode material changes the effect of the triple phase boundary on the in terfacial reaction resistance [3, 4, 126, 127]. In addition, the
125 interfacial reaction has an unstab le nature. The variations in the dependence of the individual interfacial reaction resistance on the LTPB have been reported by Suzuki et al. and Sasaki et al.. These changes occur because the dominant rate limiting step shifts from the dissociative adsorption and the charge transfer to the oxygen diffusion in micropores [133, 134]. The last but not the least, capability of qua ntification of the TPB length [4, 129, 130] is compromised by locally taking SEM images. Limited SEM images were taken from a local region of the whole sample. The LTPB is not the same at different parts of the sintered sample as homogeneity study suggests (see section 3.3). Dissociative adsorption resistance as a functio n of the sintering time is shown in Appendix B Figure B-7. It increases from 125 to 521 as the sintering time increases. Figure 5-4 shows that po re surface area affects the dissociative adsorption resistance. Dissociative adsorption resistance was increased from 125 to 184 as the pore surface area decreased by 0.2 m2/m3. The dissociative adsorption resistance was dram atically decreased by two times as the pore surface area slightly increases by 0.2m2/m3. This occurs after sintering for 8h. This can be explained by the fact that the growth of pores results in the decreasing of the pore surface area. Pore area determines the area exposed for dissoci ative adsorption of oxygen and therefore affects the cathode activation polarization. Change in the increasing rate of the re sistance varies from the early sintering process to the late sintering process, this variation is consistent with the changes in the LSM microstructure of the isothermal sintering samples. 5.1.4 Conclusions The relationship between the activation polarization and the metric properties was studied under surface-diffusion and bulk-diffusion controlle d mechanisms. How the interfacial resistance was affected by TPB length, collection length and contact area was discussed. It was found that
126 the bulk-diffusion controlled mechanism gave the worst fit. It arises from the cathode fabrication. It was found that charge transfer resistance was increased from 3 to 9 as the LTPB decreased from 0.92 m/m2 to 0.46 m/m2. Charge transfer resistance increases because effective active sites for charge transfer reaction are dramatically reduced. This relationship was observed between this work and previous studies. In Mizusakis model, the experimental data matches with the predicted data. Mizusakis mo del gave reasonable estimation because charge transfer resistance is close to ze ro as the TPB length goes to infinite large. It was found that charge transfer resistance was increased from 3 to 9 as the surface diffusion area decreased from 0.11 m2/m2 to 0.28 m2/m2. The charge transfer resistance followed the prediction of the Steeles model. It might suggest that the charge transfer resist ance is affected by the collection length, the critical diffusion distance of the oxygen intermediate to the TPB site. Steeles model predicted different collection length from the experimental data and positive charge transfer resistance with the infinite surface diffusion area. It might be related to the impact of the tertiary phase on the diffusion distance. These models based on surface-diffusion controlled mechanism appeared match with the experimental data. Small deviation contributed to the change in contacts of the LSM/YSZ interface from face to face contact to point to point contact upon sintering. The biased quantification of the TPB length might cause the scattered data. Quantification of the TPB length on a local region contributed to the inconsistency of the Mizusakis result with my study.
127 5.2 Tertiary Phase Growth Kinetics 5.2.1 Literature Review Consist with previous studies in the literature, the isochronal sinter ing study supports that the tertiary phase dramatically degrades the pe rformance of the cathode by abruptly increasing activation polarization. Since the deleterious eff ect of the LZO phase could not be neglected, focus of many research has been on how electroch emical resistances are influenced by formation of the LZO phase in A-site stoichiometric or A-site deficient LSM/YSZ based on EIS analysis [98-101, 127, 135-138]. EIS is effective to de tect the blocking responses from different microstructure defects located at the LSM/ YSZ interface [139, 140]. These microstructure defects formed at the LSM/YSZ interface include the isolating LZO phase. In previous studies, the electrochemical polarization due to the LZO phase formation was characterized by analyzing modification of the shape of the EIS impedance diagram . LZO phase blocks interfacial reactions thus slowing down the interfacial reac tion rate and changing the interfacial resistance and. Changes in the magnitude of the interfacial resistance and in the kine tics of the interfacial reactions influence the shape of the EIS diagram and the location of the intercepts with the real axis. EIS studies have showed that the growth of the insulating phases at the LSM/YSZ interface has impacts on cathode electrochemical properties [127, 130, 135, 136, 138]. Brant et al. reported that the deleterious LZO phase was detected at th e LSM/YSZ interface in samples sintered higher than 1200C . LZO starts to degrade the cathode electrochemical properties [97-101, 130] after the sample is sintered at 1200C for 100h . In Brants paper, three intercepts at the high, middle and low frequency ranges with the real axis in the Nyquist plot were emphasized. The high-frequency (1.3-5*107 Hz) intercept with the real axis represents the electrolyte impedance response. The middle-freq uency intercept with the real axis is the
128 resistance that is contributed to the isolating LZO phase or other microstructure defects formed at the LSM/YSZ interface. In other words, the middle-frequency intercept with the real axis represents the blocking effect of the interfacial defects on th e interfacial reaction. The lowfrequency intercept with the real axis is th e electrode impedance. The total polarization (Rt) is the mathematical difference between the low-frequency intercept with the real axis and the lowfrequency intercept of the midd le-frequency arc with the real axis in the Nyquist plot ( Figure 55). The interfacial resis tance (Rp) was determined from the difference between the highfrequency intercept with the real axis and the low-frequency intercept of the middle-frequency blocking resistance  ( Figure 5-5). EIS result suggests that the m iddle-frequency blocking resistance changes the interfacial resistance. The interfacial resistance in creases as the sintering time is increased. The interesting result of Brant et al is that the inte rface resistance shows the square root of dependence on the sintering tim e. If this result had been related to the microstructure characterization of the LZO growth on the atomic scale, then how basic physical mechanisms dominates the interf ace reactions therefore affects th e interfacial resistance would be understood. These EIS studies have been devoted to the interfacial el ectrochemical properties or polarization effects, however, EIS could not provide structural information of the LZO phase formation. It is still not clear whether the interf acial resistance characterized by EIS represents the blocking effect of the LZO phase on the conduction and diffusion mechanisms on the atomic scale. A few HRTEM studies were performed to co llect structural information of the LZO formation. Mitterdorfer et al. provided complete structural information of the LZO nucleation using HRTEM, atomic force microscopy (AFM ) and EIS , which were summarized in Chapter 4. Of particular interest is the compre hensive analysis of the diffusion mechanisms of
129 cations, which control LZO formation at the A-site rich La0.85Sr0.15Mn0.98O3 /YSZ and at the Asite deficient La0.85Sr0.15Mn1.02O3 /YSZ interfaces. Mitterdorfer reports at the A-site rich La0.85Sr0.15Mn0.98O3 /YSZ interface, that the nucleation of the LZO cube-shaped islands is controlled by surface diffusion of Zr cations along side of the LZO island to the top of the LZO island. As soon as LZO layer becomes dense and fully covers the YSZ layer, growth of the LZO dense layer is limited by bulk diffusion of Zr4+. The supply of oxygen elec tric species within the Nernst diffusion thickness is realized mainly by the surface diffusion process of atomic species . The thickness of the Nernst diffusion layer (t he effective thickness of the diffusion layer of the dissociated adsorbed oxygen electric specie ne ar the TPB) is in the order of 50-150 nm at temperatures between 550C and 1000C. Mitterdorfer suggests that LZO islands are form ed in a distinct way at the A-site deficient La0.85Sr0.15Mn1.02O3 /YSZ interface. LZO nuclei at an early stage are formed by surface diffusion of cations. After that, LZO island growth at a la te stage is controlled by surface diffusion of cations and the supply of lanthanum. LZO growth is controlled by the reductive decomposition of the LSM, which is the only way to supply La cations. LZO formation at the La0.85Sr0.15Mn1.02O3 /YSZ interface has been significan tly retarded as compared to LZO formation at the La0.85Sr0.15Mn0.98O3 /YSZ interface, because the supply of La cations in the primer is insufficient for LZO formation. It has been proposed that LZO nucleation rate in A-site deficient La0.85Sr0.15Mn1.02O3 is about one or two orders of ma gnitude lower than that in A-site rich LSM/YSZ. However, Mitter dorfer et al. rather emphasi zed the kinetics of the LZO nucleation at A-site rich LSM/ YSZ interface than the kinetics of the LZO growth at A-site deficient LSM/YSZ. Kinetics study of the LZO growth is crucial to understand degradation of the SOFC performance under the operating conditions.
