論文 / 著書情報
Article / Book Information
題目(和文)

吸着種領域モデル及び反応サイトイメージングによる固体酸化物型燃料電池多孔質電極における反応動力学に関する研究

Title(English)

Reaction Kinetics and Dynamics on Solid Oxide Fuel Cell Porous
Electrodes through Species Territory Adsorption Model and Active Sites
Imaging

著者(和文)

長澤剛

Author(English)

Tsuyoshi Nagasawa

出典(和文)

学位:博士(工学),学位授与機関:東京工業大学,
報告番号:甲第10789号,
授与年月日:2018年3月26日,
学位の種別:課程博士,
審査員:花村 克悟,佐藤 勲,平井 秀一郎,山中 一郎,伏信 一慶

Citation(English)

Degree:Doctor (Engineering),
Conferring organization: Tokyo Institute of Technology,
Report number:甲第10789号,
Conferred date:2018/3/26,
Degree Type:Course doctor,
Examiner:,,,,

学位種別(和文)

博士論文

Type(English)

Doctoral Thesis

Powered by T2R2 (Tokyo Institute Research Repository)Reaction Kinetics and Dynamics on Solid Oxide Fuel Cell
Porous Electrodes through Species Territory
Adsorption Model and Active Sites Imaging

byTsuyoshi Nagasawa

A dissertation submitted in partial fulfillment of the requirements for the
degree Doctor of Philosophy in Mechanical Engineering

Supervised by Prof. Dr. Katsunori Hanamura

Tokyo Institute of Technology
March 2018

Copyright © 2018
Tsuyoshi Nagasawa
All rights reserved.

Abstract

Reaction Kinetics and Dynamics on Solid Oxide Fuel Cell
Porous Electrodes through Species Territory
Adsorption Model and Active Sites Imaging
byTsuyoshi Nagasawa
Department of Mechanical and Control Engineering
Tokyo Institute of Technology

Supervised by Prof. Dr. Katsunori Hanamura

The reaction kinetics and dynamics on solid oxide fuel cell porous electrodes were studied
based on kinetic modeling and active sites imaging. The analytical model for hydrogenoxidation at anode, species territory adsorption model, was newly developed. Based on
the model, explicit expression of anode overpotential could be obtained, which combines
the overpotentials at low and high current density regions. The model was compared anddiscussed with experimental results of Ni/YSZ anodes. In addition, in order to visualize
active sites of porous electrodes, a power generation equipment with a quench system byhelium gas impinging jet was constructed. By using the equipment and oxygen isotope
labeling, active sites of LSM/ScSZ cathode was visualized. The obtained 18O mapping
first imaged highly-distributed active sites in microstructure scale.

Table of Contents

Chapters
1 Introduction ........................................................................................... 1
1.1 Background .......................................................................................................... 1
1.2 Solid oxide fuel cell (SOFC) ................................................................................ 3
1.3 Principles and components of SOFC ................................................................... 6
1.4 Current status and challenges of SOFC ............................................................... 9
1.5 Objectives and contents of thesis ....................................................................... 12
References ................................................................................................................... 14

2 Species territory adsorption model for hydrogen oxidation in SOFC
anode ........................................................................................................... 18
2.1

Introduction ........................................................................................................ 18

2.2 Model construction ............................................................................................ 21
2.2.1 Assumptions ................................................................................................ 21
2.2.2 Reactions under chemical equilibrium ........................................................ 23
2.2.3 Reaction rate controlled by the surface reaction in Areas 1 and 2 .............. 26
2.2.4 Competitive adsorption model and species territory adsorption model ...... 28
2.2.5 Explicit expression of anode overpotential with current density ................ 33
2.3 Analytical results based on the model................................................................ 36
2.3.1 Typical curves of current density and anode overpotential ......................... 36
2.3.2 Coverages of adsorbed species on Areas 1 and 2 ........................................ 40
2.4 Summary ............................................................................................................ 42
References ................................................................................................................... 43

3 Comprehensive analysis of Ni/YSZ anode using species territory
adsorption model ....................................................................................... 46
3.1

Introduction ........................................................................................................ 46

3.2 Experimental section .......................................................................................... 48
3.2.1 Cell fabrication and microstructure characterization................................... 48
3.2.2 Experimental setup of fuel cell operation .................................................... 50
3.2.3 Electrochemical measurements ................................................................... 52
3.3 Basic formulas and related parameters of the model ......................................... 54
3.4

Identification of parameters for Ni/YSZ anode ................................................. 57

3.4.1 Quantities of state and activation energy predicted by DFT ....................... 57
3.4.2 Parameters identified through fitting to the experimental results................ 58
3.4.3 Estimation of effective anode thickness for reported Ni/YSZ experiments 60
3.5 Discussions......................................................................................................... 66
3.5.1 Dependence on fuel compositions and temperature .................................... 66
3.5.2 Effective anode thickness ............................................................................ 70
3.5.3 Sensitivity analysis ...................................................................................... 73
3.5.4

Insights into oxygen migration process ....................................................... 76

3.6 Summary ............................................................................................................ 77
References ................................................................................................................... 79

4 Imaging of microstructure-scaled active sites in porous composite
cathode........................................................................................................ 82
4.1

Introduction ........................................................................................................ 82

4.2 Experimental section .......................................................................................... 86
4.2.1 Power generation equipment with quench system ...................................... 86
4.2.2 Cell fabrication ............................................................................................ 87
4.2.3 Power generation in 18O2 and quench experiment ....................................... 89
4.2.4 SIMS analysis .............................................................................................. 90
4.3 Results and discussion ....................................................................................... 90
4.3.1 Evaluation of cooling performance ............................................................. 90
4.3.2 Electrochemical performance and monitored temperature .......................... 93
4.3.3 Secondary ion mappings .............................................................................. 95
4.3.4 Effect of contact area between cathode and current collector ..................... 98
4.3.5

Line profile analysis of 18O concentration mappings ................................ 100

4.3.6 Grain boundary diffusion and inactive LSM particles .............................. 106

4.4 Summary .......................................................................................................... 107
References ................................................................................................................. 109

5 Analysis method of oxide ion flux at cathode/electrolyte interface
through oxygen isotope labeling ............................................................ 112
5.1

Introduction .......................................................................................................112

5.2 Experimental section .........................................................................................112
5.3 Results and discussion ......................................................................................115
5.3.1

Secondary ion mappings .............................................................................115

5.3.2

18

O diffusion profile analysis in YSZ electrolyte .......................................119

5.3.3 Oxide ion flux incorporated from the cathode/electrolyte interface.......... 121
5.4 Summary .......................................................................................................... 125
References ................................................................................................................. 126

6 Conclusions ........................................................................................ 127
6.1 Key findings and contributions ........................................................................ 127
6.2 Future perspective ............................................................................................ 128

Appendices
A Derivation of coverage formulas ..................................................... 131
B Oxygen transport and reaction described by chemical potential 133
B.1

Introduction ..................................................................................................... 133

B.2 Equation for particle transport in solid ............................................................ 133
B.3 Fick’s first law and equation for ion conduction ............................................. 136
B.4 Chemical potential distribution in SOFC ........................................................ 137
B.5 Overpotentials described by oxygen activity .................................................. 140
References ................................................................................................................. 142

C IV curves and fitting results of impedance spectra ....................... 143
D Thermal design of quench system ................................................... 148
D.1 Detailed structure of quench nozzle ................................................................ 148

D.2 Assumed temperature distribution .................................................................. 148
D.3 Heat transfer calculation ................................................................................. 150
References ................................................................................................................. 155

E Oxygen tracer diffusion coefficient and surface exchange coefficientof LSM ...................................................................................................... 156

Acknowledgements .................................................................................. 161
Publications .............................................................................................. 164

Chapter 1

Introduction

1.1

Background
The population growth and accelerated modernization in the world are followed by

the increase in energy consumptions and greenhouse gas emissions. In order to reduce
those consumptions/emissions, the development of energy conversion technology withhigher efficiency is strongly required in modern society. Compared to the current
combustion-based energy conversion technologies which are generally used forautomotive engines or power plants, fuel cells offer higher energy conversion efficiency
and lower greenhouse gas emissions. This feature is originated from the principle of fuelcells: chemical energy is directly converted to electricity, resulting that the efficiency is
not limited by the Carnot cycle [1]. The absence of high-temperature combustion process
and of open flame front is also followed by the elimination of harmful pollutants
formations such as SOx, NOx, volatile organic carbon (VOC), and particulate matters(PM) [1]. Moreover, fuel cells are expected to play a central role of future energy system
based on hydrogen, which can be produced from various energy sources such as fossil
fuels or renewable energy [2].
Figure 1-1 summarizes the efficiency of fuel cells and other energy conversion
devices with respect to system size. This figure was made based on several informationcollected from websites and literatures [2-14]. Generally, the efficiency of combustion-

1

Distributed power plant

Automotive
Residential

Large-scale power plant

80
Ceramic Fuel Cells Ltd.
(SOFC)MHPS Ltd.
(SOFC+GT)

Efficiency [%] (LHV)70
60

SOFC+GT+ST
Triple-combined
SOFC+GT
GT+ST
Combined

SOFC

50
ENE-FARM

MCFC

40

PEFC

30

Diesel engine

20
10

Abbreviations
SOFC: Solid oxide fuel cell
PEFC: Polymer electrolyte fuel cell
PAFC: Phosphoric acid fuel cell
MCFC: Molten carbonate fuel cell
GT: Gas turbine cycle
ST: Steam turbine cycle
LNG: Liquefied natural gas

1.00E-01
10-1

PAFC

Gasoline engine

1.00E+00
100

1.00E+01
101

1.00E+02
102

GT

ST

Fuel cellvehicle(PEFC)

Chiba thermal
power plant(GT+ST, Fuel:
LNG)

1.00E+03
103

1.00E+04
104

1.00E+05
105

1.00E+06
106

1.00E+07
107

Power scale [kW]Figure 1-1. Efficiency of fuel cells and other energy conversion devices with respect
to system size. The figure was made based on several sources [2-14].

based energy conversion increases with increasing the system size. In the case of heatengine, when the ratio of surface area to volume of the system decreases with increasingsystem size, the ratio of heat loss from surface to energy kept in its volume also decreases,
resulting in the efficiency gain. For instance, the gas and steam turbines combined cyclein Chiba thermal power plant (Japan) shows the thermal efficiency of more than 55% at
the system size of 106 kW scale [10]. On the other hand, the efficiency of fuel cells is, inprinciple, independent of power scale. Therefore, fuel cells have the advantage over heatengines especially at small system size (< 103 kW). In this scale, combustion-based
technologies such as diesel or gasoline engines, or gas turbine cycle, show the efficiency
of around 15 to 35% while fuel cells show 35 to 55% (LHV: lower heating value). Thisadvantage has accelerated the development of fuel cell technologies for residential-scale2

power generation system (1-5 kW), automotive power (~100 kW), and distributed power
plant for smart grid energy system (100-1000 kW) as major applications (Fig. 1-1).
Fuel cells are generally categorized by their electrolyte material, such as phosphoricacid fuel cell (PAFC), molten carbonate fuel cell (MCFC), polymer electrolyte fuel cell
(PEFC), and solid oxide fuel cell (SOFC). The main difference of those is operating
temperature, which also determine the suitable applications. PAFC is typically operated
at ~200 ℃ and possibly most-commercially developed fuel cells [2]. PAFC is mainly
used for combined-heat-and-power (CHP) system in residences or buildings. PEFC canbe applied for automotive power as well as stationary CHP system due to its low operating
temperature (50-80 ℃). In Japan, the 1 kW-class residential CHP system with PEFC
(ENE-FARM) was released in 2009 [7]. Moreover, the fuel cell vehicle (FCV) “MIRAI”
with 100 kW-class PEFC has been commercialized by Toyota Motor Corporation in 2014[8]. In contrast to PAFC or PEFC, MCFC and SOFC are typically operated at hightemperature range, ~650 ℃ and 700-1000 ℃, respectively. In addition to stationary CHP
system for residences or buildings, these high-temperature fuel cells can be combinedwith heat engines such as gas or steam turbines. The combined system, which can givehigher total thermal efficiency compared to individual utilization, is a promising
candidate for distributed base-load power plants at 103 kW (MW) scale [1,2,11].

1.2

Solid oxide fuel cell (SOFC)
In this thesis, an SOFC is selected as a research object. The high operating

temperature (700-1000 ℃) of SOFCs offers many advantages over other fuel cell
technologies. First, SOFC gives highest conversion efficiency among all fuel cells asshown in Fig. 1-1. When hydrogen and oxygen is used as a fuel and oxidant, respectively,

3

maximum conversion efficiency of a fuel cell 𝜂max is described as follows.

max 

G f (H 2O)(1.1)

H f (H 2O)

Here, ∆𝐺𝑓° (H2 O) and ∆𝐻𝑓° (H2 O) represent the standard Gibbs free energy and enthalpyof H2O formation, respectively. Although 𝜂max decreases with increasing temperature,
actual conversion efficiency of SOFCs is higher than that of low-temperature fuel cells
such as PEFC or PAFC. This is because ion conductions and electrochemical reactions
are generally enhanced at higher temperature, resulting that an internal resistance of a fuelcell decreases with increasing temperature [15]. Ceramic Fuel Cell Ltd. (Australia) has
developed 1-2 kW class SOFC stack for residential units and achieved an electricalefficiency of 60%, which is extremely high for such a small power scale [11,12].
Second, precious metals such as Pt need not to be used as a catalyst for electrodereactions because the reaction rate is high enough at elevated temperature (~800 ℃),
which is effective to reduce material costs. Third, in addition to hydrogen, various fuelssuch as hydrocarbon or biogas can be directly supplied to SOFCs because those fuels canbe reformed to hydrogen on anode at high temperature. Subsequently, produced hydrogenis used for fuel cell reactions. Owing to the fuel flexibility, SOFCs can be operated withhydrocarbon-based fossil fuels such as natural gas. As a result, SOFC can be introducedon current hydrocarbon fuel infrastructure [16]. In other word, new hydrogen
infrastructure needs not to be prepared for SOFCs, which is one of the biggest advantage
over low-temperature fuel cells. Forth, high temperature exhaust heat generated in SOFC
operation can be recovered and reused to further increase total thermal efficiency of thesystems. As shown in Fig. 1-1, SOFC-gas turbine combined cycle and SOFC-gas turbinesteam turbine triple combined cycle can achieve electrical efficiency of 55-60% and 60-

4

70% (LHV), respectively [6].
In addition to above features originated form high operating temperature, design
simplicity and flexibility of SOFCs, which are consisting of only solid components, isalso advantages over other fuel cells. Two representative designs are planar and tubular
types. Generally, the former shows higher performance and takes lower manufacturing
cost while the later has higher mechanical strength and needs not to be sealed at hightemperature to separate oxidant and fuel. Therefore, from a view point of the stability ofstacks during long-term operation (several years), tubular design has the advantage [11].
Many advantages mentioned above have accelerated the development of SOFC
technologies from components to systems, and the technology is currently in the earlycommercialization stage [17]. Several companies are conducting demonstration tests ofSOFC operation, or have just started to sell SOFC power generation systems in the 2010’s[11]. SOFCs with small power (less than ~10 kW) are generally applied to CHP systems

(a)

(b)

Figure 1-2. Commercialized SOFC products. (a) A 700 W SOFC combined heat andpower (CHP) unit, ENE-FARM Type S [14]. (b) A 250 kW SOFC-micro gas turbine(MGT) hybrid system developed by Mitsubishi Hitachi Power Systems, Ltd. [18].