130 To better understand the degradation of the SOFC electrochemical properties due to the LZO growth at the A-site deficient LSM/YSZ inte rface, it is necessary to study how LZO growth affects the interfacial chemical reaction kinetics. Therefore, th e quantitative dependence of the resistance of the specific reaction in the oxygen reduction mechanism on the corresponding cathode microstructure parameters has to be id entified. An understanding of how LZO growth influences quantitatively activation polarization and ohmic polarization in the A-site deficient LSM/YSZ needs to be developed. In other word s, how LZO phase affects diffusion mechanism of the oxygen intermediates, thus increasing th e activation polarization, and how it affects the ohmic polarization by affecting conduction mechanism of the oxygen reactants. There are many reports on measurements of the LZO electrical conduc tivity in the literature [30, 101, 123, 142145], value of the LZO electri cal conductivity ranges from 10-5 to 3*10-3 Scm-1. Most of measurements were performed by impedance spectroscopy [101, 123, 144, 145], however, geometric factors (contact area between the cathode and the electrolyte, and the thickness of the cathode) were simplified in these measurements. In my study, geometric factors are quantified based on FIB/SEM and TEM images. Isothermal sintered samples at 1200C from 2 h to 25 h are selected since LZO has been observed at such a high temperature for one hou r sintering based on th e isochronal sintering study. Chapter 4 addressed the different results between my study and previous TEM studies of the LZO formation in details. This section will expand the kinetics study of the LZO growth, and it will emphasize that LZO phase changes cath ode activation and ohmic polarizations on the micron scale by interruption of conduction and di ffusion mechanism of r eactant species for the oxygen reduction on the atomic scale. In addition, the following section will address calculation of the LZO conductivity. The LZO ohmic re sistance will be measured by impedance
131 spectroscopy (EIS), TEM, FIB/SEM and the classical stereology will provide geometric factors in calculation of th e LZO conductivity. 5.2.2 Experimental Design The isochronal sintering study provides basic knowledge of the LZO phase formation. The same kind of TEM analysis and rate constant calculation was applied (see Chapter 4) for seven samples in this isothermal sintering study. Hi gh-frequency intercepts of the impedance plot on the real impedance-axis in the Nyquist plot were extracted to calculate ohmic resistance of the LZO. The Ohms law ( l R A ), was applied to calculate the YSZ ohmic resistance and LSM ohmic resistance. l is the dimension parallel to the conduction direction and A is the crosssection area, perpendicular to the conduction dire ction, The contact area (S c) is defined as A(1Vv) (see section 5.1.2) and was used to calcu late LSM ohmic resistance. LZO thickness was taken into account to understand the blocking eff ect of the LZO on the impedance of the sample. The surface diffusion area, which is blocked by LZO phase, is equal to the product of the LZO thickness and TPB length. The magnitude of the LZO thickness (30-80nm) in my study is comparable to the thickness of the Nernst diffusion layer discussed in Mitterdorfers paper. The LZO thickness represents the diffusion distance of the oxygen electric and ionic species through the isolating LZO phase . The blocked volume between the LSM grains and the YSZ surface was calculated by multiplying blocked contact area and LZO thickness. The blocked contact area is the contact area between the LSM grains and YSZ because LZO phase covers the contact area between the YSZ surface and the LSM grains. Mitt erdorfer reports that LZO islands covers 90% of the YSZ surface after sinteri ng for 12h and sintering at 1100C. These samples have the A-site to the B-site ratio of 1:0.98. In my study, sample s have A-site to the B-site ratio of 1:1.02. Rate constant of the LZO phase in my study is three orders of magnitude lower than that of LZO
132 phase formation in Mitterdorfers paper. TEM st udy shows that LZO phase covers the interface region between the LSM grains and the YSZ su rface. Therefore, blocked contact area by LZO phase is assumed to be the initial contact area between the LSM grains and the YSZ surface. The ohmic contribution of the LZO phase (R) to the overall ohmic resistance was related to geometric factors (LZO thickness and TPB le ngth) as a function of sintering time. The normalized LZO resistivity (LZOO, ) is the product of the LZO oh mic resistance and the LZO thickness for simplification. In order to study the interruption of the oxygen ion conduction by LZO formation, half of the slope of the LZO ohmic resistance vs the quotient of the LZO thickness by the effective contact area is de fined as the LZO elec trical resistivity (LZO ). CLZO LZO LZOSt R/ 1 [5-5] 5.2.3 Results and Discussion 220.127.116.11 Epitaxial relationship LZO phase formation was characterized by STEM-EDS diffusion profiles, diffraction patterns and lattice images at in terfaces for the isothermally sintered samples (see description in Chapter 4). Diffraction patterns and lattice images taken at the YSZ/LZO interface confirm that LZO shows the epitaxial relationship to the YSZ not to the LSM in the isochronal sintering study (see section 4.2). The epitaxial relationship was observed in diffraction patterns of all samples sintered at 1200C. Figure 5-6 demonstrates the epita x ial relationships between the polycrystalline YSZ and the LZO, observed in two samples. Figure 5-6a shows that the epitaxial relationship was observed when the electron beam was parallel to the Y SZ zone axis of ]130[ after the sample was sintered for 2h, and the same relationship was shown when the electron beam was parallel to the YSZ zone axis of ]105[ after the sample was sintered for 6h ( Figure 5-
133 6b). Diffraction patterns ta ken at the YSZ/LZO interface suggest th at this epitaxial relationship is independent on the different crys tal orientations of the polycry stalline YSZ. One degree tilt was apparent in both Figure 5-6a and Figure 5-6b, tilt degree does not change as the s intering time increases. It does not change as a function of the sintering temperature (1473K-1673K for one hour sintering), and the sinter ing time (1h-25h at 1473K). 18.104.22.168 LZO growth kinetics Figure 5-7a shows changes in the LZO thickne ss as a function of time, and Figure 5-7b compares LZO rate constants. It suggests that LZO thickness is increased from 38.25.6 to 844nm by increasing the sintering time from 60 to 268s. A direct linear relationship was observed between the LZO thickness and the squa re root of the sintering time. The power dependence of the LZO thickness on the sintering tim e is two. It suggests that LZO growth is dominated by a diffusion-controll ed mechanism . This conclusion is consistent with the diffusion results of the STEM-EDS analysis at the LSM/YSZ interface in this work and other previous work [6, 7]. The diffusion of cations (La, and Mn) to the chemical reaction zone is the determining process for the formation of the LZO phase at the interf ace. In addition, the diffusion-controlled LZO growth might explain why the interf ace resistance measured by EIS shows the same dependence on the sintering tim e in Brants paper . If the interface resistance represents the blocking effect of the LZO phase instead of other microstructure defects at the LSM/YSZ interface, then th e interface resistance should disp lay characteristics of the LZO growth mechanism. The power dependence of the LZO thickness on sintering time is two in the Mn-excess LSM. This dependence is smaller than an expone nt of 2.48 in the Mn-deficient LSM reported by Mitterdorfer . The rate constant of the LZO phase formation (see slope in Figure 5-7a) is
134 equal to 0.039nm2/s in the 1200C sintering stud y. It is at least one or der of the magnitude lower than that of Mn-deficient LSM at 1100C reporte d in Mitterdorfers paper ( Figure 5-7b). Mn in my study is at least 4 mol% excess than Mn-defici ent LSM in Mitterdorfer s study. In addition, La in my study is ~7mol% less than La in the Mn -deficient LSM. The rate constant of the LZO formation at 1200C is comparable to the result of Mitterdorfer at 1100C. Both studies use LSM with the same A-site (La, Sr) to B-site (Mn) ratio, whereas there is ~7mol% less La in my study than La in the Mitterdorfers study. The less La in the LSM, the smaller activity of La in the reaction of the LZO formation . It is possibl e that the decrease in Asite to B-site ratio stabilizes the LSM thus retard ing LSM decomposition. Mn inhib its decomposition of the LSM. The less LSM is decomposed, the less amount of the La is supplied to reactions between the LSM and the YSZ. As a result, LZO formation is delayed. Therefore, La deficiency and Mn excess delay the LZO formation . LZO phase formed between the A-site deficien t LSM and the YSZ is expected to affect electrochemical properties. At low-overpotential re gion, the insolating gap is expected to change the cathode diffusion mechanism or conduction mechanism [6, 28]. 22.214.171.124 Contributions of LZO formatio n to activation polarization In the early discussion, the amount of the LZO phase increases as the square root of the sintering time. The interfacial re sistance shows a power dependence of two of the square root of the sintering time (see Appendix B Figure B-5). The effect of the LZO phase on the interfacial resistance is shown in Figure 5-7c. The increasing LZO thickness increases the interfacial resistance. It suggests that LZO phase blocks some electrode reactions, which include charge transfer reaction, dissociative adsorpti on reaction or surface diffusion of the oxygen intermediates, subsequently, interfacial resistan ce increases. It appear s that the interfacial resistance follows a power dependence of two of th e LZO thickness.
135 Impacts of the LZO phase on the interfacial resi stance in previous thr ee models are shown in Figure 5-7d, Figure 5-7e and Figure 5-7f. Figure 5-7d shows that in creasing the ratio of the LZO thickness to the TPB length increases linearly the interfacial resistance. The experimental data matches better than the Mizusakis model, in wh ich deviation of the experimental data from the model was pointed out at the early stage of the isothermal sintering. Because the interfacial resistance in the Mizusakis model was substitute d by the charge transfer resistance. It appears that LZO blocks some TPB sites, in other wo rds, effective TPB sites are reduced. Both LZO phase formation and reduction in the TPB lengt h increase the interfaci al resistance. After integrating impacts of the LZO phase, interfacial resistance shows a linear relationship than the predication of the Mizusakis model. The interfacial resistance incr eases as a function of the tLZO 2 /(LTPBlc) as shown in Figure 5-7e, data points are not scattered at the early stages of the sinterin g, as what was observed in the Steeles model ( Figure 5-3d). LZO phase is expected to block porosity, porosity of the LSM decreases as LZO phase is form ed, as a result, interfacial resistance in creases . LZO phase affects the diffusion distance of the oxygen intermed iates in the LSM to the TPB sites, collection length, has to be extended in order to maintain the sufficien t current density at the TPB. Increasing the collection length increases the interf acial resistance . Figure 5-7f shows that the inte rfacial resistance reduces by in creasing the ratio of the LZO thickness and the product of the c ontact area and the TPB length. Scattered data at the early sintering process was absent, alt hough it was apparent in the Kuzn ecovs model. It suggests that LZO phase causes the slow reacti on rate of the interfacial reac tions. The power dependence of the LZO thickness varies from 1.1 in the Mizusa kis 1-D model to 2 in the Steeles 2-D model (the surface-diffusion controlled mechanism) and th en decreases to be 0.6 in the Kuznecovs 3-D
136 model (bulk-diffusion controlled mechanism). However, Steeles model assumes that the collection length is a constant. Collection length varies in this se t of the isothermal sintering samples. Therefore, the power depe ndence of the LZO thickness is expected to be close to 1.1. The bulk-diffusion controlled mechanism is not a pplicable for the LSM system (see details in Section 5.1.3) , this corrected Kuznecovs model can be ruled out. It should be noted that LZO phase change s the interfacial reaction by affecting TPB boundary. Since the charge transfer reaction is the reaction, which o ccurs directly at the TPB, it should be interesting to study the impact of the LZO phase on the charge transfer reaction. The effect of the LZO phase on the charge transfer resistance is shown in Fi gure 5-7g. The increasing LZO thickness increases charge transfer resistance. The charge transfer resistance is larger with the presence of the LZO phase th an with the absence of the LZO phase. It indicates that LZO phase blocks the supply of the r eactants (electrons or/and oxygen intermediates), and then slows down the charge transfer reac tion, as a result, charge transfer resistance increases. Section 5.1.3 showed that the TPB length is not only geometric f actor to the charge transfer resistance (CT R ). If the effect of the TPB length on the charge transfer resistance is compared to the effect of LZO thickness, then it a ppears that the latter ha s the stronger effect. In other words, the charge transfer resistance incr eases as a function of a squared LZO thickness, whereas, the LTPB shows a contribution of a single power. LZO phase aligns data points, which correspond to the large TPB length ( Figure 5-7f). The large TPB length is caused by the early sintering process, duri ng which the LZO nucleates at some TPB sites and grows laterally along the LSM/YSZ interface, the charge transfer re sistance keeps increasing due to the gradual reduction in TPB sites. The qualification of the TP B length is offset from the real magnitude of the TPB length. Because the TPB boundary, in fact, is covered by LZO phase, this part of the
137 TPB boundary is invisible using SEM. After the LZO phase covers the whole LSM/YSZ interface, charge transfer reaction still occur at TPB sites, the qua ntification of the TPB length is not affected by the coverage of the TPB sites. As a result, small TPB length does not show deviation from the straight line. At this late si ntering process, LZO layer grows parallel to the normal of the LSM/YSZ interface, as a result, LZ O thickness increases, then charge transfer reaction slows down due to blocking the incorp oration of the oxygen ion in the zirconia and inhibiting surface diffusion of the oxygen intermediate to TPB , as a result, the charge transfer resistance is increased by both increasing LZO thickness and reducing TPB length ( Figure 57h). Because number of active sites for charge tr ansfer reactions is reduced by increasing amount of LZO phase formed at the LSM/YSZ inte rface and by decreasing TPB length. Figure 5-7g shows a power dependence of two of the LZO thickness. Applying relationships between the interfaci al resistance and the TPB length in the previous models into the charge transfer resi stance, the power dependence of the LZO thickness was 1.88 in Figure 5-7h, 2 in Figur e 5-7i and 0.86 in Figure 5-7g. It should be noted that the interfacial resistance has different dominated electrode reactions. However, the tLZO 2 or tLZO 1.88 is consistent with the interfacial resistance as a function of the tLZO, it represents the blocking effect of the LZO phase on supply of the surface diffusion of the oxygen reactant species for the charge transfer reaction from YSZ and or LSM to the TP B. It is possible that LZO phase affects the surface diffusion  or bulk diffusion mechan ism of the oxygen reac tant species . In addition, the charge transfer resistance (tLZO=0) is predicted to be 3 and 3.3 and is close to the experimental char ge transfer resistance of 3.8 which was measured from one sample without LZO formation. LZO phase fo rmed at the LSM/YSZ interface dramatically increases the energy barrier fo r the reactions to overcome by increasing charge transfer
138 resistance, thus the activation polarization increa ses. Therefore, charge transfer resistance is dominated by LZO phase formation. It appears that the study of the effect of TPB boundary on the charge transfer resistance should take the impact of the LZO phase into account. 126.96.36.199 Effect of LZO phase formation on ohmic polarization Table 5-1 shows results of th e ohmic polarizations (ohmic resistance) of the SOFC components and values of the geometric factors. Figure 5-8a and Figure 5-8b show changes in ohm ic polarization of the LSM and ohmic polariza tion of the LZO as a fu nction of the sintering time, respectively. The total ohmic resistance (hig h-frequency intercepts of the impedance plot on the real impedance-axis) consists of the YS Z ohmic resistance, the LSM ohmic resistance and the LZO ohmic resistance. YSZ is a fully dense material. Thickness of the YSZ layer (l) and cross-section area (A) are determined by the fabrication pr ocessing of tape casting. Conductivity of YSZ (YSZ), A and l were used to calculate YSZ ohmic resistance using Ohms law. The YSZ ohmic resistance (O,YSZ) is a constant of 0.07 although the sintering time increases. Figure 5-8a shows that LSM ohmi c resistance is not a cons tant, and it falls into a range of 4-6*10 -9. It is decreased as the sintering time incr eases. With the increasing sintering time, the contact area increases ( Figure 5-3a). It should be noted that the cross-se ction area of the LSM in O hms law was normalized by the effectiv e area fraction of LSM grains (1-Vv) at the crosssection area and the dimensionless connectiv ity among LSM grains (Cv), because Ohms law states an ohmic loss for a dense and connected conducting material. LSM is porous so that pores and isolated LSM grains are not contributed to electron conducti on within the cathode bulk. The effective cross-section area, ALSM, should be the area of the connected LSM grains in the cathode bulk. ALSM was calculated as the following equation: VV TLSM LSMCVAA)1( [5-6]
139 where TLSMAis the total cross-section area of the scr een-printed LSM layer and is determined by the screen-printing fabrication of the SOFC material. The product of the total cr oss-section area and area fraction of LSM grains is defined as the effective c ontact area (Sc) at the LSM/YSZ interface at the TPB ( Figure 5-3a). Sc was calculated by )1(V TLSM CVAS [5-7] Conductivity of the LSM (LSM)  and LSM thickness (l) were used to calculate the ohmic resistance of the LSM. LSM thickness was measured from the cross-section FIB/SEM images. LZO ohmic resistance (LZOR) was calculated by subtracting YSZ and LSM ohmic resistance from the total ohmic resistance of the whole sample. Figure 5-8b shows that LZO ohm ic resistance falls into the range of 3.67-6.43 as the sintering time increases. Large LZO ohmic polarization is ascribed to much lowe r of electronic conductiv ity than LSM [23,27]. LZOR can be defined as the following equation: TPBLZO LZO LZO LZOA t R, [5-8] where LZO is the LZO electrical resistivity and TPBLZOA, is the contact area of SC, which is the LSM grain area at the LSM/YSZ interface ( Figure 5-3a). This assumption is based on TEM study, which shows that LZO covers the layer between the LSM grains and the YSZ surface at the late sintering process (see ch apter 4). The bigger contact ar ea between the LSM and the YSZ, which is blocked by LZO phase, and the thicker the LZO layer, the more conducting electronic carriers, which are blocked by LZO phase. Therefore, the larger ohmic resistance at the late sintering process as the si ntering time increases ( Figure 5-8b).