5for residential buildings utilizing natural gas as a fuel. These CHP units have beendeveloped by e.g. Ceramic Fuel Cell Ltd. (Australia), Hexis AG (Switzerland), and Osaka
Gas in collaboration with Kyocera, Aisin, and Noritz (ENE-FARM Type S sold since2012, Japan, shown in Fig.1-2(a) [14]). At present (2017), an electrical efficiency of the
ENE-FARM Type S reaches 52% (LHV) [14]. Large scale (> ~100 kW) SOFC systems
for distributed power generation have been also developed by e.g. Versa Power Systems(USA), Mitsubishi Hitachi Power Systems, Ltd. (MHPS, Japan), and Bloom Energy(USA). MHPS has commercialized 250 kW class SOFC-micro gas turbine (MGT) hybrid
system with an electrical efficiency of 55% (LHV) in August 2017 as shown in Fig. 12(b) [6,18].

1.3

Principles and components of SOFC
SOFC generally consists of three main components, anode, electrolyte, and cathode.

Figure1-3(a) shows the schematic of operated SOFC when hydrogen and oxygen is
supplied at anode and cathode side, respectively. At the cathode, oxygen gas receives
electrons from external circuit and becomes oxide ion. Generated oxide ion conducts
through the electrolyte from the cathode to the anode. At the anode, water vapour is
produced from hydrogen gas and oxide ion followed by the release of electrons to theexternal circuit, resulting in the production of electricity. The chemical equations at
cathode and anode side are as follows.
(Cathode)

1/2O2 +2e-  O2-(1.2)(Anode)H2 +O2-  H2O+2e-(1.3)

As a result, total reaction in fuel cell operation is described as follows.

6

(Total)1/2O2 +H2  H2O(1.4)

The driving force of SOFC operation is equivalent to the oxygen partial pressure
difference between two electrodes, and the electromotive force (EMF) of a cell isqualitatively expressed by Nernst Equation as follows.

EMF  RT  PO2 ,cathode ln 
4F  PO2 ,anode (1.5)

Here, Γ is the ionic transference number (ionic conductivity/total conductivity), 𝑇 is
operating temperature, 𝐹 is Faraday constant, 𝑃O2 ,anode is oxygen partial pressure on
the anode side, and 𝑃O2 ,cathode is on the cathode side. When no current passes throughthe cell, cell voltage corresponds to EMF (OCV: Open Circuit Voltage). Under cell
operating conditions, cell voltage 𝑉 decreases from EMF with increasing current
density 𝑖 due to the increase in several voltage losses as shown in Figure 1-4, and is
described as follows.

V  EMF  iRohm a c(1.6)

Here, 𝑖𝑅ohm shows an ohmic loss caused by conduction of ion and electron in theelectrolyte, anode, and cathode. 𝜂a and 𝜂c shows anode and cathode overpotential,
which is related to the electrochemical reactions and gas diffusions on each electrode.
Each voltage loss should be reduced to increase power density of the cell.
Voltage losses mentioned above are strongly linked to the components of SOFCs.
As an electrolyte, oxide materials with high oxide ionic conductivity at elevatedtemperature (600-1000 oC) are used such as Y2O3-stabilized ZrO2 (YSZ), Sc2O3stabilized ZrO2 (ScSZ), Gd2O3-doped CeO2 (GDC), and Sm2O3-doped CeO2 (SDC) [19].
Although ceria-based electrolyte shows higher oxide ion conductivity than those ofzirconia-based ones, YSZ is the most practical electrolyte due to its high chemical

7

(a)2eSOFC
overview

2eH2

O2-

1/2O2

H2O

CathodeAnodeElectrolyte (YSZ)(b)
CathodeAnodeElectron-conductive oxide
(LSM)

Ni

O2

e~1 μm

~1 μm
O2-

O2-

e-

H2

O2O2-

e-

H2O

Oxide ion conductor (YSZ)

Oxide ion conductor (YSZ)

Cathode TPB

Anode TPB

(c)

O2

H2O

H2

eeLSM

O2-

O2-

YSZ

YSZ

Ni

Figure 1-3. (a) Schematic of SOFC operated with hydrogen at anode and oxygen at
cathode. (b) Schematics of porous composite cathode and Ni-cermet anode. (c)Enlarged views of electrodes particles near the triple phase boundary (TPB) in bothanode and cathode.

stability and mechanical strength at elevated temperature in addition to the relatively low
cost [11,19]. Figure 1-3(b) shows the detailed schematic of typical anode and cathode8

used with YSZ electrolyte. Generally, porous composite electrodes are used for state-ofthe-art SOFCs, such as Ni/YSZ for anodes or strontium-doped lanthanum manganite(LSM)/YSZ for cathodes [20,21]. These electrodes have micro/nano-scale complex
structures consisting of electron conductors (Ni, LSM), oxide ion conductors (YSZ), andpore phases, where chemical species are transported and accompanied by electrochemical
reactions. In these electrodes, electrochemical reaction is considered to occur at the triple
phase boundary (TPB) of Ni/YSZ/gas phase for anode or LSM/YSZ/gas phase forcathode, as shown in Figure 1-3(c), because both anode and cathode reactions involve
electrons, oxide ions, and gas species.

Cell voltage 𝑉 [V]EMF (OCV: Open Circuit Voltage)𝑖𝑅ohm: Ohmic loss𝜂a : Anode overpotential
𝜂c : Cathode overpotential

Cell voltage
Current density 𝑖 [A/cm2]

Figure 1-4. Terminal (cell) voltage of an SOFC with respect to current density. The
voltage loss from OCV consists of ohmic loss, anode overpotential, and cathodeoverpotential.

1.4

Current status and challenges of SOFC
Intensive research and development on SOFCs has been conducted for more than 30

years, and the technology is currently in the early commercialization stage [17], asmentioned in section 1.2. For the widespread introduction of SOFC technologies to the9society, however, its material and system costs should be reduced and performancedegradation issues during long-term operation need to be solved [22]. Lowering theoperating temperature to intermediate range (600-800 oC) is one of the major approach toovercome the former issues because cost-effective metallic materials can be used in thistemperature range as an interconnect or other related components [16]. In order to achievesufficient power density for practical applications, improvement of both electrolyte andelectrodes performance at lower temperature is accelerated in SOFC field [16,22]. The
latter issues, performance degradation, are originated from several factors such as sulfur
poisoning [23,24], carbon deposition by hydrocarbon fuel [25-27], redox cycle [28,29],
and Ni coarsening [30,31] on anode side or chromium poisoning [32,33], secondary phaseformation between cathode and electrolyte [34,35], and segregation of strontium
component [36,37] on cathode side. Intensive research and development for further
understanding of these degradation mechanisms and improvement of SOFC durability
has been conducted in recent days.
It is an inevitable and critical issue to enhance SOFC electrodes performance andstability in order to accomplish the operation at lower temperature and improvement of
the lifetime for the widespread utilization. The performance of porous electrodes isdominated by following two phenomena; electrochemical reaction at the active sites andtransport of gases, oxide ion, and electron in the porous structure. Moreover, degradationof electrodes performance mentioned above results from the change of active sites ortransport paths of chemical species, which are blocked or reduced by deposited impurities,
formed secondary phases, and microstructure changes through coarsening. Therefore, it
is important to understand species transport phenomena coupled with electrochemical
reactions proceeding inside porous electrodes precisely for further improvement of SOFC

10

performance and durability.
Species transport and electrochemical reactions in SOFC porous electrodes havebeen intensively investigated by numerical modeling and simulations [38-46]. Typicalmodels based on effective medium theory make it possible to calculate averaged
electric/ionic current distributions and to identify electrochemically active regions incomposite electrodes [38-40]. In addition, numerical simulations of SOFC electrodes
have been recently conducted based on actual microstructures obtained by a focused ion
beam scanning electron microscope (FIB-SEM) [41-46]. In those simulations, gases, ions,and electron transport are solved by lattice Boltzmann method (LBM) [41,42], volume of
fluid (VOF) method [43], finite element method (FEM) [44], sub-grid scale (SGS)
method [45], or finite volume method (FVM) [46], and local three-dimensional
distributions of ionic/electronic flows or electrical potential are provided. The
development of those analysis and simulations can provide accurate description oftransport phenomena inside SOFC electrodes. On the other hand, electrochemical
reaction at the TPB has been mainly described by Butler-Volmer equation and exchange
current density, which has been originally developed for reactions at interface between
metal and liquid electrolyte [20]. In this scheme, all detailed reaction kinetics are lumped
together into exchange current density, which is not established via phenomenologicaldescription but treated as fitting parameters [43] or given by empirical expressions[41,42,45,46]. For accurate prediction and physically-based interpretation of electrode
performance, development of reliable electrochemical reaction model at the TPB basedon elementary chemical reactions, such as adsorption of gas species, oxide ion migration,or surface reactions, are desired [45].
Several experimental studies have been also conducted to directly investigate

11electrochemical reactions on SOFC electrodes. Oxygen chemical potential distributionsof model (thin film) or porous cathodes were investigated at biased condition by
microprobe oxygen sensor [47] or in-situ micro X-ray adsorption spectroscopy (XAS)[48,49]. Surface potential distribution of a cross section of the operated SOFC was
detected by in-situ Kelvin force microscopy (KFM) [50]. In addition, atomic labelingusing oxygen isotope has been introduced to visualize active reaction sites in thin film
electrodes [51,52] or overall oxide ion flows in a practical SOFC [53]. However,experimental information about active reaction sites distribution or oxide ion paths in the
microstructure of SOFC porous electrodes has not been reported so far. For validation ofnumerical results mentioned above, deeper understanding of species transport coupledwith electrochemical reactions in the electrodes, and optimization of its microstructures,a visualization technique of active reaction sites and oxide ion paths in microstructure
scale should be realized and developed.

1.5

Objectives and contents of thesis
For more accurate understanding and description of species transport phenomena

coupled with electrochemical reactions proceeding inside SOFC, two main specificobjectives toward construction of the detailed reaction kinetics and dynamics on porous
electrodes are raised as the contents of current thesis below.
(i) Construction of analytical model for hydrogen oxidation in a TPB of SOFC anode based onelementary chemical reactions.
(ii) Development of visualization technique of active reaction sites and oxide ion paths in

SOFC porous electrodes with microstructure scale.
In Chapter 1, background, principle, current status, and challenges of SOFC are

12reviewed and summarized. In addition, the main specific targets of the thesis are raised
and the structure of the thesis is explained. In Chapter 2, analytical model for hydrogenoxidation in an anode TPB, named as species territory adsorption model, is constructedbased on elementary chemical reactions. It is shown that explicit expressions of current
density and anode overpotential, and theoretical limit of current density can be derived
from the model. In addition, the physical meaning of analytical results based on the model
is discussed. In Chapter 3, the quantitative validation of species territory adsorption model
is discussed. The dependence of anode overpotential on hydrogen partial pressure isexperimentally investigated, which is compared to the model. All thermodynamic andkinetic parameters for the model are determined from referenced density functional
theory (DFT)-database and careful fitting process between the analytical andexperimental results. The analytical results are compared with several reported
experimental results using Ni/YSZ cermet, and effective anode thickness predicted by themodel is discussed. In Chapter 4, visualization technique of active reaction sites in SOFC
porous electrodes with microstructure scale is developed. In order to quench a reaction, aSOFC power generation equipment with a nozzle for direct helium gas impinging jet tothe cell is prepared. Using constructed quench system and oxygen isotope labeling, active
sites of LSM/ScSZ composite cathode are visualized in microstructure scale. In Chapter
5, oxygen isotope exchange and quench experiment is conducted at 973 K. From theanalysis of oxygen isotope diffusion profiles in YSZ electrolyte, quantitative oxide ion
flux incorporated from a cathode/electrolyte interface to an electrolyte is estimated.
Finally, the key findings and contributions in this study are summarized and future
perspective is presented in Chapter 6.