140 Comparison of the total ohmic polarization to the LZO ohmic polarization is showed in Figure 5-8c. Figure 5-8d shows the normalized LZO el ectrical res istivity. Normalized LZO ohmic resistance dominates the total ohmic resistance, and it varies the total ohmic resistance of the LZO ( Figure 5-8c). Large LZO ohmic polarization is as cribed to five orders of magnitude lower of the electrical th an that of LSM [27,23], and two orders of magnitude lower than that of YSZ [29-33], therefore the magnitude of the LZO ohmic resistance is comparable to the total ohmic resistance. In addition, changes in the to tal ohmic resistance follow the same direction as variations in the LZO ohmic re sistance. It might suggest th at LZO phase formed at the LSM/YSZ interface changes cathode conduction mechanism by decreasing the effective conducting area at the cathode/electrolyte interface, therefore, cathode performance is degraded [127, 135, 136, 130, 138]. Figure 5-8d shows LZO nor m alized resistivity (LZOO, ), which is the slope of the product of the RLZO and Sc vs tLZO. Sc is equal to TPBLZOA,, which is blocked by LZO phase, then LZO c LZO LZOt S R [5-9] The slope (the LZO electronic resistivity) in Figure 5-8d is a constant, ~5.4*105 (cm), at a fixed temperature of 900 C. The temperature was determined by furnace temperature when impedance data was collected. The electrical conductivity of the LZO phase (the reciproc al of the slope) is approximated to be 2*10-6 Scm-1. It should be noted that the magnitude of the LZO electri cal conductivity is calculated from the TEM measurement of th e LZO layer. It is one tenth of ~1e-5 Scm-1 [101, 145, 144] of the LZO conductivity and much lower than ~1e-3 Scm-1 [30, 142], close to 1.1e-4 Scm-1
141 , 2e-4 Scm-1  as well. This difference depe nds on techniques of the measurement, various defect chemistry of the dopant s as well as different operating PO2 ranges. The degradation of the SOFC performance can be explained by cont ributions of the LZO phase to the ohmic polarization. LZO electrical resistivity is four orders of magnitude lower than conductivity of the YSZ [ 29-31] and seven orders of magnitude lower than c onductivity of the LSM [14,23,27,101]. LZO electrica l resistivity repres ents the interruption of the conduction mechanism of the electronic ca rriers through the contact region causes the increases in ohmic polarization. 5.2.4 Conclusions Epitaxial relationship exists between the LZO and the polycrystalline YSZ. It was found that LZO growth was retarded by increasing Mn composition from a Mn-deficient LSM to a Mnexcess LSM. At the same time, reduction in La composition also retards LZO formation. Mn stabilizes the LSM and Mn-excess inhibits LSM decomposition thus decreasing supply of the La. As a result, LZO growth was delayed by reduc ing supply of the La to the LZO reaction. Quantitative microstructure analysis of the LZO growth was first time related to the cathode polarization in th e literature. The contributions of the LZO phase to the activation polarization and the total ohmic pol arization of the SOFC were di scussed. It is found that the calculated LZO electrical conductivity of 2*10-6 Scm-1 based on the microscopic analysis is smaller than the electrical conductivity of the LSM and YSZ. As a result, LZO phase becomes the major factor and attributes to the total ohmic resistance by changing conduction of the electrical species from the LSM to the TP B. The LZO phase has poor ionic conductivity compared to conductivity of the YSZ , LZO pha se formed at the LSM/YSZ interface inhibits charge transfer reaction by bloc king the supply of the oxygen reacta nt species from YSZ or LSM
142 to the TPB. In addition, LZO phase increases ener gy barrier for the charge transfer reaction to be activated. 5.3 Effect of the Topology Propertie s on Concentration Polarization 5.3.1 Literature Review Pore-network models coupled with skeleton ization models have been applied into simulations of the microvascular blood flow in some brain tissues to determine neuronal nutrition and development , the filtering process in some filtering cakes to design the filtering equipment  and the gas or oil transport in porous permeable rock to develop a successful hydrocarbon recovery pr ocess . This is because th e relationship between the bulk flow or transport properties of the media ( quantified by the pore-net work models) and the geometrical properties of the pore microstructure (characterized by the skeletonization models) is established. Pore-network modeling enables to gain fundamental understanding of multiphase fluid or gas flow in porous medi a. In conjunction with the skel etonization modeling in 3-D image analysis, it becomes possible to predict the fluid or gas transport properties of a porous media. Then the cathode concentration pol arization can be associated w ith the gas transport properties of a porous media. The goal of this work is to understand how the geometric properties of the porous cathode affect the gas tr ansport properties and therefore change cathode concentration polarization of SOFC. Unfortunate ly, development of a pore-netw ork model is beyond the scope of this work to achieve the relationship between the geometric propertie s and the gas transport properties, therefore, relati onships of two pore-network models developed by Mason and Koponen are applied into this work. However, this is the first study of quantifying the geometric property (tortuosity) of the porous cathode by implementing an elementary skeletonization model in 3-D image analysis. Three-dimensiona l images of the porous media are acquired by focus ion beam. Two pore-network models in clude Masons dusty-gas model and Kopneons
143 lattice-gas model. Two models predict gas transpor t properties of a porous cathode (effective diffusivity and permeability). The cathode concentr ation polarization is associated with the gas transport properties of a porous cat hode by applying Kims model. 188.8.131.52 Skeletonization model Quantification of effective diffusivity and pe rmeability need a way to quantify tortuosity, open porosity and pore surface area. Quantificati on of open porosity and pore surface area were explained in Chapter 3 and 4, the focus of this section is on quantification of the diffusional and hydraulic tortuosity by calculati ng geometric tortuosity using an elementary skeletonization model in 3-D image analysis. Despite its widesp read use in petrophysics, tortuosity has various meanings to describe different transport processes ta king place in a porous material, values for geometrical, diffusional, hydraulic and electrical tortuosity are generally different from one another . Geometric tortuosity is the ratio of the pore length to the projection of the pores in the direction of flow . In Masons model, diffusional tortuo sity is applied to study diffusion kinetics of a binary gas mixtur e. In Koponens model, hydraulic tortuosity is used to analyze flow kinetics of a binary gas mixture. Differen ces in diffusion tortuosity and hydraulic tortuosity will be explained later. An advanced skeletonization model in 3-D imag e analysis calculates geometric, diffusional and hydraulic tortuosity. It estim ates transport distance of th e gas through interconnected pore channels along the sinuous diffusion path when the transport is in the continuum diffusion domain  or approximates gas flow distance along the tortuous flow direction when transport is in the viscous flux domain . In other words, gas transport distance is equal to the length of the skeleton of a connected porenetwork (the length of the median axis of a pore-network). Additionally, skeletonization model determines the major flow channels of pores for the gas transport. In other words, connected flow channe ls with a large radius of pore throats are more
144 likely for gas transport to occur. Finally, it pr edicts efficiency of the gas transport through different topologies of connected pore channels In other words, the higher volume fraction of the large radius of pore throats is within the porous cathode, the higher efficiency of the gas transport is through the porous cathode. The elementary skeletonization model pe rforms three main algorithms: homotopic, chamfer distance map and thinning algorithms in se ries. These algorithms are described in details in Fouards paper . Homotopic algorithm pr eserves the original to pology of the 3-D pore space. Distance map algorithm ensures that the corre ct skeleton is located on media axis (center) of the original topol ogy of the 3-D pore space. Euclidea n distance map is similar to the topological map. It represents th e shortest distance from a poin t of the 3-D pore space to its background in a unit of grey level. The background has th e lowest grey level of zero. The media axis consists of points with the maxima di stance maps. Thinning algorithm keeps crucial topological properties of the entire pore space an d removes the redundant topological properties. 184.108.40.206 Pore-network models Quantification of effective diffusivity and perm eability become important in order to relate physical transport of gas in th e porous cathode to th e electrochemical prope rty. The effective diffusivity of a binary gas is a key paramete r to study gas transport kinetics . Mason developed a two dimensional model to estimate th e effective diffusivity of a binary gas under a steady-state in a porous media. The dust-gas model shows that effective binary diffusivity (() ceffD) is proportional to binary diffusivity of O2-N2, 22OND, porosity, VV, and reciprocal of the tortuosity, as the following : 22()'V ceffONV DD [5-11]
145 The magnitude of the() ceffDof a composite anode ranges from 0.1cm2/s to 0.2cm2/s between 650C and 800C with the total porosity of 30%. Th e tortuosity of the composite anode is ~14.5 . The flux dominated by the binary diffusi on (continuous diffusion) is equal to the total flux of oxygen flowing in a porous media. Porous media was visualized as a matrix occupied by some immobile spherical molecules. VV represents the total porosity instead of the open porosity. Diffusion tortuosity is defined as the ratio of the gas diffusivity through the porous media (()ceffD) to the gas diffusivity through a dense bulk (22OND). On the other hand, permeability is another important parameter to study fluid flow through a porous media . The prediction of the perm eability for various porous media has been performed either by the experimental methods or by the theoretical models. The experimental methods include mercury porosimetry, nuclear magnetic resonance, measurements of the electrical conductivity, and acoustic properties of the me dium [151-156]. Th e theoretical simulation of the permeability involves models with the simplified pore geometries, microscopic fluid pattern and statistic met hods [47, 157, 158]. However, various correlations between the permeability and the parameters describing the geometrical properties of the medium have been suggested. The simulated permeability of different types of sandstones varies from 116 to 5370 between porosity of 21.6% and porosity of 27%, although the same type of conduit simulation model was used to calc ulate permeability . Koponen et al. studied the viscous flow in a complex porous microstructure in a twodimensional lattice-gas model [18, 42]. The la ttice-gas model relates the permeability (physical properties of the viscous flow in a porous me dia) to the geometry of microstructures (microstructure properties of the porous media) by modifying a simple capillary theory of Kozeny et al. . Koponen et al. devised collections of two-dimensional model of
146 microstructure with various open porosity, Vv, then the fluid flow through each of these microstructures was simulated, finally, the perm eability, K, was calculate d as a function of open porosity. On the other hand, the relationship of permeability and geometry of the microstructure was achieved after tortuosity ( ), and pore surface area (SV) were expressed in terms of open porosity (VV). In other words, a theoretical relatio nship between the perm eability (K) and the geometry of the microstructure was e xpressed as a function of open porosity (VV). Then the simulated K vs VV and the theoretical K vs VV were compared for f our different equations, which gave different re lationships between K and the micr ostructure geometry. The following equation (5-11) fits very we ll with the open poros ity of 33%-90% and is showed as the following: 3 2 2 v VV csK [5-11] where c is a fitting parameter of the Kozeny coefficient (shape factor of the particle) with a range of 2-12. The magnitude of the normalized permeability (K/R2) ranges from 5*10-4 to 2*10-3 with an open porosity of 33% and an open porosity of 43% respectively. The value of the tortuosity is ~1.7 . R is the averaged pa rticle size in the simulation model. The hydraulic tortuosity is interpreted as the average of the relative lengths of the flow lines of all fluid elements with a fixed volume, passing through a given cross section during a give n period of time (weighted averaging flux). Based on this two-dimensi onal lattice-gas model, a three-dimensional ab initio lattice-Boltzmann model has been developed to simulate the creeping flow through large random fiber webs. The simulated permeability is in good agreement with the experimental permeability in the fiber webs.
147 One of the differences between the Masons model and the Koponens model is the assumption of the controlled mechanism of the total oxygen flux. The flux of oxygen controlled by viscous flow is the major flux of oxygen flowing into a porous media in the Koponens model. The porous media is envisaged as few hundreds of randomly positioned particles in two dimensions. The Masons model assumes that c ontinuum diffusion dominat es the total flux of oxygen through a porous media, which consists of fixed particles. Two domains are possible for SOFC under operations. A second difference be tween the Masons model and the Koponens model is the definition of the porosity. Porosity in Masons model includ es porosity of closed pores and open pores. Whereas, porosity of open pores is taken into account in the Koponens model. Open porosity of the porous media is de termined by the fraction of the overlapped region between particles in the whole region. The third difference between two m odels is the definition of the tortuosity. Mason uses the diffusional tortuosity in his mode l, which is the averaged ratio of effective diffusivity to bulk diffusivity  formulated to porosity. In most SOFC models, the diffusional tortuosity is a function of the geometric to rtuosity [13, 160-162], which is the ratio of the pore length to the projection of the pores in the direction of flow . The value of the geometric tortuosity is 3 for an ideal isot ropic porous media , and most often in the range of 2-10 for porous sintered ceramics [ 164] and 10-17 for anode tortuosity [13, 160,165]. Koponen utilizes the Kozeny hydraulic tortuosity (a weighted averag ing flux in a flow field) in the calculation of the permeability. In unsolidated granular aggregates, the value of Kozeny hydraulic tortuosity ranges from 20.5 to 2 and it rises up to ~5 in consolidated rocks and soils . Witt et al. suggest that an upper limit on to rtuosity in uncemented granular media is ~10 with platy grains .
148 220.127.116.11 Impact of gas transport on concentration polarization Kim related microstructure parameters to th e concentration polariza tion of SOFC by first introducing dusty-gas model as described in Ch apter 1. Later on, the dusty-gas model was applied into SOFC models to simulate pe rformance of the electrodes [13, 160-162]. Equation 1-12 shows that the concentration pol arization is increased as decreasing the cathode limiting current density. The tortuosity and open porosity are related to the concentration polarization by ln(1) 4c conc VRT iC FV [5-12] where i is the current density and C is a function of oxygen par tial pressure on the cathode side,2c Op, operation temperatures, T atmosphere pressure, p and cathode thickness, cl, Thus, 2(,,,)c OcCfpTpl. In this study, C is assumed to be a constant. If the viscous flux dominates the total flux of oxygen flowing into the LSM/Pore surface (2,V O CPJ), the permeability is related to the concentration polarization by 2 2 3ln(1 ') 4c V conc vs RT iC F V [5-13] where C is affected by a Kozeny coefficient and C in equation 5-12. Under a steady-state operational condition, C is a constant. Ideal gas law states that permeability is proportional to effective diffusivity. The permeability can be asso ciated with the concentration polarization by using Kims model. 5.3.2 Experimental Design Symmetric SOFC samples were prepared (see s ection 4.1.3). This set of eight isothermal samples was sintered at 1200C from 2h to 25h. The resulting symmetrical samples had a
149 cathode thickness of about 43m and YSZ thickness of 180m. A set of fiduciary marks was patterned beside of the region of interest for accurate alignmen ts. Few hundreds of plane-serial sections with a spacing of 0.044m-0.064m were taken from an area of 15m m parallel to the LSM/YSZ interface and ~5 m away from the LSM/YSZ interface. A Ga ion beam current of 300pA was used to mill mate rials layer by layer (see section 3.3.3). The contrast and brightness of each plan-view image was kept as clos e as possible for accurate skeletonization of one whole set of plane-serial images. Before quantification of the topo logy of the cathode microstruc ture, the stacks of the planesection images were load into a ResolveRT software. The pixel size of the plan-view images is 0.019m by 0.024m on the plane parallel to the LSM/ YSZ interface. The pixel size in the direction away from the normal of the YSZ/LSM interface ranges from 0.044m to 0.064m. After plane-view images were aligned and were segmented, the segmented images were skeletonized. The elementary skeletonization consis ts of pre-correcting ar tifacts of the planeview images, adjusting threshol d, reconstructing 3D pore space, thinning 3D pore space to the 3D pore networks, and calculating diameter of each branch in the 3D pore networks. In one whole set of serial slices, the decreased average intensity in some slices was pre-corrected by the CorrectZDrop module. The intensity changed in some slices due to excessive light absorption in other slices during the FIB/SEM operation. In order to recons truct the 3D pore space, the thresholding images were segmented to differentia te pores from grains. A consistent value of the threshold was used for all images of eight samp les. The main algorithm in the skeletonization model is the thinning algorithm. It peels off the exterior skin of the 3D pore space layer by layer until the skeleton of the 3-D pore space is the me dia axis of the 3-D pore space. Evalonlines module provides radii of branches (pore channel) and branch junctions (pore throats) in a 3-D
150 skeleton of a pore-network. Linese t module was used to provide 3D coordinates of the center of the pore channels. A matlab script was compiled to identify pore throats and to calculate the distance between adjacent connect ed pore throats (the length of the branch between connected pores). The connected pore throats have the maxi ma of the radii of pore channels. The tortuosity was normalized by the total length of the connected branches in the 3-D pore network divided by the total spacing of the stacks of the plane-section images (total distance is milled away toward the LSM/YSZ interface). Area probe was applied to the segmented plane-section images to quantify area fraction of open pores and pore surface area. 5.3.3 Results and Discussion The elementary skeletonization model was im plemented for eight isothermally sintered samples. The skeletons of the 3-D pore space in the isothermally sintered samples are shown in Figure 5-9. Figure 5-9a shows the typical skeleto n of a 2-D pore cha nnel with the dimension of 15m by 15m. Most pores are connected by a con tinuous pore skeleton. Three-point and fourpoint junctions are most common ( Figure 5-9a). It is noted that the skeleton of the 2-D pore channel follows the m edia axis of the 2-D pore structure. It means that the homotopic skeleton of the 2-D pore channel is achieved. The 3-D skelet ons of a pore network were constructed based on the homotopic skeleton in 2-D ( Figure 5-9b). These skeletons in 3-D were from the same volume for the set of the isothermally sintered samples. Pore-network density changes as the sintering time increases. Radius of the branches of the skeleton varies within one pore-network. Changes in the radii of the skeleton branches we re also visible between different pore-network. Figure 5-9b indicates that varies in ra dii of the branches of th e skeleton as well as changes in skeleton density become apparent between the sa mple sintered for 15h and the sample sintered for 25h. It indicates differences in tortuosity between these samples ( Figure 5-10a).