13

References[1] P. Singh, N.Q. Minh, Int. J. Appl. Ceram. Technol. 1 (1) (2004) 5–15.
[2] O.Z. Sharaf, M.F. Orhan, Renew. Sust. Energ. Rev. 32 (2014) 810–853.
[3] AIST website (http://www.aist.go.jp/aist_e/list/latest_research/2009/20091204/2009120
4.html).
[4] Shibaura Institute of Technology, Power & Energy Systems Lab. website (http://www.
web.se.shibaura-it.ac.jp/kimi/study.php). (in Japanese)[5] Ministry of Economy, Trade and Industry website, document “MHPS の燃料電池について” (http://www.meti.go.jp/committee/kenkyukai/energy_environment/jisedai_karyoku/p
df/003_01_00.pdf) (2015). (in Japanese)[6] Fukuoka prefecture website, document “水素社会へ向けた MHPS における SOFC－
マイクロガスタービンハイブリッドシステムの開発状況と今後の展開” (http://www.
pref.fukuoka.lg.jp/uploaded/life/267507_52640768_misc.pdf) (2016). (in Japanese)[7] Ministry of Economy, Trade and Industry website, document “家庭用燃料電池について” (http://www.meti.go.jp/committee/kenkyukai/energy/suiso_nenryodenchi/suiso_nenr
yodenchi_wg/pdf/002_01_00.pdf) (2014). (in Japanese)[8] Toyota Motor Corporation website (http://toyota.jp/mirai/spec/). (in Japanese)[9] Ministry of Economy, Trade and Industry, Agency for Natural Resources and Energy
website, document “火力発電における論点” (http://www.enecho.meti.go.jp/committee/
council/basic_policy_subcommittee/mitoshi/005/pdf/005_07.pdf) (2015). (in Japanese)[10] TEPCO Fuel & Power, Inc. website (http://www.tepco.co.jp/fp/thermal-power/list/chiba.html). (in Japanese)[11] S.C. Singhal, WIREs Energy Environ. 3 (2014) 179–194.

[12] R. Payne, J. Love, M. Kah, ECS Transactions 25 (2) (2009) 231–239.

14[13] Panasonic Corporation website (https://panasonic.biz/appliance/FC/house_07.ht
ml). (in Japanese)[14] AISIN SEIKI Co., Ltd. website (http://www.aisin.co.jp/cogene/enefarm.html).
(in Japanese)[15] 田川博章，固体酸化物燃料電池と地球環境，アグネ承風社 (1998). (inJapanese)[16] E.D. Wachsman, K.T. Lee, Science 334 (2011) 935–939.
[17] N.Q. Minh, J. Mizusaki, S.C. Singhal, ECS Transactions 78 (1) (2017) 63–73.
[18] Mitsubishi Hitachi Power Systems, Ltd. website (http://www.mhps.com/jp/new
s/20170809.html). (in Japanese).
[19] K.C. Wincewicz, J.C. Cooper, J. Power Sources 140 (2005) 280–296.
[20] R.J. Gorte, J.M. Vohs, Annu. Rev. Chem. Biomol. Eng. 2 (2011) 9–30.
[21] J. Hanna, W.Y. Lee, Y. Shi, A.F. Ghoniem, Prog. Energy Combust. Sci. 40 (2014)
74–111.
[22] J.T.S. Irvine, P. Connor (Eds.), Solid Oxide Fuel Cells: Facts and Figures, Green
Energy and Technology, Springer (2013).
[23] L. Yang, Z. Cheng, M. Liu, L. Wilson, Energy. Environ. Sci. 3 (2010) 1804–1809.
[24] D. Papurello, A. Lanzini, S. Fiorilli, F. Smeacetto, R. Singh, M. Santarelli, Chem.
Eng. J. 283 (2016) 1224–1233.
[25] W. Wang, C. Su, Y. Wu, R. Ran, Z. Shao, Chem. Rev. 113 (2013) 8104–8151.
[26] K.S. Blinn, H. Abernathy, X. Li, M. Liu, L.A. Bottomley, M. Liu, Energy. Environ.
Sci. 5 (2012) 7913–7917.
[27] H. Xu, Z. Dang, Appl. Energy 178 (2016) 294–307.
[28] H. Yokokawa, H. Tu, B. Iwanschitz, A. Mai, J. Power Sources 182 (2008) 400–412.

15[29] T. Shimura, Z. Jiao, S. Hara, N. Shikazono, J. Power Sources 267 (2014) 58–68.
[30] F. Abdeljawad, B. Völker, R. Davis, R.M. McMeeking, M. Haataja, J. Power
Sources 250 (2014) 319–331.
[31] J.S. Cronin, J.R. Wilson, S.A. Barnett, J. Power Sources 196 (2011) 2640–2643.
[32] E. Park, S. Taniguchi, T. Daio, J-T. Chou, K. Sasaki, Solid State Ionics 262 (2014)421–427.
[33] K. Miyoshi, H. Iwai, M. Kishimoto, M. Saito, H. Yoshida, J. Power Sources 326(2016) 331–340.
[34] S-Y. Park, J.H. Ahn, C-W. Jeong, C-W. Na, R-H. Song, J-H. Lee, Int. J. Hydrog.
Energy 39 (2014) 12894–12903.
[35] F. Wang, M.E. Brito, K. Yamaji, D-H.Cho, M. Nishi, H. Kishimoto, T. Horita, H.
Yokokawa, Solid State Ionics 262 (2014) 454–459.
[36] G.M. Rupp, A.K. Opitz, A. Nenning, A. Limbeck, J. Fleig, Nat. Mater. 16 (2017)
640–645.
[37] H. Ding, A.V. Virkar, M. Liu, F. Liu, Phys. Chem. Chem. Phys. 15 (2013) 489–496.
[38] P. Costamagna, P. Costa, V. Antonucci, Electrochim. Acta 43 (1998) 375–394.
[39] J. H. Nam, D. H. Jeon, Electrochim. Acta 51 (2006) 3446–3460.
[40] A. Banerjee, O. Deutschmann, J. Catal. 346 (2017) 30–49.
[41] N. Shikazono, D. Kanno, K. Matsuzaki, H. Teshima, S. Sumino, N. Kasagi, J.
Electrochem. Soc. 157 (5) (2010) B665–B672.
[42] K. Matsuzaki, N. Shikazono, N. Kasagi, J. Power Sources 196 (2011) 3073–3082.
[43] P.R. Shearing, Q. Cai, J.I. Golbert, V. Yufit, C.S. Adjiman, N.P. Brandon, J. Power
Sources 195 (2010) 4804–4810.
[44] T. Carraro, J. Joos, B. Rüger, A. Weber, E. I-Tiffée, Electrochim. Acta 77 (2012) 315–

16

325.
[45] M. Kishimoto, H. Iwai, M. Saito, H. Yoshida, J. Electrochem. Soc. 159 (3) (2012)
B315–B323.
[46] K. Miyoshi, T. Miyamae, H. Iwai, M. Saito, M. Kishimoto, H. Yoshida, J. Power
Sources 315 (2016) 63–69.
[47] T. Kawada, M. Sase, M. Kudo, K. Yashiro, K. Sato, J. Mizusaki, N. Sakai, T. Horita,
K. Yamaji, H. Yokokawa, Solid State Ionics 177 (2006) 3081–3086.
[48] Y. Fujimaki, H. Watanabe, Y. Terada, T. Nakamura, K. Yashiro, S. Hashimoto, T.
Kawada, K. Amezawa, ECS Transactions 57 (1) (2013) 1925–1932.
[49] K. Amezawa, Y. Fujimaki, T. Nakamura, K.D. Bagarinao, K. Yamaji, K. Nitta, Y.
Terada, F. Iguchi, K. Yashiro, H. Yugami, T. Kawada, ECS Transactions 66 (2)(2015) 129–135.
[50] S.S. Nonnenmann, R. Kungas, J. Vohs, D.A. Bonnell, ACS Nano 7 (7) (2013) 6330–
6336.
[51] T. Horita, K. Yamaji, N. Sakai, H. Yokokawa, T. Kawada, T. Kato, Solid State Ionics
127 (2000) 55–65.
[52] J. Fleig, A. Schintlmeister, A.K. Opitz, H. Hutter, Scripta Mater. 65 (2011) 78–83.
[53] T. Horita, T. Shimonosono, H. Kishimoto, K. Yamaji, M.E. Brito, Y. Hori, H.
Yokokawa, Electrochem. Solid-State Lett. 13 (12) (2010) B135–B138.

17

Chapter 2

Species territory adsorption model for hydrogenoxidation in SOFC anode2.1

Introduction
Porous composite electrodes such as Ni/YSZ, Ni/ScSZ, or Ni/GDC are widely used

for state-of-the-art SOFC anode [1]. In these anodes, hydrogen oxidation is considered tooccur mainly at the triple phase boundary (TPB) consisting of Ni, YSZ (ScSZ, GDC), andgas phases because hydrogen should be reacted with oxide ion accompanied with releaseof electrons [2,3]. For accurate prediction and physically-based interpretation of anode
performance, clarifying the reaction mechanism at the TPB is indispensable and thedevelopment of reliable electrochemical reaction model based on elementary chemical
reactions is desired. Various reaction mechanisms around the anode TPB have been
proposed and discussed for past two decades [4-11]. Among these works, Ihara et al.
regarded a Ni/YSZ/gas TPB as one dimensional line and proposed competitive adsorption
mechanism among adsorbed species, i.e., Had, H2Oad, and Oad on the TPB as shown in
Figure 2-1 [7]. They assumed that the reaction rate is determined by surface reaction
between Had and Oad to produce H2Oad (Langmuir-Hinshelwood mechanism). Based on
their model, the analytical expression of current density is derived as a function of oxygen
activity in anode TPB, which could demonstrate experimental trends qualitatively.
On the other hand, some researches have recently shown that addition of perovskite

18

H2

H2O

Had HadH2OadRate-determining stepOad + Had + Had

H2Oad

Competitive
adsorption
Oad + 2e-(Ni)e-(Ni)NiYSZ

O2-(YSZ)e-(YSZ)

Oxygen activity ao O (YSZ) + 2e-(YSZ)

Figure 2-1. Schematic of competitive adsorption mechanism on Ni/YSZ anodeproposed by Ihara et al [7].

proton conductors, such as SrZr0.95Y0.05O3-x (SZY) or BaCe0.8Y0.2O3-x (BCY) to Ni/YSZ
or Ni/GDC cermet anodes is an effective way to improve anode electrochemical
properties in hydrogen and hydrocarbon fuel [12-17]. Among them, it was shown thatanode overpotential is reduced by adding BCY particles to Ni/GDC cermet anode [12].
In addition, thermal desorption spectroscopy (TDS) measurement disclosed that BCY
adsorbs a significant amount of hydrogen [13]. Consequently, it was concluded that
adsorbed hydrogen on BCY is supplied to Ni/GDC/gas TPB and the anodic reaction isenhanced as shown in Figure 2-2, resulting in the reduction of anode overpotential [13].
However, the above enhanced anodic reaction cannot be explained well by thecompetitive adsorption mechanism [7] because in this model, additionally suppliedhydrogens from BCY adsorb on the TPB and fill the vacancy sites, resulting in a reductionof adsorbed oxygen, i.e., a decrease in reaction rate.
In a conventional cermet anode consisting of Ni and oxide ion conductor, hydrogenis mainly adsorbed onto the Ni surface, which has been confirmed by thermal desorption
spectroscopy (TDS) measurement [13]. On the other hand, most of oxygen would be
19

H2
BCY

Ni

Had
H2O

eH2OadGDC
H2Oad

O2Triple Phase Boundary(TPB)
Figure 2-2. Schematic of the reaction mechanism for overpotential reduction in
Ni/GDC-BCY anode [13].

adsorbed onto the surface of the oxide ion conductor around the TPB after the oxide ionsreleased their electrons to the Ni bulk. Then, the adsorbed hydrogen reacts with theadsorbed oxygen at the TPB. Consequently, these species are adsorbed in a finite areaaround the TPB and do not necessarily occupy the same adsorption sites.
In this chapter, new analytical model for hydrogen oxidation in an anode TPB,
named as species territory adsorption model, is constructed based on the Langmuir-typesurface reaction between adsorbed hydrogen and oxygen, and on the other reactions at
chemical equilibrium. The chemical species are assumed to be adsorbed in a finite surface
area of Ni and oxide ion conductor around the TPB. First, explicit expressions of current
density and anode overpotential, and theoretical limit of current density are derived based20

on the model. Next, typical analytical results obtained by the model are shown, and thephysical meanings of those are discussed.

2.2

Model construction

2.2.1 Assumptions
In this model, hydrogen oxidation at conventional cermet anode consisting of Ni andoxide ion conductor particles is considered. According to the percolation theory, to retain
the network structure of each particle for conduction of ion or electron, the particle
number concentration in the anode should be greater than 30% [18]. For simplicity, it isassumed that the particle size is uniform and the concentrations are the same. As a result,the unit structure of cermet anode consisting of Ni and oxide ion conductor can beconsidered as shown in Figure 2-3(a). Herein, the following assumptions are considered:(i) The overall reaction rate is controlled by the surface reaction between the adsorbedhydrogen, Had, and the adsorbed oxygen, Oad. The other reactions take place underchemical equilibrium conditions [equilibrium constants are expressed as Ki (i: eachspecies)] because the reaction rates are much faster than the surface reactions.
(ii) Chemical species are adsorbed within finite areas, described as Area 1 and Area 2, on
the surface of each material around the TPB.
(iii) H2 molecules are adsorbed in Area 1, whereas H2O molecules are adsorbed in Areas
1 and 2.
(iv) Adsorbed hydrogen, Had, can be moved between Areas 1 and 2.
(v) Adsorbed water, H2Oad, and oxygen, Oad, can be moved between Areas 1 and 2.
Fig. 2-3(b) shows a schematic of the cross section of the TPB consisting of Ni, oxide
ion conductor, and gas phases. The following assumption is considered:21

(vi) In a reaction process from oxide ions in the conductor to adsorbed oxygen on Area 2,
each reaction takes place under chemical equilibrium [7].