151 Figure 5-10 shows tortuosity, open porosity an d pore surface area as a function of the sintering time. Open porosity is initially increased by 33% as the sintering time increases up to 10h ( Figure 5-10b). It might be contributed to the growth of continuous pore channels as the sintering time starts to in crease, therefore the area fraction of the open pores in the FIB/SEM image increases. Connectivity density is gradually increased and then reduced ( Figure 5-10c). After sintering for 10h, continuous pore channels pinch off and connections between continuous pore channels are los t to the minimum ( Figure 5-10c), therefore open porosity is decreased by 16% at the sintering time of 25h. Pore surface area is decreased and the m inimum occurs after the sintering time for 10h ( Figure 5-10d). It means that growth of pore channels is the m aximum at this time. After sintering for 10h, the growth of pore channels is abruptly slow down, and the pore surface area is slig htly decreased. Tortuosity value of the porous cathode ranges from 2 to 17 [164, 160, 165]. Tortuosity shows a trend of th e slow increase followed by the fast increase after sintering for 10h ( Figure 5-10a). The number of connect ions between pore channels and radii of pore throats affect tortuosity. If wide pore throats are connected to other continuous pore channels, gas is m ore likely to transport through these wide pore throats than por e throats with narrow opening, therefore the to rtuosity is small. However, if wide open pore throats are connected to isolated pore channe ls, gas prefers to flow through the pore throats with the narrow opening, because such kind of pore throats are conn ected to continuous pore channels, therefore, the tortuosity is large. After sint ering for less than 10h, the loss of connections to other channels competes over the growth of pore channels, although pore throats become wide, tortuosity slightly increases by redu cing connectivity density ( Figure 5-10c). Shrinkag e or pinching-off of the continuo us pore channels causes the decreasing of the diameter of the pore throats as well as the decreasing of the number of the wide pore throats within the cat hode bulk. Additionally,
152 reduction in connections between adjacent pore channels results in the decrease of the connectivity density of po res in the cathode bulk ( Figure 5-10c). Loss of connectivity density and reduction in num ber of wide open throats ( Figure 5-10b) dramatically increases tortuosity after sintering for 10h. The ef fective diffusion coefficient (open porosity over tortuosity) and the permeability are plotted as increasing the sintering time ( Figure 5-11). The relationships between the gas transpo rt resistance and the geometric properties are shown in Figure 5-11 (effective diffusivity) and Figure 5-12 (permeability), respectively. Figure 5-11a shows that increase in tortuosity reduces the effective diffusion of the O2-N2, by at most two times. The value of the effective diffusivity of the O2-N2 ranges from 4*10-3 cm2/s to 2.1*10-2 cm2/s at 1200C. It is lower than Kims result of 0.2cm2/s for the effective diffusivity of the H2-H2O at 850C. It has been confirmed that effective diffusivity of the O2-N2 is lower than that of H2-H2O . The gas transport resistance appears to increase by decreasing the effective diffusivity ( Figure 5-11c). The higher effective diffusivity, the f aster ki netics of the gas trans ports through the porous cathode, therefore the less resistan ce to the gas transport [13, 167]. The expected logarithmic relationship in Kims mo del was not observed in Figure 5-11b. This difference is caused by a wide range of tortuosity and open porosity that has been studied in this w ork. The relationship between the gas transport resistance and the effective diffusi vity is analyzed by varying tortuosity (2-12) and open porosity (0.23-0.41). A dditionally, usage of the total porosity in Kims model is one reason. The difference between the open porosity and total porosity can be up to 100% in case of open por osity of 20% . The magnitude of the normalized permeability ( 2 pK R ) is between 10-4 and 3*10-3 with an open porosity of 23%-41% ( Figure 5-12a). Rp represents pore radius. It is consistent with
153 Koponens normalized permeability. It ranges from 5*10-4 to 2*10-3 for the open porosity of 33%-43%. The normalized permeability appears to be insensitive to the sintering time. Permeability describes two competitive microstructure evolutions: volume changes in pore channels and connections change s in pore channels within the porous cathode. If volume of open pores as well as connection among pores are decreased at a same rate, then permeability will decreases. If the connections among pores decreas e faster than volume fractions of open pores reduces, then permeability will not monotonically decrease. If the viscous flux dominates the total flux of oxygen flowing into the LSM/pore surface (2,V O CPJ), the gas transport resistance is reduced by increasing the permeability as showed in Figure 5-12b. The ineffective gas transport through the porous cathode cont ributes to the starving of the oxygen therefore slows down kinetics of the oxygen reduction. As a result, con centration polarization is increased. The im pact of the permeability on the gas tr ansport resistance is compared to the effect of the effective diffusivity on the gas transport resistance ( Figure 5-11b and Figure 5-12b). A di rect relationship was observed between the perm eability and the ga s transport resistance as compared to the relationship of the effective diffu sivity. It might indicate that th e skeletonization and the latticegas models are more applicable to study gas tr ansport properties in a porous cathode than the dusty-gas model. In other words, the tortuos ity quantified by the skeletonization model might represent the hydraulic tortuosity (the weighted velocity of fluid fl ow in a fluid flow field) in Koponens model instead of the diff usional tortuosity in Masons model (the averaged ratio of the diffusion through a porous material to the diffusion through a dense bulk). In addition, changes in connections among pore channels are important to study gas transport properties. Masons model neglects variati ons in connections between po re channels, therefore, the
154 contribution of the effective diffusivity to the gas transport resistance is not as direct as that of the normalized permeability. An accurate skeleton model needs to preserve the topological properties of the original object (homotopy) [168, 169]. A homotopic skeleton depends on the thresholding algorithm . Inconsistent thresholding causes loss of branches in a sk eleton of a pore network thus under estimating tortuosity. In addition, under-threshold results in enlargement of the mean diameters of the wide-open pore throats  thus over estimating the efficiency of the gas transport through pore channels. An accurate skelet on model requires that the skeleton of a pore network is consistent with the media axis of the original object. It relies on segmentation of FIB/SEM images. Over-segmentation and under-segmentation of the edge of pores cause shift of the media axis of the skeleton in a pore-network, therefore cause inaccurate quantification of the tortuosity. A study of the gas transport efficiency through the porous cathode is compromised by two limitations of the skeletoniz ation model (over-threshold a nd under-segmentation) discussed above. The major flow channels need to be accurate ly identified before transport efficiency is qualitatively assessed. A verifi cation of the skeletonization mode l needs to be performed by a separate model. This model should reconstruct the flow field by using the ra dii of pore throats as well as the distribution of pore throats as inputs of the model, which were calculated from the elementary skeletonization model. The advanced m odel is expected to simulate skeleton of a 3-D pore-network to test the accuracy of the elementary skeletoniza tion model. In addition, main flow channels (pore throats with wide opening) should be determined based on comparing the radii of pore throats as well as the distribution of pore throats to one anot her. Then the frequency of main flow channels through wh ich gas transport can be estimated. The distribution of the main flow channels determines the gas trans port efficiency within the porous cathode.
155 5.3.4 Conclusions Topology of the LSM has been related to the con centration polarization. It is the first time that tortuosity is quantified by an elementary sk eletonization model in 3-D for this material. It appears work well to analyze concentration polarization. The magnitude of the tortuosity falls into the range of the tortuosity for the sintered ceramics. Two models with different assumptions on the major O2 flux show that increasing the geomet ric factors (effective diffusivity and normalized permeability) will reduce the gas transport resistance. The value of the effective diffusivity of the O2-N2 was confirmed lower than that of H2-H2O. In the binary diffusion dominant regime, the gas transport resistan ce was not monotonically increased by increasing logarithm of vVas predicted by Kim. The inconsistency with Kims model is due to a different range of the tortuosity, different de finition of the porosity as well as the assumption of grains in a porous media. On the other hand, in the visc ous flux dominant regime, the magnitude of the normalized permeability is consistent with Koponens normalized permeability. A direct relationship was observed between the increasing of the permeabil ity and the decreasing of gas transport resistance. The limitation of the elementary skeletonization model was addressed. Future work on the development of the skeletonization model was suggested.
156 Figure 5-1. Three paths of oxygen reduction: P1 , P2  and P3 [107, 110]
157 A B Figure 5-2. Cross-section images of the isothe rmal sintered samples. A) 2hrs-8hrs. B) 10hrs25hrs
158 A B C D Figure 5-3. Continued
159 E F G H Figure 5-3. Effect of the LTPB on the activation polarization. A) Contact area between the LSM and YSZ for the isothermal sintered samples. B) LTPB for the isothermal sintered samples. C) Impact of the LTPB on interfacial resistance. D) Effect of the collection length and LTPB on interfacial resistance. E) E ffect of the contact area and LTPB on interfacial resistance. F) Impact of the LTPB on charge transfer resistance. G) Effect of the collection length and LTPB on charge transfer resistance H) Effect of the contact area and LTPB on charge transfer resistance.
160 Figure 5-4. Effect of the SV on the activation polarization of the isothermal sintered samples Figure 5-5. Nyquist plot of the interfacial resistance 8h
161 A B Figure 5-6. Epitaxial relations hip between the LZO and the polyc rystalline YSZ. A) LZO vs. YSZ with]130[ B. B) LZO vs. YSZ with ]105[ B.
162 A B C D Figure 5-7. Effect of the LZO on the activ ation polarization. A) Thickness of the LZO for the isothermal sintered samples (tLZO vs. t0.5). B) Rate constants of LZO formation for Mn deficient LSM and Mn excess LSM. C) LZO phase contribution to the interfacial resistance. D) Cooperative c ontribution of LZO thickness to the Mizusakis model. E) Cooperative contribution of LZO thickness to the Steeles model. F) Cooperative contribution of LZO thickness to the Kuze nocovs model. G) LZO phase contribution to the charge transfer resi stance. H) Cooperative contri butions of LZO thickness and TPB length to the charge transfer resist ance. I) Cooperative co ntributions of LZO thickness, collection and TPB length to the ch arge transfer resistance. J) Cooperative contributions of LZO thickness, contact ar ea and TPB length to the charge transfer resistance.
163 E F G H I J Figure 5-7. Continued
164 A B C D Figure 5-8. Effect of metric pr operties on Ohmic polarization of th e isothermal sintered samples. A) LSM ohmic polarization B) LZO ohmi c polarization C) Contribution of the LZO phase to the ohmic polarizati on. D) LZO electrical resistivity.
165 A B Figure 5-9. Skeleton of pore networks for the isothermal sintered samples. A) Homotopic skeleton of a 2-D pore structur e, (note that line loop matc hes with the media axis of the 2-D pores). B) Skeleton of a 3-D pore space (note that different colors represent different radii of skeletons)
166 A B C D Figure 5-10. Microstructure prop erties for the isothermal sintered samples. A) Tortuosity. B) Porosity. C) Connectivity density. D)Pore surface area. A B Figure 5-11. Effect of microstructure properties on concen tration polarization by Kim's model. A) Effective diffusivity for the isothermal si ntered samples. B) Impact of the effective diffusivity on concentration polarization .
167 A B Figure 5-12. Effect of micros tructure properties on concen tration polarization by Koponen's model. A) Permeability for the isothermal sintered samples. B) Impact of the permeability on concentration polarization
168 Table 5-1. Calculation of the LZO ohmic polarization (resistance) Time (h) O,T ( ) O,LSM,LZO ( ) O,LSM ( ) RLZO ( ) O,LZO ( m) TPBL1 (m) TPB LZOL t(m2) 2 5.35 5.28 7e-9 5.28 0.20 1.37 0.052 4 5.31 5.24 7e-9 5.24 0.23 1.15 0.051 6 4.59 4.52 6e-9 4.52 0.25 1.09 0.061 8 3.74 3.67 6e-9 3.67 0.21 1.24 0.072 10 4.73 4.66 6e-9 4.66 0.27 1.14 0.067 15 5.29 5.22 6e-9 5.22 0.36 1.60 0.111 20 6.50 6.43 5e-9 6.43 0.47 2.00 0.148 O,T-Total ohmic polarization; O,LSM,LZOSum of ohmic polariza tion of LSM and LZO ; O,LSMLSM ohmic polarization, cross section area normalized by SC CV; RLZO-LZO ohmic resistance, cross section area normalized by SC CV; O,LZO-O,LZO multiply by tLZO; O,YSZOhmic polarization of YSZ, 0.07
169 CHAPTER 6 SUMMARY AND FUTURE WORK 6.1 Summary Understanding of the influences of the microstructure properties on kinetics of the oxygen reduction mechanism and subsequently on cathode pol arization is necessary to engineer designs of the SOFCs. Before it can be fully implemented, it is crucial to develop effective FIB techniques in order to investigate these mate rials and to combine new techniques with other analytical methods for advanced analyses. This thesis has attempted to characterize 3D and 2D microstructure of the SOFCs a nd to discuss the effects of the specific geometric factors on components of the cathode polarization. A deep investigation of the contributions of a deleterious phase to the cathode performance has been performed. In this final chapter, the contributions of this research will be review ed and areas for further study will be suggested. 6.1.1 FIB Technique Developments Characterization of the metric and topologic properties of the cathode microstructure is an important area of study. Micros tructure properties can be op timized during the fabrication processes, and the optimized microstructure properties can improve cathode performance by affecting kinetics of the oxygen re duction mechanism that occurs on the cathode side. The FIB automated serial-sectioning techniques provide opportunities for characterizing the bulk metric properties and topologic propertie s of the cathode microstructure on micron scale. FIB sample preparation techniques, which ha ve been developed, also en able characterization of the interfacial metric propert ies of the cathode/electro lyte interface on the atomic scale. The study of the geometric properties of the cat hode microstructure brings a new angle to the understanding of the dependence of the cathode polarization on the geometric propert ies of the cathode microstructure on both micron and atomic scales.