(a)
TPB
( )
( )
( )
( )
( )

( )

Adsorption
site

( )

Ni
Area 1

Area 2Oxide ion
conductor(b)
Oxide ion conductor

Ni
(

)
(

)

(

(

)

)

Figure 2-3. (a) Schematic of the TPB consisting of Ni and oxide ion conductor
assumed in present model. (b) Schematic of the cross section of the interface between
Ni and oxide ion conductor.

222.2.2 Reactions under chemical equilibrium
Based on the above assumptions for reactions under chemical equilibrium, theadsorption of H2 and H2O from the gas phase to Area 1 is described as follows:
KH
H2  2Vad(1) 2Had(1)(2.1)

H2O
H2O  Vad(1)  H2Oad(1)

(2.2)

K

Here, V represents adsorption sites on the surface and the subscript (1) denotes Area 1.
Similarly, the adsorption of H2O on Area 2 is expressed as follows:K

H2O
H2O  Vad(2)  H2Oad(2)(2.3)

Adsorbed species, Had, Oad, and H2Oad are assumed to be exchanged between Areas 1 and2 through the following reactions:H(ex12)
H ad(1)  Vad(2)  Had(2)  Vad(1)(2.4)

O(ex12)Oad(2)  Vad(1)  Oad(1)  Vad(2)(2.5)

H2O(ex12)
H2Oad(1)  Vad(2) 
 H2Oad(2)  Vad(1)

(2.6)

K

K

K

Reactions for the process from oxide ions in oxide ion conductor bulk to adsorbed oxygen
on Area 2 are expressed as follows [7]:
K 2


2
O
O(O-bulk)  2e(O-bulk) O(O-bulk)

(2.7)

KO
O(O-bulk)  Vad(2) Oad(2)

(2.8)

2

Oad
O(O-bulk) Vad(2)  Oad(2) +2e(Ni-bulk)

(2.9)

K

Ke


e(Ni-bulk)e(O-bulk)(2.10)

Here, O(O-bulk) refers to oxygen atoms in the conductor bulk and corresponds to the oxygen
activity, 𝑎O , in experiments.

23

For Had, Oad, and H2Oad, competitive adsorption should be assumed on Areas 1 and2. The coverage of the adsorbed species i (i = H, O, H2O, V) in Area k (k = 1, 2) isexpressed by 𝜃𝑖(𝑘) , which means the ratio of adsorbed species to all adsorption sites. On
the surfaces of Areas 1 and 2, the summations of coverages should be both equal to unity
as follows:H(1)  O(1)  H O(1)  V (1)  1(2.11)

H(2)  O(2)  H O(2)  V (2)  1(2.12)

2

2

Using the coverages and partial pressure of molecules in the gas phase, the equilibrium
constants of reactions (2.1), (2.2), (2.3), and (2.8) are described as follows:H(1) 2KH 
PH V (1) 2(2.13)

2

 H O(1)PH OV (1)2(2.14)

 H O(2)PH OV (2)2(2.15)O(2)aOV (2)(2.16)K H2O 2

K H 2O 2KO 

Here, 𝑃H2 and 𝑃H2 O are the partial pressures of hydrogen and water vapour,respectively. 𝑎O expresses the oxygen activity in the oxide ion conductor bulk near thesurface in Area 2. Moreover, the equilibrium constant, 𝐾O , can be expressed using 𝐾O2 ,𝐾Oad , and 𝐾e in reactions (2.7), (2.9), and (2.10) as follows

KO  KO2 KOad Ke 2

(2.17)In addition, the equilibrium constants of reactions (2.4)–(2.6) are described as follows.

24

K H(ex12)  H(2)V (1) H(1)V (2)(2.18)K O(ex12)  O(1)V (2) O(2)V (1)(2.19)

KH2O(ex12) H O(2)V (1) KH O
H O(1)V (2) KH O
2

2

2

2

(2.20)

Here, Eq. (2.20) shows that 𝐾H2 O(ex12) can be described by Eqs. (2.14) and (2.15).
Using Eqs. (2.11)–(2.20), all coverages in Areas 1 and 2, 𝜃𝑖(𝑘) , can be solved andexpressed explicitly as follows:V (1)  H(1) O(1) 1
1  KH PH2  KO(ex12) KO aO  KH2O PH2O
K H PH2
1  K H PH2  K O(ex12) K O aO  K H2O PH2O
K O(ex12) K O aO
1  K H PH2  K O(ex12) K O aO  K H2O PH2O

 H O(1) 2

V (2)  H(2) O(2) K H2O PH2O
1  K H PH2  K O(ex12) K O aO  K H2O PH2O

1  KH(ex12)

1
K H PH2  KO aO  K H 2O PH2O
K H(ex12) K H PH2

1  K H(ex12) K H PH2  K O aO  K H 2O PH2O

KO aO
1  KH(ex12) KH PH2  KO aO  K H 2O PH2O

25

(2.21)(2.22)(2.23)(2.24)(2.25)(2.26)(2.27)

 H O(2) 
2K H 2O PH2O

(2.28)

1  K H(ex12) K H PH2  K O aO  K H 2O PH2O

The details of derivation are shown in Appendix A.

2.2.3 Reaction rate controlled by the surface reaction in Areas 1 and 2
Based on assumption (i), the overall reaction rate is controlled by the surface reaction
between Had and Oad to produce H2Oad (Langmuir-type reaction). In this case, ten
combinations of reactions can be considered as shown in Table 2-1. For instance, in thecase of reaction (I) in Table 2-1, two adsorbed hydrogens, Had, in Area 1 react with Oad in
Area 2 to produce H2Oad in Area 1, and the adsorption sites, Vad, in Areas 1 and 2 aresimultaneously produced as follows:kaI H2Oad(1)  Vad(1)  Vad(2)2Had(1)  Oad(2) (2.29)

kcI

Here, 𝑘𝑎𝐼 and 𝑘𝑐𝐼 are the rate constants of anodic and cathodic reactions in reaction (I).
The rate constants 𝑘𝑎𝑗 and 𝑘𝑐𝑗 for reaction 𝑗 (= 𝐼 − 𝑋) [A/cm2] include factors of
the surface reaction rate and the length of the TPB as follows:

Table 2-1. Combination of the surface reaction in the anode; 1 and 2 represent Areas
1 and 2, respectively.
Reaction no.
(I)
(II)
(III)
(IV)
(V)
(VI)
(VII)
(VIII)
(IX)
(X)

Had
1
1
1
2
2
2
1
1
1
1

Had
1
1
1
2
2
2
2
2
2
2

Oad
2
2
1
1
1
2
1
1
2
2

26

H2Oad
1
2
1
1
2
2
1
2
1
2

Vad
1
1
1
2
1
2
1
1
2
1

Vad
2
1
1
2
2
2
2
1
2
2

ka (c ) j  zFlTPBka(c ) j(2.30)

Herein, a valence z (=2), Faraday constant F [C/mol], length of the TPB per unit area lTPB
[cm/cm2], and rate constant per unit TPB length 𝑘 𝑎(𝑐)𝑗 [mol/(s•cm)] are used, wherelTPB is calculated by the anode thickness t [µm], and the TPB density 𝜌TPB [µm/µm3](𝑙 𝑇𝑃𝐵 = 𝑡𝜌TPB × 104 ).
The net current density generated by reaction (I), iI, is described as the difference
between the anodic current density, iaI, and the cathodic current density, icI, as shown in
Eq. (2.31). Each current density is described by the reaction rate constants and thecoverages of adsorbed species.

iI  iaI  icI  kaIH(1) 2O(2)  kcIH2O(1)V (1)V (2)(2.31)

Similarly, ij for 𝑗 = 𝐼𝐼 − 𝑋 is described as Eqs. (2.32)–(2.40), respectively.

iII  iaII  icII  kaIIH(1) 2O(2)  kcIIH2O(2)V (1) 2(2.32)iIII  iaIII  icIII  kaIIIH(1) 2O(1)  kcIII H2O(1)V (1) 2(2.33)

iIV  iaIV  icIV  kaIV H(2) 2O(1)  kcIV H2O(1)V (2) 2(2.34)iV  iaV  icV  kaV H(2) 2O(1)  kcVH2O(2)V (1)V (2)(2.35)iVI  iaVI  icVI  kaVIH(2) 2O(2)  kcVI H2O(2)V (2) 2(2.36)iVII  iaVII  icVII  kaVIIH(1)H(2)O(1)  kcVIIH2O(1)V (1)V (2)(2.37)iVIII  iaVIII  icVIII  kaVIII H(1)H(2)O(1)  kcVIII H2O(2)V (1) 2(2.38)iIX  iaIX  icIX  kaIX H(1)H(2)O(2)  kcIX H2O(1)V (2) 2(2.39)iX  iaX  icX  kaX H(1)H(2)O(2)  kcX H2O(2)V (1)V (2)(2.40)

27

As a result, the total current density, 𝑖total, is expressed by the summation of current
densities ij (𝑗 = 𝐼, 𝐼𝐼, ⋯ , 𝑋) for each reaction from (I) to (X) in Table 2-1 [summation of
Eqs. (2.31)–(2.40)].
X

itotal   i j(2.41)jI

2.2.4 Competitive adsorption model and species territory adsorption model
The equilibrium constants for the exchange of species, 𝐾H(ex12) , 𝐾O(ex12) , and𝐾H2 O(ex12) can be assumed to be a value from 0 to unity, and these values correspond to
the distribution of coverage of adsorbed species as shown in Figure 2-4.
When 𝐾H(ex12) = 𝐾O(ex12) = 𝐾H2 O(ex12) = 1 , the coverage for each species inAreas 1 and 2 are the same, i.e., 𝜃𝑖(1) = 𝜃𝑖(2) (i = H, O, H2O, V) in Eqs. (2.11), (2.12),
and (2.18)–(2.20). As a result, this model is mathematically reduced to that of theconventional competitive adsorption at the TPB [7].
On the other hand, there is no mutual migration of adsorbed hydrogen and oxygen
when 𝐾H(ex12) = 𝐾O(ex12) = 0. As a result, hydrogen can only be adsorbed in Area 1 andoxygen only in Area 2; that is, 𝜃O(1) = 𝜃H(2) = 0. As a result, only surface reactions (I)and (II) among the combinations listed in Table 2-1 would be dominant in this model. We
defined this model as the “species territory adsorption model”.
For any values of 𝐾H(ex12) and 𝐾O(ex12) between 0 and unity, hydrogen andoxygen can be assumed to be adsorbed on both surfaces in Areas 1 and 2. In this case,even if the hydrogen coverage in Area 1 reaches unity, hydrogen will migrate and becontinuously adsorbed in Area 2 with a uniform coverage. Similarly, even if the coverageof oxygen in Area 2 reaches unity, oxygen will migrate and be continuously adsorbed in
Area 1. The migration of adsorbed species is described by the equilibrium constants for28Species territory
adsorption model

Competitive
adsorption model

Coverage ofadsorbed species

Area 1 Area 2

Area 1 Area 2

Area 1 Area 2

Area 1 Area 2

Had
0

Oad
0
(

)

(

)

Diffusion dynamics

Figure 2-4. Relationship between the coverage of the adsorbed species near the TPB
between Areas 1 and 2 and the equilibrium constants for species exchanges. Schematicfor practical diffusion dynamics is also shown.

exchange instead of the diffusion coefficients in practical dynamics, as shown in Fig. 24.
To discuss the physical meaning of 𝐾H(ex12) and 𝐾O(ex12) , the effect of thosevalues on variations of the current density with respect to the oxygen activity, 𝑎O , wasinvestigated based on Eq. (2.41) as shown in Figure 2-5. In order to focus on the mutual
migration of adsorbed hydrogen and oxygen between Areas 1 and 2, 𝐾H2 O(ex12) was
fixed to unity (𝐾H2 O = 𝐾 H2 O ), and 𝐾H(ex12) and 𝐾O(ex12) were varied from zero tounity. The assumed parameters for the calculation of Eq. (2.41) are shown in Table 2-2.
Here, all equilibrium constants and reaction rate constants, 𝑘𝑎𝑗 and 𝑘𝑐𝑗 , for 𝑗 = 𝐼, 𝐼𝐼
are the same as those used for comparison between analytical and experimental results of
Ni/YSZ in Chapter 3.
When (𝐾H(ex12) , 𝐾O(ex12) ) = (0,0), the current density is kept constant in the range

29

of 𝑎O ≥ 10 7, as shown in Fig. 2-5. This indicates that the coverage of oxygen in Area
2 reaches unity.
On the other hand, when (𝐾H(ex12) , 𝐾O(ex12) ) = (0,1), the current density is slightly
higher than that of the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (0,0) in the range of2 × 10 11 ≤ 𝑎O ≤ 10 9 . This is because reaction (III) in Table 1 takes place throughmigration of the adsorbed oxygen from Area 2 to Area 1. However, in the range of 𝑎O ≥4 × 10 9 , the current density drastically decreases with increasing oxygen activity

𝐾H(ex12), 𝐾O(ex12) =2
1.00E+02

100, 0

1 × 10 4, 1 × 10 4

0, 1

1, 0

1, 1

Current density [A/cm2]

1
1.00E+01

10

01.00E+00

10-1
1.00E-01

10-2
1.00E-02

10-3
1.00E-03
1.00E-13
-13

10

10

1.00E-11-11

10

1.00E-09-910

1.00E-07-7

10

1.00E-05-5

10

1.00E-03-3

10

Oxygen activity 𝑎O [-]Figure 2-5. The effect of equilibrium constants for species exchange between Areas 1
and 2 (𝐾H(ex12) and 𝐾O(ex12) ) on varieties of current density with oxygen activity,
𝑎O . 𝐾H2 O(ex12) is fixed to unity ( 𝐾H2 O = 𝐾 H2 O ). The analytical results were
calculated by Eq. (2.41) assuming parameters listed in Table 2-2.

30

Table 2-2. Assumed partial pressures of H2 and H2O, equilibrium constants,
and reaction rate constants for the calculation of Figure 2-5. All equilibrium
constants and reaction rate constants, 𝑘𝑎𝑗 and 𝑘𝑐𝑗 , for 𝑗 = 𝐼, 𝐼𝐼 are thesame as those used for comparison between analytical and experimental
results of Ni/YSZ in Chapter 3.

Parameter

Value

𝑇 [K]

1073

∆𝐺 °𝑓 H2 O [kJ/mol]]-377.372

𝑃H2 at anode [atm]0.97

𝑃H2O at anode [atm]0.03

𝐾H [/atm]

5.5×10-3

𝐾O [-]

1.66×108𝐾H2O [/atm]

3.47×10-4

𝐾 H2O [/atm]

3.47×10-4

𝑘𝑎𝑗 (𝑗 = 𝐼, 𝐼𝐼) [A/cm2]

1.23×103𝑘𝑐𝑗 (𝑗 = 𝐼, 𝐼𝐼) [A/cm2]

2.11×103𝑘𝑎𝑗 (𝑗 = 𝐼𝐼𝐼 − 𝑋) [A/cm2]

1.23×103𝑘𝑐𝑗 (𝑗 = 𝐼𝐼𝐼 − 𝑋) [A/cm2]

2.0×102

because the coverage of the adsorbed hydrogen decreases with increasing coverage ofoxygen in Area 1.
Similarly, when (𝐾H(ex12) , 𝐾O(ex12) ) = (1,0), the current density becomes higher
than that of the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (0,0) in the range of 10 11 ≤ 𝑎O ≤10 7 through reactions (VI), (IX), and (X) in Table 2-1, which relate to migration of theadsorbed hydrogen into Area 2. On the other hand, the current density is constant in therange of 𝑎O ≥ 10 7 , similar to the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (0,0) because theoxygen coverage reaches unity, i.e., the adsorbed hydrogen in Area 2 is completely

31

replaced by adsorbed oxygen.
In the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (1,1), which is the conventional competitive
adsorption model [7], the current density increases with increasing oxygen activity in therange of 10 11 ≤ 𝑎O ≤ 10 9 as compared to the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (0,0)
because all reactions in Table 1 take place. However, similar to the case of(𝐾H(ex12) , 𝐾O(ex12) ) = (0,1) , the current density drastically decreases with increasing
oxygen activity in the range of 𝑎O ≥ 4 × 10 9 .
Ni-patterned electrodes on YSZ with well-defined TPB geometry were developed toinvestigate the mechanism of hydrogen oxidation by Mizusaki et al. [19], Bieberle et al.
[5], and Boer [20]. All of their works indicated that hydrogen oxidation mainly occurs at
the Ni-YSZ-gas TPB. Additionally, the TDS measurement [13] disclosed that hydrogenis mainly adsorbed onto the Ni surface in Ni/GDC or Ni/YSZ cermet anodes. Moreover,recent first-principle calculations [21,22] predicted that the hydrogen oxidation reaction
in a Ni/YSZ anode occurs at the interface between Ni and YSZ, not on the surface of Ni
or YSZ. Based on the above prior works, it can be assumed that surface reactions (I) and(II) in Table 2-1 are the dominant reactions. Consequently, the equilibrium constants forthe exchange of adsorbed hydrogen and oxygen can be assumed to be much smaller thanunity. For example, Fig. 2-5 also shows a result for (𝐾H(ex12) , 𝐾O(ex12) ) = (1 ×
10 4 , 1 × 10 4 ) . The current density corresponds to that for (𝐾H(ex12) , 𝐾O(ex12) ) =(0,0) in the range of 𝑎O ≤ 4 × 10 6 , whereas in the range of 𝑎O ≥ 4 × 10 6 , thecurrent density decreases with increasing oxygen activity. Consequently, the modified
model proposed here is useful for a wide range of oxygen activities up to a high value
where the coverage of the species reaches unity.
The current density in the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (1 × 10 4 , 1 × 10 4 )32

corresponds to that in the case of (𝐾H(ex12) , 𝐾O(ex12) ) = (0,0) for a wide range ofoxygen activities. Therefore, for simplicity, the assumption of (𝐾H(ex12) , 𝐾O(ex12) ) =(0,0) , that is, the species territory adsorption model, will be used in the following
discussion.

2.2.5 Explicit expression of anode overpotential with current density
As mentioned above, it can be assumed that reactions (I) and (II) in Table 2-1 will
be dominant. As a result, the current density described in Eq. (2.41) can be reduced asfollows:

itotal  iI  iII

  iaI  icI    iaII  icII   kaI  kaII  H(1) 2 O(2)  kcI H2O(1)V (1)V (2)  kcII H2O(2)V (1) 2 kaI  kaII  K H PH KO aO   kcI K H O PH O  kcII K H O PH O 

1  K P  K
H H2

2O(ex12)

2

K O aO  K H2O PH2O

 1  K

2

2

2

2

K H PH 2  K O aO  K H 2O PH 2O

H(ex12)(2.42)
Herein, the terms multiplied by 𝐾H(ex12) and 𝐾O(ex12) can be neglected based on thediscussion in the previous section 2.2.4. As a result, Eq. (2.41) can be reduced to thefollowing:i kaI  kaII  K H PH KO aO   kcI K H O PH O  kcII K H O PH O 
2

2

2

2

O O

H 2O H 2O21  K P  K P  1  K a  K  P 2

H H2

H 2O H 2O(2.43)

Because Eq. (2.43) is a linear equation of oxygen activity, 𝑎O , the explicit expression of𝑎O can be obtained as shown in Eq. (2.44). (On the other and, the expression of current
density by the conventional competitive adsorption model is a cubic polynomial of 𝑎O[7], and it is difficult to solve for 𝑎O .)

33

aO 

1  K  P  i  C
H2O H2O2(2.44)K O  C1  i Here, 𝐶1 and 𝐶2 are described as follows:
C1  kaI  kaII  K H PH

1  K P  K P 
H H2

C2 

(2.45)

2

2

H 2O H 2O

kcI K H2O PH2O  kcII K H 2O PH2O



1  K H PH2  K H2O PH2O

(2.46)

2

The oxygen activity, 𝑎O , in the oxide ion conductor bulk near Area 2 is related tothe anode potential, 𝐸𝑎 , as follows:Ea RT  aO 
ln 
2 F  aO(CR) (2.47)

where F is the Faraday constant, R is the gas constant, T is the absolute temperature, and𝑎O(CR) is the oxygen activity of reference electrode at the cathode side (CR). The detailsof Eq. (2.47) are shown in Appendix B. Here, the oxygen is assumed to be in equilibriumwith the outer gas phase at the CR. Then, 𝑎O(CR) is described as follows [23].

aO(CR)  aO (g)  PO2 1 2(2.48)

where 𝑎O (g) is the oxygen activity of the outer gas phase and 𝑃O2 is the oxygen partialpressure at the cathode side. As a result, substitution of Eqs. (2.44) and (2.48) into Eq.
(2.47) gives following equation:

Ea 





RT  1  K H 2O PH2O i  C2  RTln ln  PO 
2F 
KO  C1  i 
 4F  2 

(2.49)

Figure 2-6(a) shows a schematic of the electrolyte-supported single cell discussed
here [7,12]. On both the anode side and the cathode side, working and reference electrodes
are prepared. Figure 2-6(b) shows the electrical potential of each electrode under the

34

(a)

(b)

0
CR

i
AR

CR

CW

Anode

AW

IR

Terminal
voltage

CW

Cathode

ηc

AW
Ea

AR

OCV

IR
ηa

AW, AR (i = 0)
ΔVR-R

Figure 2-6. (a) Schematic of SOFC single cell with working and reference electrodes.
(b) Electrical potential of each electrode under the condition that current density, i, isapplied between anode working (AW) and cathode working (CW) when the electricalpotential of cathode reference (CR) is set to zero.

condition that current density i is applied between anode working (AW) and cathodeworking (CW) when the electrical potential of cathode reference (CR) is set to zero. From
Fig. 2-6(b), the anode overpotential, 𝜂𝑎 , is described as the sum of the anode potential,
𝐸𝑎 , and the voltage between CR and the anode reference (AR), 𝑉𝑅 𝑅 [7]. In addition, we
can define the decrease in the electromotive force as ∆𝑉𝑅 𝑅 , which is a result of thechange in the fuel composite condition followed by a DC current between the anode andcathode working electrodes. As a result, the anode overpotential is described as follows:a  Ea  VR  R  Ea   OCV  VR R 

(2.50)

Here OCV is the open circuit voltage, which is described in H2-H2O atmosphere at theanode side (𝑃H2 , 𝑃H2 O ) and O2 at the cathode side (𝑃O2 ) as follows [24].

OCV  G f (H2O)
4F



RT  PH2O  RTln ln  PO 
2F  PH2  4F  2 

35(2.51)

where ∆𝐺𝑓° (H2 O) is the standard Gibbs free energy of formation of H2O. In addition, we
assume that ∆𝑉𝑅 𝑅 is negligibly small [12]. By substituting Ea in Eq. (2.49) and OCV
in Eq. (2.51) into Eq. (2.50), the anode overpotential can be described as a function of thecurrent density for given partial pressures of H2 and H2O at the anode side:

a 





RT  1  K H 2O PH2O i  C2  G f (H 2O) RT  PH2O 

ln 

ln 

2F 
KO  C1  i 
4F
2F  PH2 

(2.52)

Here, 𝐶1 and 𝐶1 are given by Eqs. (2.45) and (2.46), respectively. As shown in Eq.
(2.52), anode overpotential is independent of 𝑃O2 at the cathode side.
As shown above, the analytical expression of anode overpotential with current
density could be directly obtained based on the species territory adsorption model.
Generally, the anode overpotential in a region of low current density is proportional toln 𝑖, whereas in a region of high current density, it is proportional to [1/(𝑖limit − 𝑖)];herein, 𝑖limit is the limiting current density [25]. These two terms, which areconventionally expressed independently, are combined in the kernel of the logarithmic
function, as shown in Eq. (2.52).

2.3

Analytical results based on the model

2.3.1 Typical curves of current density and anode overpotential
Figure 2-7(a) and (b) show typical curves of current density as a function of oxygen
activity, 𝑖(𝑎O ), calculated by Eq. (2.43), and of anode overpotential as a function ofcurrent density, 𝜂𝑎 (𝑖), by Eq. (2.52). The assumed parameters for the calculation of Eq.
(2.43) and (2.52) are shown in Table 2-3. All equilibrium constants and reaction rate
constants are the same as those used for comparison between analytical and experimental
results of Ni/YSZ in Chapter 3. The partial pressures of hydrogen and water vapor, 𝑃H2
36

and 𝑃H2 O , were fixed at 0.57 and 0.03 atm, respectively.
In Fig. 6(a), the cathodic and anodic currents are dominant in the ranges of 𝑎O ≤3.5 × 10 11 and 𝑎O ≥ 3.5 × 10 11 , respectively. When the anodic current is dominant( 𝑎O ≥ 3.5 × 10 11 ), the current density is initially proportional to 𝑎O , that is, thegradient of 𝑖 with respect to 𝑎O is almost unity (this region is defined as Region I in the
figure). As 𝑎O increases, the gradient of 𝑖 with 𝑎O becomes smaller than unity and thecurrent density asymptotes to a constant value (this region is defined as Region II). As
mentioned in section 2.2.4, this means that the coverage of oxygen in Area 2 (𝜃O(2) )approaches unity. In other words, the current density approaches a limiting value, 𝑖limit ,when 𝐾O 𝑎O approaches infinity. Using Eq. (2.43), 𝑖limit can be described as follows:

ilimit  lim

KO aO  kaI  kaII  K H PH K O aO   kcI K H O PH O  kcII K H O PH O 
2

2



2

O O

H 2O H 2O21  K P  K P  1  K a  K  P 
H H2



2

2

 kaI  kaII  K H PH

2

1  K H PH2  K H2O PH2O

H 2O H 2O(2.53)2  kaI  kaII  H(1) 2
 C1
From Eq. (2.53), it is disclosed that 𝑖limit is equal to 𝐶1 in Eq. (2.45) and is determinedby the rate constants 𝑘𝑎𝐼 and 𝑘𝑎𝐼𝐼 and the coverage of adsorbed hydrogen in Area 1[𝜃H(1) ; in Eq. (2.22), 𝐾H(ex12) and 𝐾O(ex12) are zero]. Similarly, the model proposed byWilliford and Chick illustrated that the coverage of oxygen at the TPB reaches unity as
the current density approaches the limiting value [8].
In Fig. 2-7(b), it is shown that the anode overpotential is proportional to ln 𝑖 in therange of 𝑖 ≤ 5.7 A/cm2 (Region I), whereas it drastically increases in the range of𝑖≥

5.7 A/cm2 (Region II) because the term [1/(𝐶1 − 𝑖)] in Eq. (2.52) diverges when thecurrent density approaches the limiting value, 𝑖limit (= 𝐶1 ). The drastic increase of anode37

overpotential, as shown in Region II of Fig. 2-7(b), is generally called a concentration
overpotential, which is conventionally explained by gas diffusion in a porous electrode[25-29]. On the other hand, based on the reaction model discussed here, the limit of(a)1
1.00E+01

Current density [A/cm2]

10

Region I

1.00E+00
010

Region II-1
1.00E-01

10

1.00E-02-2

10

1
1.00E-03
10-3

1.00E-13-13 1.00E-12-12 1.00E-11-11 1.00E-10-10 1.00E-09-9 1.00E-08-8 1.00E-07-7 1.00E-06
-6

10

10

10

10

10

10

10

10

Oxygen activity 𝑎O [-](b)
Anode overpotential [V]

0.5
0.4

Region I

0.3

Region II

0.2
0.1

0
0

1

2

3

4

5

6

7

8

Current density [A/cm2]
Figure 2-7. Typical curve of (a) current density as a function of oxygen activity by Eq.
(2.43) and (b) anode overpotential as a function of current density by Eq. (2.52). The
parameters listed in Table 2-3 were used for the calculation.