170 Although FIB/SEM enables to characterize effe ctively the geometric properties of the cathode, it is a site-specific char acterization tool. This limitation of FIB/SEM has been overcome by combining FIB/SEM with the classical and adva nced stereology. In order to offer unbiased quantification of geometric prope rties of the SOFC microstructure, for this reason, FIB/SEM automated serial-sectioning techniques have b een developed to stat istically characterize microstructure feature in 2D combining with stereology. The homogeneity of topological properties of the cathode has been explored by the disect or analysis coupled with the T-test. The optimized number of the cross-section images fo r 2-D microstructure prop erty analysis, and of the plane-view images for 3-D microstructure quantification were decided. The optimized numbers ensure unbiased quantific ation of geometric properties of the sintered SOFC samples on the micron scale. A new method of preparing TEM cross-sectional sample of the LSM/YSZ interface by FIB and Omniprobe mani pulator appears to work well for so porous microstructure of the cathode. This technique al lows study of the initial stages of LZO formation by using the TEM/EDS analysis. The kinetics study of the LZO formation cl arifies the delay of the LZO formation predicted in previous thermodynamic studies. In addition, this technique opens a brand-new research field: the study of contributions of the LZO phase formation to the cathode activation polarization and cathode ohmic polarization. 6.1.2 Dependence of the Activation Polari zation on the Metric Properties It is well-known that TPB length has been the most crucial metric properties, which affect the interfacial reactions between the cathode and the electroly te. Kinetics of the interfacial reactions dominates the performa nce of the SOFC. However, dive rse relationships between the interfacial resistance and the LTPB complicate the understanding of the charge transfer reaction. Different conclusions are ascribed to the biased quantification of the TPB length, and to its dependence of the overall polariz ation resistance instead of the individual charge transfer
171 resistance. It is clear that in literatures, the LZO phase formation has been discounted by ignoring the attributions of the LZO phase to the interfacial resistance. Based on unbiased analyses of the cathode and interfacial microstructure, a comprehensive investigation of the impact of TPB length on the ch arge transfer resistance was performed. Both the isochronal and the isothermal sintering studies showed that specific metric properties of the microstructure affect the kinetics of the corr esponding possible rate limiting steps, thus they influences the corresponding comp onents of the activat ion polarization. D ecreasing of the TPB length increases the charge transfer resistance. De nsification of the microstructure dramatically reduces the available TPB boundary area for the ch arge transfer reacti on. Charge transfer resistance increases because effective active site s for charge transfer re action are dramatically reduced. In addition, isolated pores inhibit tr ansport of oxygen molecule s or diffusion of the oxygen intermediates to reaction sites at the LSM/YSZ interface. The dissociative adsorption resistance is increased as the pore surface area is reduced. This can be explained by the fact that the growth of pores results in the decreasing of the pore surface area. Pore area determines the area exposed for dissociative ad sorption of oxygen and therefore affects the cathode activation polarization. Dramatic changes in the charge transfer resi stance as well as the dissociative adsorption resistance were observed in th e isochronal sintering between 1200C and 1300C. The isothermal sintering study of 1200C suggests that dramatic changes in the activation polarization are caused by the LZO phase formation. Although it was not considered in previous studies, LZO phase varies the activation polariz ation with different extents under different sintering conditions. This expl ains why conclusions about TP B length vs. charge transfer resistance are different. LZO phase hinders the transport of oxygen molecules or obstructs
172 diffusion of the oxygen intermediates to reaction s ites at the LSM/YSZ interface. In other words, LZO phase covers some distance that the reac tion zone extends beyond the TPB , thus reducing reactive zone area, in which charge tr ansfer occurs. LZO phase increases an energy barrier, which oxygen reactant specie s must overcome before they ar rive at TPB sites. After LZO formation, more activation energy is needed for the charge transfer and the dissociative adsorption reactions to occur. As a result, increasing the energy barrier of the reactions increases the activation polarization. In other words, insu fficient amount of the reactant species result in the reduction in the reactions rate, thus increasi ng reaction resistances (both charge transfer and dissociative adsorption resistances). It should be noted that the de finition of the TPB length is m odified due to the LZO phase formation at the cathode/electrolyte interface, therefore TPB length is not the only geometric factor that affects the charge transfer resistance. The isot hermal sintering study allows a comparison between it and three models to study how charge transfer re sistance is affected by geometric factors. Different effects of LTPB on the charge transfer resistance were observed between Kleitzs model and my study. The power dependence of the charge transfer resistance contradicts Kuznecovs model on the product of the LTPB and Sc. Kuznecovs and Kleitzs models assume that the oxygen reduction mechanism is controlled by the bulk diffusion mechanism. The controversy between my study and the two models suggests that the bulkdiffusion model is not a pplicable to explain the relationshi p between the activation polarization and the metric properties in this material. Diverse relationships between the interfacial resistance and the LTPB are ascribed to neglect the effect of the LZO phase on the charge transfer resistance in previous work. The LZO phase formation at the cathode/electrolyte interface modifies the number of the effective active sites (the ideal definition of the TPB sites) for the charge transfer
173 reaction. The relationship between the TPB length and the charge transfer resistance with LZO phase formation is different from the case wit hout LZO phase formation. Therefore, previous models report different conclusi ons about the effect of the TP B length on the charge transfer resistance from the experiment al observations in my study. 6.1.3 Tertiary Phase It is well known that for cathode materials with Sr<30mol%, the LZO phase was observed at the LSM/YSZ interface for co-sintering at temperatures higher than 1000C. LZO phase degrades the cathode electrochemi cal properties due to its lower ionic conductivity than YSZ. It is very important to control the formation and th e growth of LZO phase at an initial stage to improve electrochemical propert ies. Previous thermodynamic studies reported that LZO formation either can be avoided by reducing La composition down to 86mol% or not. Isochronal and the isothermal sintering studies in this work answered this question: La insufficiency in the LSM avoids or retards the LZO phase formation. These studies investigated the basic diffusion mechanism of an initial stage of the LZO phase formation and an alyzed structural correlation between the LZO and the YSZ phase on the atomic scale. Structural analysis of the LZO phase growth at the LSM/YSZ interface on the atomic scale was related to the microstructure evolution at the LSM/YSZ interface on the micron scale. Thus, the result that the LZO phase changes cathode activation and ohmic polar izations on the micron scale is explained by the interruption of conduction and diffusion mechanism of reactant species for the oxygen reduction on the atomic scale. The isochronal and the isothermal sinteri ng studies on the kinetics of the LZO phase formation showed that changing in the ratio of A-site (La,Sr) to B-site (Mn) does not prevent but only delays the LZO formation. In other words, LZO phase cannot be avoided by only
174 decreasing the composition of La less than 86m ol%. This conclusion has been confirmed by strong evidence. Rate constants of the LZO formation in low A-site to B-site ratio of LSM were lower than those of LZO phase in high A-site to B-site ratio of LSM und er the same sintering conditions. It is possible that the decrease in A-site to B-site ratio stabilizes the LSM thus retarding LSM decomposition. Mn inhibits the decomposition of the LSM. The less LSM is decomposed, the less amount of th e La is supplied to reactions between the LSM and the YSZ. As a result, LZO formation is delayed. Theref ore, La deficiency and Mn excess delay the LZO formation. LZO phase polarization dominates the increas ing of the activation polarization and the total ohmic polarization in the SOFC. Activation polarization (charge tran sfer resistance) show the same power dependence of theLZOtin three oxygen reduction models. This is because the number of active sites for char ge transfer reactions is redu ced by increasing amount of LZO phase formed at the LSM/YSZ interface and by decreasing TPB length. In addition, LZO phase formed at the LSM/YSZ interface dramatically increases the charge transfer resistance by increasing the energy barrier for the reactions to overcome, t hus the activation polarization increases. On the other hand, LZO thickness repr esents the effect of the LZO phase on reduction in supply of the oxygen reactant species from YSZ or LSM to the TPB. Supply of the oxygen is controlled by a surface diffusion mechanism. LZ O phase reduces surface diffusion area in a close proximity to the LSM/YSZ interface. Surf ace diffusion of reactant species for the charge transfer reaction, especially surface diffusion of the oxygen ion/ vacancy is blocked by the LZO phase. The normalized LZO conductivity (2*10-6Scm-1) calculated from the microscopic analysis is slightly lower than the LZO conductivity using electr ochemical measurements. LZO
175 normalized resistivity represents the impact of the LZO phase on conduction mechanism of carriers. LZO reduces the rate of the electrons conducting from th e LSM to the TPB. It blocks bulk diffusion of the oxygen vacancy away from the TPB to the YSZ. Because LZO electrical conductivity 2e-6Scm-1, is four orders of magnitude lo wer than that of YSZ ,1.3e-1Scm-1, and seven orders of magnitude lowe r than that of LSM, 218.7Scm-1 at 1000C. Resistance due to these deleterious effects contributes to increase the ohmic polarization. 6.1.4 Dependence of the Concentration Polarization on Topological Properties The magnitude of the concentr ation polarization is at leas t 40% of the total cathode polarization. If gas transport pr ocess through the porous cathode is fast by optimizing geometric properties, then cathode polarizati on will be effectively controlled. Several SOFC models report that the effective diffusivity of O2-N2 (one of the gas transport prope rties) affects concentration polarization. However, the effective diffusivity of O2-N2 is quantified by a two-dimensional dusty-gas model. This dusty-gas model neglects changes in connections among pore channels and considers gas transport through the closed pores under sintering cond itions. The impropriate quantification of the geometric pr operties might cause inaccurate calculations of the effective diffusivity of O2-N2. In addition, only continuum diffusion domain is considered for the gas transport. This work calculated the geometric tortuosity using an elementary skeletonization model in 3-D FIB/SEM image analysis. This method of quantifying the ge ometric tortuosity of the porous cathode has never been tried before. In conjunction with tw o pore-network models (Masons dusty-gas and Kopneons la ttice-gas models), the elementa ry skeletonization model is effective to study the fluid tran sport property (permeability) or gas transport property (effective diffusivity) of the oxygen. Then the cathode concentration polarizat ion was associated with the gas transport properties of a porous cathode by applying Kims SOFC performance model.