38

Table 2-3. Assumed partial pressures of H2 and H2O, equilibrium constants,
and reaction rate constants for the calculation of Figures 2-7 and 2-8. All
equilibrium constants and reaction rate constants are the same as those used
for comparison between analytical and experimental results of Ni/YSZ in
Chapter 3.

Parameter

Value

𝑇 [K]

1073

∆𝐺 °𝑓 H2 O [kJ/mol]]-377.372

𝑃H2 at anode [atm]0.57

𝑃H2O at anode [atm]0.03

𝐾H [/atm]

5.5×10-3

𝐾O [-]

1.66×108𝐾H2O [/atm]

3.47×10-4

𝐾 H2O [/atm]

3.47×10-4

𝑘𝑎𝑗 (𝑗 = 𝐼, 𝐼𝐼) [A/cm2]

1.23×103𝑘𝑐𝑗 (𝑗 = 𝐼, 𝐼𝐼) [A/cm2]

2.11×103

current density and concentration overpotential is determined not by gas diffusion
coefficient in a porous anode but by the maximum coverage of the adsorbed species at
the TPB. Similarly, Williford and his coworkers have proposed a model in which theconcentration polarization is controlled by competitive adsorption and surface diffusionnear the TPB, and their model was in good agreement with experimental results [30]. In
addition, some researchers have mentioned that surface processes, such as competitive
adsorption and/or surface diffusion near the TPB, strongly affect the performance ofanodes [8,31,32]. The validity of the reaction model proposed here is discussed based on
a comparison between analytical and experimental results in Chapter 3.

39

2.3.2 Coverages of adsorbed species on Areas 1 and 2
Figure 2-8 shows coverages of adsorbed species on Areas 1 and 2 as a function ofoxygen activity 𝑎O calculated by Eqs. (2.21)–(2.28) with the parameters listed in Table
2-3. In Eqs. (2.21)–(2.28), 𝐾H(ex12) and 𝐾O(ex12) are set to zero. The analytical resultof current density with oxygen activity is also shown in Fig. 2-8. As shown in this figure,coverages on Ni ( 𝜃H(1) , 𝜃H2 O(1) , 𝜃𝑉(1) ) are constant against oxygen activity because
oxygen atom adsorbs only on the oxide ion conductor surface and does not occupy
adsorption site on Ni surface in this model. While vacancy site is dominant, 𝜃H(1) is lessthan 0.1 and 𝜃H2 O(1) is much smaller than all other coverage on Ni. This trend
corresponds to some results predicted by other models [9,10,33]. In the case of oxide ion
conductor surface (Area 2), while coverage of oxygen atom (𝜃O(2) ) increases with 𝑎O
and approaches unity, 𝜃H2 O(2) and 𝜃𝑉(2) decrease because adsorbed oxygen and wateroccupy adsorption sites on Area 2 competitively.
In Region I, the low-current-density area (𝑖 ≤ 5.7 A/cm2), the coverage of adsorbed
oxygen is of the same order as that of adsorbed hydrogen (for example, at 𝑎O = 4.0 ×
10 10 and 𝑖 = 0.39 A/cm2, 𝜃H(1) = 5.3 × 10 2 and 𝜃O(2) = 6.2 × 10 2 ). Therefore,
the amount of excess adsorbed oxygen that is not consumed by adsorbed hydrogen issmall, and 𝜃O(2) is kept to a value less than unity. Schematic of the TPB corresponding
to Region I is shown in Figure 2-9(a).
In Region II, the high-current-density area (𝑖 ≥ 5.7 A/cm2), the amount of adsorbed
oxygen is quite large as compared to that of adsorbed hydrogen (for example, at 𝑎O =3.0 × 10 8 and 𝑖 = 5.8 A/cm2, 𝜃H(1) = 5.3 × 10 2 and 𝜃O(2) = 8.3 × 10 1 ), thesituation corresponding to which is shown in Figure 2-9(b). In other words, the amountof adsorbed hydrogen is not sufficient to consume the adsorbed oxygen. As a result,40𝜃𝑉(1)
1

2
1.00E+02

10

1.00E+00

𝜃H(1)

𝜃H(1)

Coverage 𝜃 [-]10

1
1.00E+01

10

𝜃O(1)

𝜃𝑉(2)
1.00E+00
100

1.00E-04
10-4

𝜃H2 O(1)-6
1.00E-06

10-1
1.00E-01

10𝑖

𝜃H2 O(2)-8
1.00E-08

10

10-10
10

1.00E-10
1.00E-13-13

𝜃H2 O(1)Current density [A/cm2]-2
1.00E-02

𝜃𝑉(1)

𝜃O(2)
𝜃H2 O(2)𝜃𝑉(2)Current
density 𝑖-2
1.00E-02

10

10-3

1.00E-11-11

10

1.00E-09-910

1.00E-07-7

10

1.00E-03
1.00E-05-5

10

Oxygen activity 𝑎O [-]Figure 2-8. Calculated coverages of adsorbed species on the anode as a function ofoxygen activity. Subscript 1 and 2 represents Area 1 (Ni surface) and Area 2 (oxide
ion conductor surface), respectively. The analytical result of current density withoxygen activity is also shown by dotted line. The parameters listed in Table 2-3 wereused for the calculation.

excess adsorbed oxygen occupies the vacancy sites in Area 2, and the coverage of oxygenin Area 2 (𝜃O(2) ) approaches unity, which is followed by the limiting current density,𝑖limit .
As discussed above, the change and limitation of current density can be explainedby the change of coverages of adsorbed species in the species territory adsorption model
because the reaction rate [current density, Eq. (2.42)] is determined by the coverages. In
addition, each coverage in Area 1 or 2 is assumed to be uniform, in other words, surface
diffusion rate of adsorbed species to the TPB is infinity as described in Fig. 2-4. As aresult, the effective width of Area 1 or 2 from the TPB line does not affect the current
density in this model.

41

(a) Region I(b)Region II
TPB

TPB

Ni

Ni
Area 1

Area 2Oxide ion
conductor

Area 1

Area 2Oxide ion
conductor

Figure 2-9. Schematic of the TPB corresponding to (a) Region I (low-current-densityarea) and (b) Region II (high-current-density area).

2.4

Summary
New analytical model for hydrogen oxidation in the TPB of Ni/oxide ion conductor

cermet anode of SOFC, named as species territory adsorption model, was constructed. It
was assumed that the chemical species could be adsorbed within a finite narrow area on
Ni or oxide ion conductor around the TPB. The reaction rate in the anode was controlled
by the surface reaction between the adsorbed hydrogen and adsorbed oxygen; all otherreactions took place under chemical equilibrium. Based on the reaction model, analyticalexpressions of the current density with respect to oxygen activity and the anodeoverpotential with respect to current density could be obtained. The latter could combine
the anode overpotential at low- and high-current-density regions, which wereconventionally expressed independently. Moreover, it was clarified that the current
density asymptotes the limiting value as the oxygen coverage around the TPB approaches
unity. The theoretical limitation of current density given here is determined by the rate
constants of surface reactions and the coverage of adsorbed hydrogen on Ni.

42

References[1] N. Mahato, A. Banerjee, A. Gupta, S. Omar, K. Balani, Prog. Mater. Sci. 72 (2015)
141–337.
[2] W.G. Bessler, M. Vogler, H. Störmer, D. Gerthsen, A. Utz, A. Weber, E. I-Tiffée, Phys.
Chem. Chem. Phys. 12 (2010) 13888–13903.
[3] B.S. Prakash, S.S. Kumar, S.T. Aruna, Renew. Sust. Energ. Rev. 36 (2014) 149–179.
[4] J. Mizusaki, H. Tagawa, T. Saito, T. Yamamura, K. Kamitani, K. Hirano, S. Ehara, T.
Takagi, T. Hikita, M. Ippommatsu, S. Nakagawa, K. Hashimoto, Solid State Ionics
70/71 (1994) 52–58.
[5] A. Bieberle, L.P. Meier, L.J. Gauckler, J. Electrochem. Soc. 148, 6 (2001) A646–A656.
[6] C. Wen, R. Kato, H. Fukunaga, H. Ishitani, K. Yamada, J. Electrochem. Soc. 147, 6(2000) 2076–2080.
[7] M. Ihara, T. Kusano, C. Yokoyama, J. Electrochem. Soc. 148, 3 (2001) A209–A219.
[8] R.E. Williford, L.A. Chick, Surf. Sci. 547 (2003) 421–437.
[9] M. Vogler, A. B-Hütter, L. Gauckler, J. Warnatz, W.G. Bessler, J. Electrochem. Soc.
156, 5 (2009) B663–B672.
[10] D.G. Goodwin, H. Zhu, A.M. Colclasure, R.J. Kee, J. Electrochem. Soc. 156, 9(2009) B1004–B1021.
[11] W. Yao, E. Croiset, J. Power Sources 248 (2014) 777–788.
[12] S. Yano, S. Nakamura, S. Hasegawa, M. Ihara, K. Hanamura, J. Therm. Sci. TechJpn. 4(3) (2009) 431–436.
[13] K. Masuda, M. Ihara, K. Hanamura, Mech. Eng. J. 1(3) (2014) Paper No. 14-00017.
[14] T. Nagasawa, D. Chen, S.Y. Lai, M. Liu, K. Hanamura, J. Power Sources 324 (2016)
282–287.

43

[15] Y. Jin, H. Saito, K. Yamahara, M. Ihara, Electrochem. Solid-State Lett. 12(2) (2009)
B8–B10.
[16] Y. Jin, H. Yasutake, K. Yamahara, M. Ihara, J. Electrochem. Soc. 157(1) (2010)
B130–B134.
[17] Y. Jin, H. Yasutake, K. Yamahara, M. Ihara, Chem. Eng. Sci. 65 (2010) 597–602.
[18] M.J. Powell, Phys. Rev. B 20(10) (1979) 4194–4198.
[19] J. Mizusaki, H. Tagawa, T. Saito, K. Kamitani, T. Yamamura, K. Hirano, S. Ehara, T.
Takagi, T. Hikita, M. Ippommatsu, S. Nakagawa, K. Hashimoto, J. Electrochem. Soc.
141(8) (1994) 2129–2134.
[20] B. de Boer, Ph.D. Thesis, University of Twente, The Netherlands (1998).
[21] M. Shishkin, T. Ziegler, J. Phys. Chem. C 114 (2010) 11209–11214.
[22] C.S. Cucinotta, M. Bernasconi, M. Parrinello, Phys. Rev. Lett. 107 (2011) 206103.
[23] J. Mizusaki, K. Amano, S. Yamauchi, K. Fueki, Solid State Ionics 22 (1987) 313–
322.
[24] 田川博章，固体酸化物燃料電池と地球環境，アグ ネ承風社 (1998). (inJapanese)[25] S. Kakac, A. Pramuanjaroenkij, X.Y. Zhou, Int. J. Hydrogen Energ. 32 (2007) 761–
786.
[26] H. Yakabe, M. Hishinuma, M. Uratani, Y. Matsuzaki, I. Yasuda, J. Power Sources 86(2000) 423–431.
[27] R. Suwanwarangkul, E. Croiset , M.W. Fowler, P.L. Douglas, E. Entchev, M.A.
Douglas, J. Power Sources 122 (2003) 9–18.
[28] J.W. Kim, A.V. Virkar, K.Z. Fung, K. Mehta, S.C. Singhal, J. Electrochem. Soc. 146(1999) 69–78.

44

[29] A.S. Joshi, K.N. Grew, A.A. Peracchio, W.K.S. Chiu, J. Power Sources 164 (2007)
631–638.
[30] R.E. Williford, L.A. Chick, G.D. Maupin, S.P. Simner, J.W. Stevenson, J.
Electrochem. Soc. 150(8) (2003) A1067–A1072.
[31] Y. Shi, N. Cai, C. Li, J. Power Sources 164 (2007) 639–648.
[32] V.P. Zhdanov, Phys. Rev. E 67 (2003) 042601.
[33] W.G. Bessler, J. Warnatz, D.G. Goodwin, Solid State Ionics 177 (2007) 3371–3383.

45

Chapter 3

Comprehensive analysis of Ni/YSZ anode using species
territory adsorption model

3.1

Introduction
As an anode material for SOFCs, a cermet electrode consisting of Ni and YSZ is

widely used because of its high catalytic activity for hydrogen oxidation and of highchemical stability at elevated temperature [1-3]. The hydrogen oxidation at the Ni-YSZgas TPB is one of the key processes in SOFC operation, and numerous efforts have been
made to understand its mechanism from the view point of experimental [4-8], numerical[9-15], or analytical [16,17] approaches. Among them, detailed electrochemical reaction
models based on elementary chemical reactions have been presented by Vogler et al. [9]or Goodwin et al. [10] to explain the experimental results of Ni-patterned anode on YSZ
substrate [7,8], which has well-defined TPB geometry. These models include
adsorption/desorption of the gas-phase species, surface reactions and diffusions ofadsorbed species, and charge transfer processes at the TPB.
Although such multi-step elementary kinetic approaches are useful to investigate
detailed reaction mechanism, it is difficult to combine with numerical simulations atanode microstructure because it requires high computational power and many unknown
parameters. The number of needed parameters such as quantities of state, activationenergy, or frequency factor increases with the number of assumed elementary reactions.