176 Two models with different assumptions on the major O2 flux showed that the higher effective diffusivity or permeability, the faster ki netics of the gas transport is through the porous cathode, therefore the less resistance to the gas transport is. The ineffective gas transport through the porous cathode contributes to the starving of the oxyge n, thus slowing down oxygen reduction on the cathode side. As a result, con centration polarization is increased by affecting kinetics of oxygen reduction. In the binary diffusion dominant regime, the gas transport resistance is not monoton ically increased by incr easing the logarithm of vV. The assumption of the LSM grains as immobile particles in a porous matrix is not consistent with changes in connections among LSM grains. In addition, diffu sion rate of the gas transport through the porous cathode is overestimated by introducing total poros ity. On the other hand, in the viscous flux dominant regime, a direct relationship was observed between the permeability and the gas transport resistance as compared to the relationshi p of the effective diffusivity. It might indicate that the skeletonization and the la ttice-gas models are more app licable to the study of the gas transport properties in a porous cathode with respect to the dusty-gas model. 6.2 Future Work An initial stage of the LZO phase formation ha s been studied in an A-site deficient LSM. The 1/2 power dependence of the LZO thickness on the sintering tim e shows that LZO growth is controlled by a diffusion mechanism. The STEM -EDS analysis has been performed to study diffusion of the chemical species at the LSM/YSZ interface, thus determining where the initial LSM/YSZ is located. The STEM-EDS technique gives more accurate analysis of the diffusion than SEM-EDS. The latter collects characteristic X-rays from a larger interactive volume than the STEM-EDS. However, STEM-EDS provides semi-quantitative analysis of the diffusion mechanism at the LSM/YSZ interface. STEM-EDS could not accurately estimate the
177 composition of a trivial element (<1mol %). In addition, the capability of the STEM-EDS of detecting concentration change is limited by its la teral resolution. In other words, STEM-EDS is not effective to study diffusion in a region of less than 15nm. If quantitative chemical composition of materials is known, then the ques tion that LZO phase formation is controlled by either the uniaxial diffusion of La and Mn in to YSZ or interdiffusion between LSM and YSZ will be answered. In other words, location of the initial interface of the LSM/YSZ will be determined. Atomic probe tomography is an effective tool that will be used to study quantitatively the diffusion mechanism of chemic al species at the LS M/YSZ interface at the early stage of the LZO formation. Because its de tection limit of the chemi cal composition is less than 0.1mol %, and its lateral resolution is a bout 5. In addition, LZO thickness of 30-80nm fits well with the scale of the 3-D microstructure feature that atomic probe can effectively characterize . It has been confirmed that LZO growth degrades cathode activa tion and cathode ohmic polarizations by changing reaction mechanis m and conduction mechanism at the LSM/YSZ interface. This is the conclusion based on the study of the ini tial stage of the LZO formation (<20h). However, SOFC lifetime is longer than few tens of hours. It is important to know whether or not the LZO phase consistently de grades cathode polarizat ion under the long-term operational condition. In other words, it is still not clear if the degrada tion rate of the cathode polarization is dependent or independent of the sintering time. Some research show that LZO phase disappears when atmosphere of the in side LSM/YSZ interface becomes more reductive than that of the surface along TPBs [36-38]. Improvement of the TEM sample preparation technique becomes important for a study of LZO phase under a sinter ing time of longer than 20h. TEM sample preparation becomes challenging because contact area between the LSM and the
178 YSZ dramatically decreases with the increasing sintering time. Continuous pore channels at the interface make connections between the LSM and YSZ fragile. Impregnation of epoxy in samples might reduce challenges of making a TEM sample. Epoxy will increase connections between the LSM and the YSZ. In addition, if low electron-beam energy and low current of Ga ion beam are used, then the epoxy, which is fi lled in pores between the LSM and YSZ layer, might protect YSZ layer from Ga ion b eam milling at the epoxy/YSZ interface. Tortuosity has been quantified based on more than one thousand of FIB/SEM plane-view images. Image processing, especially the segmen tation and the image thre shold steps are time consuming. Segmentation and image threshol d determine the accurate quantification of geometric properties. In accurate segmentation and image threshold cause loss of the skeletons reproducibility of the 3-D pore space to the original object. Ove r-threshold and undersegmentation were avoided by manual operation, because auto-threshold and auto-segmentation functions lose some of the orig inal images and increase errors of the skeletonization process. However, manual threshold and segmentation step s are labor intensive. A subsidiary model which is capable of optimizing and homogenizing threshold is necessary to be developed. It can save time and provide high-quality images. An accurate quantifica tion of the geometric properties depends on effective re duction in image artifacts. The elementary skeletonizati on model has limited usage in th e study of the gas transport properties. An advanced skeleton model should be developed to an alyze gas transport efficiency within the porous cathode. This model will reconstruct the flow field usi ng radii of pore throats as well as the distributio n of pore throats as inputs of the model, which were calculated from the elementary skeletonization model. The advan ced model will simulate skeleton of a 3-D porenetwork to test the accuracy of the elementary skeletonization m odel. In addition, main flow
179 channels (pore throats with wide opening) will be determined based on comparing the radii of pore throats as well as the distribu tion of pore throats to one anothe r. Then the frequency of main flow channels through which gas transport can be estimated. The distribu tion of the main flow channels will determine the gas transpor t efficiency within the porous cathode.
180 APPENDIX A FIB MANUAL Part one: TEM sam ple preparation manual Prepare samples: A. make trenches (Figure 3-5 in section 3.2) 1. regular mount ,polish cross section [I = 5000pA, 45um(// to the cross-section) 2. rotate 180, deposit Pt to cover both LSM and YSZ [I=300pA, 15.2 (interface).8um (thickness of Pt)] 3. make two trenches on both front and back sides[I=5000pA, 19 (interface ) 3um(//interface); polish the left side by bulk milling box (), which will touch Cu-grid [1000pA, 20umum (interface) 4um (//interface); repeat polish with the same para but step milling box (); make a small notch on left corner, which will touch Cu-grid [1000pA, 9um.5um(interface ) z=2um (//interface) 4. rotate 180, Pt deposition on side [300pA 9um (//interface).5 (thickness of Pt)] 5. undercut the sample at 9um depth (// interface) [5000pA, 3 um( // interface) um (interface )] B. release sample ( Figur e 3-5 in section 3.2) Mount ion beam perpendicular to cro ss-section, rotate relatively -90, t=10 to undercut from the side (//interface but with a angle), put the unde rcut box on the edge of the trench box in A3 [1000pA, 25.8 um ( interface ) -8um( // interface), check complete undercut [ t=30-40 under E-beam], switch to E-beam from Ion-beam C. Mounting Cu-grid (a good way to mount sample when transfer omni-sample to the Cu-grid) 1. before Fibbing Cu-grid, put screw down a nd touch the table, put sample on right wing with the "o" close to middle screw, the order of the right wing of the Cu-grid like "O" A-B-C (B-front away from me) 2. put Cu-grid inside FIB column: put screw inside, Cu-grid is to ion beam, the order of left wing of the Cu-grid, which holds the sample, like C-B-A"O"screw(inside)-right wing (empty) Under ion beam see left C-B-A"O"right image. The sample on B finger is toward away from operator 3. take out of Cu-grid after sample preparat ion, attach "o" on the right side by the vacuum twizzer, lie down sample with "o" on the right side into sample holder. In order to protect from touching sample before TEM imaging and to avoid the broken sample
181 D. prepare Omni-Cu grid: 1. mount Cu grid // to ion beam and inward screw (on the right), image shows the order like A finger -B finger -C finger ,Screw, Empty 2. t=52, put the milling box 5um away from the middle of B finger, mill the side of B finger( toward A of Cu grid) [5000pA, Z=2 um (//side of B finger)~ real depth of 22um), polish side edge with clean-box. This step to polish corner of the Cu-grid, which will touch one side of the sample 3. mount Cu grid to ion beam and inward screw( on the left)& "O" close to middle of B finger, image shows the order like screw-O-ABC, B front is away from the operator. It is easy to put sa mple attached with Omniprobe E. final thinning: ( Figur e 3-5 in section 3.2) 1. touch hole side of the Cu-grid by vacuum twizzer; mount Cu grid to ion beam and inward screw( on the left), it is good to see front of the B finger 2. find angle1 (close to t=52),mill bottom side of the sample first ( angle1 +1) [1000pa, x=1/7 real depth];then mill top side of the sample ( angle1 -1) [1000pa, x=1/7 real depth] 3. mill twice bottom side of the sample first ( angle1+1) [300pa, 0.5z1=1(real 9um), then mill twice top side of the sample ( angle1-1) [300pa, 0.5z1]; it should be noted that mill bright part first (buttom),then mill dark part(top) 4. measure thickness at angle1; mill bottom side first ( angle1-1) [100pa, 0.22z1=2.2(real 9um), then mill top side( angle1+1) [100pa,0.22z1=2.5];untill final thick 120nm. It should be noted that in the end, milling box could not touch dark region on the top of the sample 5. tips: ion-emission current is (2-6)area; ion-milling depth: ~1/4-1/5 of the real depth for milling bulk; ~1/6-1/7 of the real depth for milling edge align x in inverse directi on =rotate 180 as origin of +, align y at horizonal pos =rotate 90 as origin of + milling box should be at bright region. b ecause dark region means top surface of the sample when sample is bent, do not mill just stop. because other cathode part will drag cathode part at the interface and finally either peal off cathode at the cathode/electrolyte interface or bend cathode behind th e cathode/electroly te interface Part two: Omniprobe-TEM sample lift-out A. Preparation work: Cu-grid:
182 Mill the side of finger B (toward A) from top [I=5000pA, z=3um] and two other milling boxes at corner of the Cu-grid [I=5000pA, z=2um] Trench sample (See part one A) B. move omniprobe close to re gion of interest in sample 1. mount sample in a way that I-beam is to cross-section of the sample at 7 tilt, heat Pt. Use SED detector for both I-beam and E-beam 2. t=7 with 45 degrees of the sample holder, move region of interest in sample to center of the screen and ad just eucentric under E-beam and align x under I-beam 3. start omniprobe software with PD: probe r, press VEL mode StageFOR tilt angle 4. pick omniprobe in first and Pt needle in with lowest mag of E-beam, try to move omniprobe center of the screen with either I-beam <=X=> and Y or electron beam z -button and <=X=> with high speed of 60um/s (because e-beam z and x as reference, from the e-column angle; i-beam x and y as reference, from the i-column angle) 5. move omniprobe close to regi on of interest (key step one ) +mag under Ebeam z-button down with 30um/s; +mag to 1000X, F11 switch to I-beam, and <=X=> Y moves right unde r I-beam with 1000X, and under E-beam z-button with +2000X. now E-beam and I-b eam mag-coupled. Under E-beam z-button down with 0.5um/s, F11 switch to I-beam with <=X=> Y down with 0.5um/s; then F11 switch to E-beam, under E-beam with 2500X z-button down with 0.5um/s; +mag 3500X and 6500X with E-beam z-button down to try to move omniprobe as close as possible to region of interest of the sample 6. Pt needle in reshape omniprobe tip with a milling box 100pa (0.64.26um) 7. touch sample (key step two): adjust fo cus to see both omniprobe and sample are at the same focused condition (=same hei ght=same fwd). Switch between E-beam and I-beam by using F11 to confirm that omniprobe and sample are at the same height, with 10kx, move omniprobe to touch sample until se e contrast change or alarm warning or sample movement.