46

Some of those are roughly estimated, taken from different studies, or obtained from fitting
to a limited data set. Therefore, generality and reliability of reaction model and parameters
are still questionable [18,19].
On the other hand, some research groups have recently developed computational
studies of anode reaction based on density functional theory (DFT) in order to investigate
detailed reaction mechanism and obtain reliable kinetic parameters [12-15,19]. Thosestudies essentially do not include any assumption or fitting parameter, however, it isdifficult to predict macroscopic electrochemical properties such as current density,
overpotential, or impedance spectra from DFT calculations directly.
In contrast to above numerical studies, the analytical model constructed in Chapter
2 (species territory adsorption model) gives simple explicit expressions of current density
as a function of oxygen activity, and anode overpotential as a function of current density.
This simple model enables to predict current density or anode overpotential with a small
number of parameters compared to multi-step reaction models reported previously [9,10].
In order to discuss the validation of the species territory adsorption model quantitatively,
the identification of reliable kinetic/thermodynamic parameters and the comparison withexperimental results are needed.
In this chapter, the model parameters for Ni/YSZ anode are determined through thecomparison with several experimental results and the introduction of referenced kinetic
and thermodynamic parameters by DFT calculations. First, the dependence of anodeoverpotential on hydrogen partial pressure is experimentally measured using anelectrolyte-supported single cell with a Ni/YSZ anode. Next, the combination ofreferenced DFT-database and fitting to the measured and reported [17,20] experimental
results gives all reaction parameters. This makes it possible to estimate effective anode47

thickness based on the model. Finally, the analytical results are compared with several
reported experimental results [17,21-25] of Ni/YSZ cermet anodes, and the quantitative
validation of the model and estimated effective anode thickness are discussed.

3.2

Experimental section

3.2.1 Cell fabrication and microstructure characterization
In the current study, an electrolyte-supported button cell with a Ni/YSZ anode and a
LSM/ScSZ cathode was fabricated for the power generation experiment. For theelectrolyte, a YSZ (8 mol% Y2O3-stabilized ZrO2) disk with a diameter of 20 µm andthickness of 300 µm was used. To manufacture the anode, a mixture of NiO, YSZ(NiO:YSZ=66:34 wt.%, corresponds to Ni:YSZ=50:50 vol.%), α-terpineol, and ethyl
cellulose was prepared and coated onto one side of the disk. The disk was dried at 90 ℃
for 12 h and sintered at 1300 ℃ for 4 h in an ambient atmosphere. The cathode wasfabricated using a composite powder of LSM (La0.85Sr0.15MnO3) and ScSZ (10 mol%

(b)

(a)
Anode side
Reference

Cathode side
Working

YSZ disk
20 mm
Figure 3-1. Pictures of (a) anode and (b) cathode side of the single cell used in the
power generation experiment.

48

Sc2O3-1 mol% CeO2-ZrO2) at a weight ratio of 80:20, and the same admixture for theanode paste was used. The paste was coated onto the other side, dried at 90 ℃ for 12 h,and sintered at 1200 ℃ for 4 h in an ambient atmosphere. Both the anode and cathodewere separated into two parts to prepare reference electrodes, as shown in Figure 3-1. The
thickness of the fabricated anode and cathode were about 20 µm and 6 µm, respectively.
The microstructure of the anode was investigated by SEM as shown in Figure 3-2.
Before taking the SEM image, the anode was reduced at 1073 K in hydrogen atmosphere.

(a)

(b)

10 μm

(c)

10 μm

Normalized number [-]

(d)
0.4

Porosity [-]0.3

Mean pore
0.44
diameter [μm]

0.2
0.1
0
0

2 μm

0.51

0.5

1

1.5

2

2.5

Pore diameter [µm]Figure 3-2. (a) SEM image of the cross section of Ni/YSZ anode taken at anacceleration voltage at 30 kV. (b) SEM image taken at 1.0 kV. White and black region
correspond to anode material and pore phase, respectively. (c) Circle approximatedimage of the pore structure of Ni/YSZ anode. (d) Pore size distribution of Ni/YSZ
anode obtained by an approximation that circles are inscribed to pores in the binarized
image. Porosity and mean pore diameter of the anode is also shown.

49

Then, the sample was infiltrated with an epoxy resin, and the cross-section of the anodewas polished by a cross section polisher in order to obtain a smooth surface. The SEM
images of cross section of the anode were taken at an acceleration voltage of 30 kV (Fig.32(a)) and 1.0 kV (Fig.3-2(b)). In Fig. 3-2(b), white and black part shows the material andepoxy resin (correspond to pore), respectively. The binarized images of Fig. 3-2(b) gives
the porosity of anode, 0.51, which is close to the value of Ni/YSZ (Ni:YSZ=50:50 vol.%)measured by FIB-SEM, 0.49 [26]. The pore size distribution was obtained by anapproximation that circles are inscribed to pores in the binarized image [27], which isshown as Fig. 3-2(c). Fig. 3-2(d) shows the pore size distribution of Ni/YSZ anode. From
this analysis, mean pore diameter of the anode, 0.44 µm, was obtained.

3.2.2

Experimental setup of fuel cell operation
Figure 3-3(a) shows a schematic of a flow line for the power generation experiment.

A mixture of humid, gaseous H2 and Ar was introduced into the anode side. The total flowrate of the mixture was fixed at 200 mL/min. The partial pressure of hydrogen was
controlled by the flow rate of gaseous H2 and Ar. The humidity was controlled by H2O
produced via oxidation of H2 through mixing with 1~3% O2 gas. On the other hand, pureoxygen was introduced on the cathode side with a flow rate of 60 mL/min. The operating
temperature was fixed at 1073 K throughout the experiment by using an electric furnace.
Figure 3-3(b) shows the detailed schematic of the single cell during power
generation. The single cell was pressed by ceramic tubes of double tube structure. The
cell was fixed with outer ceramic pipes using glass seal. Gold and platinum mesh attached
to top of inner ceramics tubes were used as a current collector, and these meshes were
contacted with the anode and the cathode surfaces, respectively. Pt wires attached to each50

mesh are used for electrochemical measurements. Prior to the power generation
experiment, the anode was reduced in 3%-humidified hydrogen atmosphere at 1073 K for
1 h.

(a)

Electric furnace
Oxidant

Fuel

SOFC
Valve

Exhaust(fuel side)

Exhaust(oxidant side)
Mass flow
controller

H2 Ar O2O2(b)Electric furnace
Au meshPt meshOxidant

Fuel

Ceramic
tube

Pt wireSOFC cell

Glass seal

Figure 3-3. (a) Schematic of a flow line for the SOFC power generation experiment.
(b) Detailed schematic of the single cell during power generation.

51

3.2.3

Electrochemical measurements
In this experiment, I-V characteristics and electrochemical impedance were

measured at 1073 K under four atmospheric conditions of anode side: (𝑃H2 , 𝑃H2 O ) =(0.97,0.03), (0.07,0.03), (0.02,0.03), and (0.015,0.01) atm. The effective electrodearea of the single cell used here was 0.368 cm2. The I-V curves in each condition aresummarized in Appendix C. Observed OCV at (𝑃H2 , 𝑃H2 O ) = (0.97,0.03), (0.07,0.03),(0.02,0.03), and (0.015,0.01) atm were 1.12 (theory: 1.14), 0.991 (1.02), 0.914 (0.959),
and 0.918 (0.997), respectively. Although measured OCV are 1.8~7.9 % lower thantheoretical ones, the magnitude trend toward atmospheric condition is consistent with the

(a)

(b)
𝑖

𝑖0 n 2𝑡

0.3

Impedance plot

Measurement

AR
CR

Anode

CathodeAW-Im(Z) [Ω•cm2]

0.2

CW

Fitting
15.8 Hz

0.1

Equivalent circuit

1000 Hz

0

0.5
-0.1
-0.2

Rohm

Rohm

31623 Hz 1

1.5

R1

R2

R1

R2

CPE1

CPE2

-0.3

Re(Z) [Ω•cm2]

𝑅1

𝜂𝑎 [V]

𝑅2 [Ω•cm2](c)𝑖𝑖 [A/cm2]𝑖𝑖 [A/cm2]

Figure 3-4. (a) Electrical circuit used to measure alternating current impedance. (b)Impedance spectra and fitting curve of Ni/YSZ anode at OCV under (𝑃H2 , 𝑃H2 O ) =(0.97,0.03) atm. The equivalent circuit for the fitting process is also shown. (c) The
mathematical relationship between anode overpotential and polarization resistance R1and R2. 𝑖𝑠 indicates certain (arbitrary) current density.

52

theory. The electrochemical impedance spectra between anode working (AW) andcathode reference (CR) were acquired by applying alternating current 𝑖

𝑖0 n 2𝑡 at

𝑖 = 0 (OCV), 0.082, 0.16, and 0.24 A/cm2 as shown in Figure 3-4(a). Here, the amplitude
𝑖0 was 20 mA and the frequency

was swept from 106 to 10-2 Hz. Figure 3-4(b) showsthe electrochemical impedance spectra (Cole-Cole plots) at OCV under (𝑃H2 , 𝑃H2 O ) =(0.97,0.03) atm. The spectra consist of two arcs around= 1000 and 15.8 Hz, andfitting process using equivalent circuit shown in Fig. 3-4(b) gives the values ofpolarization resistances R1 (high frequency range) and R2 (low frequency range). In thefitting process, ohmic resistance (Rohm) was fixed to the initiation point of high-frequency
arc. All impedance spectra, fitting curves, and obtained Rohm, R1, and R2 are summarizedin Appendix C.
Since the sum of polarization resistances (𝑅1𝑅2 ) corresponds to the gradient of

the anode overoptential to current density (𝑑𝜂𝑎 ⁄𝑑𝑖 ) [28], the anode overpotential 𝜂𝑎 (𝑖)was calculated using following expression:a (is )    R1 (i)  R2 (i)di
is

(3.1)

0

where 𝑖𝑠 indicates certain (arbitrary) current density. The relationship between anodeoverpotential and polarization resistance (𝑅1𝑅2 ) is illustrated in Figure 3-4(c).

Experimental oxygen activity 𝑎O was calculated using following expression:

 2 FEa 
aO  exp  RT 

(3.2)

Here, anode potential 𝐸𝑎 was calculated using 𝜂𝑎 obtained from Eq. (3.1) andexperimentally-observed OCV value as follows.

Ea  a  OCV

(3.3)

53

3.3

Basic formulas and related parameters of the model
The basic formulas of the species territory adsorption model and related

thermodynamic/kinetic parameters are summarized in this section. Figure 3-5 shows aschematic of the TPB consisting of Ni, YSZ, and gas phases. Area 1 and 2 are assumed
finite area on Ni and YSZ which contribute to species adsorption, respectively. All
chemical reactions considered in the model are listed in Table 3-1. As mentioned in
Chapter 2, hydrogen and oxygen are assumed to be adsorbed mainly on the surface areasof Area 1 and 2, respectively. Dissociative adsorption of hydrogen molecule on Ni surface
is well-known phenomena, however, oxygen migration from YSZ bulk to its surface is
not well understood [29]. As shown in Fig. 3-5, an oxygen atom supplied from YSZ bulk
has a possibility to be adsorbed on (i) YSZ surface or (ii) interface between Ni and YSZ.

Ni

H

O

eYSZ
Area 1

Area 2
TPB

Ni

𝑡e

(ii)

YSZ
(i)

YSZ

Figure 3-5. Schematics of the TPB consisting of Ni, YSZ, and gas phases and of theconcept of an effective anode thickness 𝑡e . Area 1 and 2 are assumed finite area on
Ni and YSZ which contribute to species adsorption, respectively. Two possible paths
for oxygen migration (i) and (ii) are shown.

54

Table 3-1. Chemical reactions considered in the model and thermodynamic/kinetic
parameters (physical quantities of state, frequency factor, and activation energy) used
for the calculation of analytical results. Vad represents surface vacancy site. Subscript
ad(1) and ad(2) means Area 1 (Ni surface) and Area 2 (YSZ surface), respectively.
Reaction

Assumption

𝐾, 𝑘

∆𝐻
[kJ/mol]∆[J/(mol•K)] [mol/(s•cm)]

𝐸𝑎𝑐
[eV]

H2

2𝑉ad(1)

2Had(1)Equilibrium

𝐾H

-92(a

-129(a––H2 O

𝑉ad(1)

H2 Oad(1)Equilibrium

𝐾H2O

-18(a

-83(a

–

–

H2 O

𝑉ad(2)-83(bH2 Oad(2)Equilibrium

𝐾 H2 O

-18(b

–

–

𝑉ad(2)

Oad(2)

Equilibrium

𝐾O-171(c-2(c––2Had(1)

Oad(2)

𝑘𝑎𝐼
and
𝑘𝑎𝐼𝐼

–

1.03×10-2(d1.02(eOad(2)

Ratedetermining
step–

2Had(1)H2 Oad(1)andH2 Oad(2)O()

𝑉ad(1)

𝑉ad(2)

2𝑉ad(1)a) Parameters for steam methane reforming on Ni(111) surface obtained from DFT calculations [30].
b) Assumed to be the same as the parameters on Ni(111) surface.
c) Obtained from fitting to the current and reported [17] experimental results of Ni/YSZ cermet anodes.
d) Obtained from fitting to the experimental result of Ni-patterned anode [20].
e) Parameters for surface reaction between Had and Oad, or Had and OHad on Ni(111) surface obtained from
DFT calculations [19].

In the case (i), oxygen atom forms chemical bond to only YSZ surface while it forms toboth YSZ and Ni surface in the case (ii). The favored adsorption site for oxygen atom is
discussed based on the comparison between the model and experiments later.
In this model, current density 𝑖 [A/cm2] is described as a function of oxygen
activity 𝑎O in the YSZ bulk near the TPB, as follows.
i kaI  kaII  K H PH KO aO   kcI K H O PH O  kcII K H O PH O 22

1  K H PH2  K H2O PH2O

2

2

O O

H 2O H 2O2

 1  K a  K  P 
2

(3.4)

In addition to this, the analytical expression of anode overpotential 𝜂𝑎 [V] is described
explicitly as a function of current density 𝑖 as follows:

a 





RT  1  K H 2O PH2O i  C2  G f (H 2O) RT  PH2O 

ln 

ln 

2F 
KO  C1  i 
4F
2F  PH2 where 𝐶1 and 𝐶2 are given by Eqs. (3.6) and (3.7), respectively.