183 In order to figure out how far omniprobe should be away from the surface under e-beam focus omniprobe tip, write down fwd1, then focus region of interest for sample, write down fwd2, fwd1-fwd2= distance betw een omniprobe and region of interest. When see contrast change, fwd1=fwd2. Detailed steps are as following: deposit Pt with Pt _tem.mtr 100pa, z=1um (remember this is important). Optimum Pt deposition time is 3mins. beam shift under i-beam and moves + close to the part that will be milled, mill a box to release top 6um from bulk sample [i=1000pa z=6um] omniprobe already attaches the sample, do not move stage, just use beam shift move omniprobe up to see whether the omni probe with sample moves up, if it does, move omniprobe up and away. Omniprobe go to park, omniprobe out Pt needle out, beams off, t=0 degree. C. transfer sample from omniprobe to Cu-grid 1. mount Cu-grid parallel to the ion beam and screw inward (on the left of the Cu grid) CBAin the unscrewed gap; adjust eccentric and link the beam with t=52;with 118x park; put omniprobe in, check vel, stagefor,t=52, 40um/s. 2. 220x t=52, put Pt needle in, move omniprobe down; switch f11 e-beam to i-beam in order to check position of the omniprobe (with sample) and Pt needle (to avoid omniprobe crash with Pt needle) 3. 2500x e-beam, then f11 switch to i-beam, unde r i-beam to observe confocal plane in order to adjust omniprobe (attached with sample) with the same height as the top surface of the Cu-grid; f11 check with e-beam; +5000x, repeat the same thing 4. get the same confocal plane of the omni probe (attached with sample) and of the top flat surface of the Cu-grid (key step th ree): +10kx, find the difference of 2.5 turns between the focused state of the omniprobe (w ith sample) higher than the focused state of the top flat surface of the flat Cu-grid. (not e: fine focus counterclockwise is for focused state at the higher position); f11 switch to ibeam with z moves down 0.5um/s; check that 0.5 turns difference between the focused state of the omniprobe (with sample) higher than the focused state of the top flat surface of the flat Cu-grid; finally there is no difference in turns between the focused stat e of the omniprobe (with sample) higher than the focused state of the top flat surf ace of the flat Cu-grid 5. move omniprobe (with sample) to the top flat surface of the flat Cu-grid until the sample touches with the Cu-grid with contrast change; mill 100pa some sample materials on top/Cu-grid interface, using the redepositi on to hold sample and Cu-grid; deposit Pt along contacted region between sample and co ntacted Cu-grid with 100pa z=2um; mill Pt from the contact region between omniprobe and sample with 100pa z=1um,( this is consistent with deposited depth of the Pt during attachment. )
184 6. solve the issue when Pt is deposited between Cu-grid and sample, but sample is milling away. Because sample height is higher th an Cu-grid, then Pt needle is in the way, therefore, only Ga ion mills materials. (theory: during milling process, valve is closed, only Ga ion functions; during depositing pr ocess, valve is open, both Pt and Ga function), solutions are as following: move omniprobe far away, go to park pos ition, then omniprobe out. (Fine focus counterclockwise is to move the confocal plane up ( higher position);counterclockwise z-stage to move the stage down mount Cu-grid in the horizo ntal holder, try to perpe ndicular in the gap of the holder: if the angle between the perpendi cular. Cu-grid top flat surface and the perpendicular sample top surface is small, Cu -grid top flat surface can be used as the reference plane to manually thin, that is, Ibeam is perpendicular to Cu-grid top flat surface; if the angle between the perpendicular Cu-gri d top flat surface and the perpendicular sample top surface is large, sa mple top flat surface can be used as the reference plane to manually thin, that is, I-b eam is perpendicular to sample top surface. Part three: FIB Auto-slice-view A. Preparation 1. vent, put sample in, calibrate height of sample by the sc ale -take the scale out of FIB 2. pump (7.5e-5), source, beams on, close N2 cylinder. 3. adjust eccentric height 4. low mag (1kx), find feature, focus,align stage, mouse double-cl ick feature.(+) 5. 10 tilt, focus, z rotate + back to initial position; 0 tilt, focus, mouse double-click ,+ at initial position, 52 tilt, focus,z rotate + back to initial position; 0 tilt, focus, mouse double-click ,+ at initial position, High mag (10kx) repeat ,ion-electron beam coincidence electron beam, 52 tilt focus, mouse double-click feat ure.(+=position a); low ion beam scan (100pA),focus, zero beam stage, beam shift x&y, (+ is coincided with position a under electron beam) pe rpendicular angle ,tilt around 52 focus, ion beam see edge of top view; tilt ( -52), focus, electron beam see edge of top view B. Pt deposition Pt on, wait till 40 C, draw a rectangular box A close to the edge, Pt_tem file (x,y,z=0.5~1.5um), ion current= (2~6)deposit area C. FIB ion-beam milling 1. tilt adjust brightness and contrast, fo cus, draw a (U) box B around box A, Si file(x,y,z=5~10um), high ion current(1K~5KpA), rough milling 2. draw a (U) box C around box A, focus, Si file(x,y,z=3~8um), low ion current(300~100pA), fine milling
185 D. serial-sectioning 1. draw a rectangular box D close to front edge of box A, focus, Si file(x,y,z=1~3um), low current (300~100pA) first serial secti oning, observe real milling depth, adjust z to be the exact um) 2. open auto-slice-view software, beam shif t correction, image save folder and directory, x,y=z in a z total and No. slices. Ion beam current, low Image scan rate. 3. run software, beam shift X&Y, milling box at the right start position E. copy image rodiox CD creater, record F.shut off 1. Pt off, beams off, open N2 cylinder, vent 2. take sample out 3. pump, close N2 cylinder Part four: AutoFIB A. in-situ 1. repeat part three A and B 2. Pt on, wait till 40 C, find feature, focus, run autoFIB 3. run script 6,continue, input width 10um, z=4um, Pt=1um ,final thick 200nm, new, finish, all. 4. run script 1, do not move stage to th e stored position, adjust focus when software could not find fiduciary mark, continue, ( note: if fiduciary mark is invisible, check magnifications: undercut at low mag; other proces sings at high mag. When do undercut, we need ion-beam shift x and y to make drawn box at the right position of the milled trench). 5. cancel undercut, note absence of Pt, stop two cuts before finish. 6. follow step F1, take sample out B.ex-situ lift out 1. check needle and exchange broken needle 2. unscrew top loose, mark the middle of the plastic one, vertically insert one plastic one, let the mark in the middle of the spring and screw tightly. 3. turn power on; temperature is 24.8 degree, press start, then wait until temp is decreased from 62 degree to be 24.8 degree. Unscrew loose, then take the bottom needle tip out.
186 4. install the plastic needle starting from the bottom part to the tip part; install it onto the needle holder. 5. exchange needle tip 6. insert the needle tip and screw the needle tip. 7. put sample stub on a sample holder and put a Cu grid on another sample holder all by vacuum twizzer 8. turn on microscope and monitor 9. low mag, move sample to center of screen and put right needle at center of screen above sample (Note that center of screen is like a reference point) 10. low down right needle more, focus on needle, repeat until the needle is really low; slightly low down the right needle, focus needle, low needle until both needle and sample are visible. (Use high magnification) Move knob to adjust right needle until it touches the sample, (wait for few seconds un til attraction between the sample and the needle are strong) pick up the sample. (now sample is attached on the needle) 11. raise up the right needle a little bit 12. move sample holder with Cu grid below the needle. Focus Cu grid and find a slot around center of the Cu grid. Make the slot stay in center of screen. 13. Slightly low down the right needle, focu s on the right needle until both right needle and slot are focus. Try to re lease sample from the right needle. 14. Use the left needle, low more down left n eedle at the beginning, then focus left needle, and slightly low down left needle+foc us left needle until two needles are at the same height. Move knob to adjust left needle until it touches the sample, make a good adjustment until sample is well oriented. Or sample is transferred from the right needle to the left needle. 15. slightly low down the left needle until it touches the slot, then release it. Try to make sample flatly lie down in th e middle of the slot in Cu grid. 16. raise one needle up at one time, make sure both needles stay at center of the screen. 17. turn off monitor and microscope 18. vacuum twizzer takes Cu grid and slide close to the TEM sample holder.
187 Part five: matlab script for cal culation of length of branches Code A clear all; close all; [dummy, filename]=xlsread('datafilename.xls'); fileindex=size(filename); for i=1:fileindex(1) [linelength, totallength]=lengthcalc(char(filename(i))); linelength=[linelength totallength];% this is to attach total length to the end of line length xlswrite('processeddata.xls',linelength','Sheet1',strcat(char(64+i),'1 ')); end Code B function [linelength, totallength]=lengthcalc(tempname) tempdata=dlmread(tempname);%this is used to load all data in datasize=size(tempdata);%this is to get how many data points in this file tempj=0;%tempj is used to record how many lines you have templinelength=0;%this is used to initialize this variable linelength=0; totallength=0; for tempi=1:datasize(1)-1 if tempdata(tempi+1,1)==tempdata(tempi,1) temppointdistance=sqrt((tempdata(tempi+1,2)tempdata(tempi,2))^2+(tempdata(tempi+1,3)tempdata(tempi,3))^2+(tempdata(tempi+1,4)-tempdata(tempi,4))^2); templinelength=templinelength+temppointdistance; else tempj=tempj+1; linelength(tempj)=templinelength; totallength=totallength+templinelength; end end tempj=tempj+1; linelength(tempj)=templinelength; totallength=totallength+templinelength;
188 APPENDIX B ELECTROCHEMICAL PROPER TIES AND SCANNING TRANS MISSION ELECTRON MICROSCOPYENERGY-DISPERSIVE X-RAY SPECTROMETRY (STEM-EDS) CONCENTRATION PROFILES Figure B-1. Charge transfer resistan ce of the isochronal sintered samples Figure B-2. Dissociative ad sorption resistance of the isochronal sintered samples
189 Figure B-3. Nyquist plot of the isothermal sintered sample Figure B-4. Bode plot of th e isothermal sintered sample Figure B-5. Interfacial resistance of the isothermal sintered samples
190 Figure B-6. Charge transfer resistance of the isothermal sintered samples Figure B-7. Dissociative ad sorption resistance of the isothermal sintered samples
191 Figure B-8. STEM-EDS of 12002h Figure B-9. STEM-EDS of 12004h Y S Z L Z O L S M Y S Z L Z O L S M
192 Figure B-10. STEM-EDS of 12008h Figure B-11. STEM-EDS of 120015h (Note no Mn) Y S Z L Z O L S M Y S Z L Z O L S M
193 Figure B-12. STEM-EDS of 120020h Y S Z L Z O L S M
194 APPENDIX C GEOMETRIC PROPERTIES OF THE ISOTHERMAL SINTERED SAMPLES Table C-1. Geom etric properties of the isothermal sintered samples Time (h) SC (m2) CV tLZO (nm) LTPB (nm) VV (%) 2 0.34 0.79 37.46 732.03 46.8 4 0.37 1.00 43.13 867.66 42.4 6 0.38 0.86 55.29 920.11 40.00 8 0.39 0.73 57.02 803.52 39.20 10 0.41 0.46 57.46 877.54 35.90 15 0.44 0.66 68.54 627.11 30.65 20 0.46 0.47 72.39 500.17 28.68 25 0.47 0.49 416.78 26.39
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205 BIOGRAPHICAL SKETCH Aijie Chen was born to Meichun So ng and Zhaoming Chen in Laiwu, Shandong, P.R. China. During her childhood, her father insti lled in her a strong sense of integrity, self confidence and perseverance. In 1991 she attende d the Northeastern University in Shenyang, Liaoning, P.R.China to earn her Bachelor of Engineering, where her focus of study was metal forming engineering. After she graduated in 1995, she joined Laiwu Steel & Iron Corp., the largest steel and iron company in Shandong province in P.R.China as a research engineer. In 2002, she moved onto graduate school at the Michigan Technological University, Houghton, Michigan, where her focus of study was material s science and engineering, conducting research of the effect of the ion implantation processi ng on optical waveguide device under Dr. Peter D. Moran. In October 2003, she welcomed birth of her son in Houghton, Michigan. After graduating with a Master of Engine ering in material science, she proceeded to the University of Florida in Gainesville, Florida, where she ha s been working toward her doctoral degree in materials science and engineeri ng since August 2004. Her PhD work commenced in the field of electronic materials under Prof. Kevi n S. Jones in the areas of clas sical stereology, 2-D, and 3-D microstructure characterization for advanced solid oxide fuel cell. During her graduate study, she interned at Caterpillar Inc., where she worked in new product development, studying the diesel particulate filter of the heavy-duty diesel en gine. Subsequently, she worked in advanced materials technology, analyzing the microstructu re evolution of the ga s turbine after heattreatment. Upon receipt of the Doctor of Philosphy in 2008, she will join Caterpillar Inc. in Peoria, Illinois.