55

(3.5)

C1 

C2 



 kaI  kaII  K H PH

2

1  K H PH2  K H2O PH2O2 ilimit   kaI  kaII  H(1) 2

kcI K H2O PH2O  kcII K H 2O PH2O

1  K P  K P 
H H2

(3.6)

(3.7)

2

H2O H2O

Here 𝐶1 corresponds to limiting current density 𝑖limit , which is determined by thecoverage of adsorbed hydrogen in Area 1, 𝜃H(1) , not by gas diffusion coefficient in a
porous anode in this model, as discussed in Chapter 2. In Eqs. (3.4)–(3.7), 𝑃H2 and 𝑃H2 O
are partial pressure [atm] of hydrogen and water vapor at the anode side, respectively. R
is the gas constant [J/(K•mol)] and T is the absolute temperature [K]. 𝐾𝑖 and 𝐾 𝑖 (i =species) express equilibrium constants, and are determined by van’t Hoff equation as
follows.
  H  T S   G 
K  exp    exp RT RT 


Here, ∆𝐺, ∆𝐻, and ∆(3.8)

represent a change of Gibbs free energy, enthalpy, and entropy,

respectively. 𝑘𝑖𝐼 and 𝑘𝑖𝐼𝐼 (i = a: anodic reaction, i = c: cathodic reaction) represents
reaction rate constants for the rate-determining step of this model described in Table 3-1.
The anodic reaction rate constant is determined by Arrhenius-type expression as follows.
 E 
kaI  kaII  zF TPBteff ka  zF TPBteff A exp   act  RT 

(3.9)

Herein, 𝑧 shows a valence (= 2) , 𝐹 the Faraday constant [C/mol], 𝜌TPB the TPB
density per unit volume [cm/cm3], 𝑡e

the electrochemically effective anode thickness[cm], 𝑘 𝑎 the anodic reaction rate constant per unit TPB length [mol/(s•cm)],thefrequency factor per unit TPB length [mol/(s•cm)], and 𝐸𝑎𝑐 [J/mol] the activationenergy. For simplicity, it is assumed that all TPB located in an area within certain distance(𝑡e ) from an anode/electrolyte interface contributes electrochemical reaction uniformly
56while the reaction does not occur in other area as shown in Fig. 3-5. The cathodic
reaction rate constant is determined to satisfy the condition of 𝜂𝑎 = 0 at 𝑖 = 0, that is,

kcI  kcII  G f (H 2O) 
2kaI K O K H
 exp 
K H2O  K H 2O
 2 RT (3.10)

3.4

Identification of parameters for Ni/YSZ anode

3.4.1

Quantities of state and activation energy predicted by DFT
In order to calculate current density or anode overpotential based on Eq. (3.4) or(3.5), quantities of state, such as ∆𝐻 and ∆ , for adsorption equilibrium and kinetic
parameters in reaction rate constants, such as

and 𝐸𝑎𝑐 , for surface reactions

described in Table 3-1 are required. However, it’s difficult to obtain these parametersexperimentally due to the complexities of the heterogeneous reactions on the surface anda short life time of reaction intermediates at high temperature. Therefore, some of thesequantities or parameters are referred from calculated results based on density function
theory (DFT) [19,30]. The quantities of state and kinetic parameters used for the
calculation of analytical results are listed in Table 3-1. In this table, subscripts ad(1) andad(2) represent Area 1 (Ni) and 2 (YSZ) in Fig. 3-5, respectively. Recently, acomprehensive DFT calculation for nickel-catalyzed steam methane reforming (SMR) on
Ni(111) has been conducted by Blaylock et al. [30]. In their work, ∆𝐻 and ∆elementary reactions of SMR on Ni(111) are presented. Here, ∆𝐻 and ∆for 36for H2 andH2O adsorption reactions on Ni are referred from their work.
In addition to this, activation energy for surface reaction between Had and Oad, or Had
and OHad on Ni(111) predicted by DFT has been presented by several groups, which issummarized in literature [19]. In the case of Oad + Had

57

OHad, a range and averaged

value of the reported activation energies are 0.79-1.06 eV and 0.95 eV, respectively. In
the case of OHad + Had

H2Oad, those are 0.87-1.23 eV and 1.09 eV, respectively. Here,the value of 1.02 eV which is an arithmetic average of 0.95 and 1.09 is used for 𝐸𝑎𝑐 in
Eq. (3.9). In contrast to abundant information on Ni, thermodynamic and kinetic data sets
on YSZ are insufficient or not well established [9,10]. Unlike the well-defined atomic
structure of Ni, YSZ atomic structure varies according to concentrations and positions ofZr, Y, O, and oxygen vacancy, which strongly affect surface reactivity and bulk property
of YSZ predicted by DFT [31]. In the current work, ∆𝐻 and ∆for H2O adsorption on

YSZ surface were assumed to be the same as those on Ni(111) surface. This assumption
should not be a problem because the results depend very weakly on these values in thismodel, which will be discussed in section 3.5. Finally, four unknown parameters, ∆𝐻and ∆between oxygen atom adsorbed on YSZ surface and in its bulk (described as∆𝐻O(2) and ∆ O(2) , respectively), effective anode thickness 𝑡e , and frequency factor
in Eq. (3.9) are remained. Determination process of these values are presented in thefollowing section.

3.4.2

Parameters identified through fitting to the experimental results∆𝐻O(2) and ∆ O(2) are determined through fitting to experimental results measured

in this study (section 3.2) and reported by Ihara et al. [17]. In the calculation of analyticalresults, 𝑃H2 and 𝑃H2 O inside the porous anode are needed. The variation of H2
concentration at anode/electrolyte interface from bulk gas composition ∆𝐶H2 [mol/m3]
can be roughly estimated by Fick’s first law as follows [32]:C H 2 ti
2 FDeff(3.11)

where 𝑡 is the anode thickness [= 20 µm from Fig. 3-2(a)], 𝑖 the current density [A/m2],58

and 𝐷e
𝐷e

the effective diffusivity in porous media [m2/s]. In the case of H2-H2O system,

is described as follows [33].

Deff 


T 1.75DH H O   4.28 104 
Ptotal2(3.12)

2

Here, 𝜀 is the porosity [= 0.51 from Fig. 3-2(d)], 𝜏 the tortuosity factor (= 1.96 fromthe FIB-SEM observation by Iwai et al [26]), and 𝑃total the total pressure (= 1.013×105
Pa). Even in the condition of highest fuel utilization of 15.7 % (0.24 A/cm2 at 𝑃H2 = 0.02
atm), the estimated decrease in H2 concentration at the anode/electrolyte interface
compared to anode surface is less than 0.13 %. Therefore, 𝑃H2 and 𝑃H2 O inside theporous anode are set to the same as supplied gas compositions in this study.
The fitting results of Eq. (3.4) or (3.5) to the experimental results of this study and
Ihara et al. [17] are shown in Figures 3-6 and 3-7, respectively. In experiments at low
𝑃H2 , the region where current density reaches or asymptotes to limiting current density(𝑖limit ) can be observed as shown in (𝑃H2 , 𝑃H2 O ) = (0.02, 0.03) and (0.015, 0.01) atm in
Fig. 3-6 or (𝑃H2 , 𝑃H2 O ) = (0.05, 0.01) atm in Fig. 3-7(a). In the model proposed here,
𝑖limit corresponds to C1 in Eq. (3.6) and is a function of the product of 𝑡e

and

(𝑡e

)

while independent of ∆𝐻O(2) and ∆ O(2) . The comparison between Eq. (3.6) andexperimentally-observed 𝑖limit gives unique value of the product 𝑡e
this study and Ref. [17], respectively. Here, 𝑡e𝑡e

for an anode in

is different for each reference because

should depend on an anode microstructure used in each experiment, especially YSZ

network [4]. The identification of 𝑡e

is followed by that of ∆𝐻O(2) and ∆ O(2) ,which are determined to achieve a best fit to all experimental results presented in Figs. 36 and 3-7. From a comparison between degrees of freedom of Oad(2) and O(YSZ), ∆ O(2)should be a negative value because Oad(2) can move two-dimensionally while O(YSZ) can59

three-dimensionally. Under this constraint condition, ∆𝐻O(2) = −171 kJ/mol and∆ O(2) = −2 J/(mol•K) are obtained by fitting with experimental data sets.
The fitting of the model to Ni-patterned anode experiments gives a value of
frequency factor

precisely. Figure 3-8 shows the fitting result of the model to Ni-

patterned anode experiment by B.de. Boer [20]. Here, ∆𝐻O(2) and ∆ O(2) are fixed tothe same values obtained above, that is, -171 kJ/mol and -2 J/(mol•K) respectively. As aresult,= 1.03 × 10 2 mol/(s•cm) is obtained from a fitting of Eq. (3.5) toexperimental results. Based on the value of, 𝑡e = 1.50 µm for this study and 1.79

µm for Ref. [17] were obtained from fitted value of the product 𝑡e

3.4.3

.

Estimation of effective anode thickness for reported Ni/YSZ experiments
From a comparison between Eq. (3.5) and experimentally-observed anodeoverpotential in various references, 𝑡eof each experiment can be estimated because allother unknown parameters, ∆𝐻O(2) , ∆ O(2) , and, have been already identified. Here,experimental results of four Ni/YSZ anodes reported previously [21-25] are comparedwith present model, and each 𝑡e

is estimated. The fitting results of the model toexperiments are shown in Figures 3-9 for Ref. [21], 3-10 for [22], 3-11 for [23], and 3-12
for [24,25]. The 𝜌TPB and estimated effective anode thickness 𝑡eof all experiments

referred in this chapter are summarized in Table 3-2. Values of 𝜌TPB of the anode usedin this study and Ref. [17] are estimated by weight ratio of NiO and YSZ based on thedata sets corrected by a FIB-SEM [34]. For other four experiments [21-25], measured
value by the FIB-SEM is presented. From Table 3-2, the value of 𝑡e

has a range from

1.12 to 2.39 µm in six Ni/YSZ anodes. The obtained fitting results and estimated 𝑡e
discussed in the following section 3.5.

60

are

Figure 3-6. Fitting of the model to Ni/YSZ anode experiments in this study todetermine the product 𝑡e , ∆𝐻O(2) , and ∆ O(2) . Analytical results in (a) and (b) are
obtained by Eq. (3.4) and (3.5), respectively. The dependence of (a) current density or(b) anode overpotential on hydrogen partial pressure are shown.

61

(a)
Ana. Exp. [17] (𝑃H2, 𝑃H2O ) (atm)(1.0, 0.01)(0.3, 0.01)(0.1, 0.01)(0.05, 0.01)

1.00E+022

Current density [A/cm2]

10

1
1.00E+01

10

T =1173 K

0
1.00E+00

10-1
1.00E-01

10-2
1.00E-02
1.00E-13
-13

10

10

1.00E-12-12

10

1.00E-11-11

10

1.00E-10-10

10

1.00E-09-910

1.00E-08-8

10

1.00E-07-7

10

1.00E-06-6

10

Oxygen activity 𝑎O [-](b)Ana. Exp. [17]1.00E+022

Current density [A/cm2]

10

T
973 K
1023 K
1173 K
1273 K

1.00E+011

10

1.00E+000

10-1
1.00E-01

10

𝑃H2 = 1.0 atm
𝑃H2O = 0.01 atm-2
1.00E-02

10-3
1.00E-03
1.00E-15
-15

10

10

1.00E-13-13
10

1.00E-11-11
10

1.00E-09-910

1.00E-07-7

10

1.00E-05-5

10

Oxygen activity 𝑎O [-]Figure 3-7. Fitting curves of Eq. (3.4) to Ni/YSZ anode experiments by Ihara et al.
[17] to determine the product 𝑡e , ∆𝐻O(2) , and ∆ O(2) . (a) and (b) shows thedependence of current density on hydrogen partial pressure and temperature,
respectively.

62

1Current density [A/cm2]

1.E+002

TPB = 570 cm/cm

10-1

1.E-01

𝑇 = 1123 K
𝑃H2 = 0.977 atm
𝑃H2O = 0.023 atm-2
1.E-0210-3
1.E-0310

Ni-patterned anode experiment by B.de. Boer [20]Fitting curve of Eq. (3.5)
𝑖0 used in LBM simulation by Shikazono et al. [24]-41.E-0410-5
1.E-0510

1.E-06
-6

10

0

0.1

0.2

0.3

Anode overpotential [V]Figure 3-8. Fitting curve of Eq. (3.5) to Ni-patterned anode experiment by B.de Boer[20] to determine a frequency factor
for hydrogen oxidation. Exchange current
density used in LBM simulation by Shikazono et al. [24] is also shown.

Table 3-2. Experimental data sets of Ni/YSZ cermet anode used for the comparison
with analytical results and estimated effective anode thickness.
ExperimentElectrode𝜌[µm/µm3]𝑡[µm]

Condition

This study

Ni/YSZ cermet
NiO 66 wt%

2.58(a1.50

𝑇 = 1073 K
𝑃H2 = 0.015 − 0.97 atm
𝑃H2O = 0.01 − 0.03 atm

Ihara et al. [17]Ni/YSZ cermet
NiO 60 wt%

2.66(a

1.79

𝑇 = 973 − 1273 K
𝑃H2 = 0.05 − 1 atm
𝑃H2O = 0.01 atm

Kishimoto et al. [21]Ni/YSZ cermet
Ni 50 vol%2.49(b

1.35

𝑇 = 1073 − 1273 K
𝑃H2 = 0.8 − 0.97 atm
𝑃H2O = 0.03 − 0.2 atm

Matsui et al. [22]Ni/YSZ cermet
Ni 50 vol%2.49(b

2.39

𝑇 = 1273 K
𝑃H2 = 0.6 − 0.97 atm
𝑃H2O = 0.03 − 0.4 atm

Kanno et al. [23]Ni/YSZ cermet
NiO 60 vol%2.11(b

1.12

𝑇 = 1023 − 1123 K
𝑃H2 = 0.8 − 0.97 atm
𝑃H2O = 0.03 − 0.2 atm

Shikazono et al. [24] andKishimoto et al. [25]Ni/YSZ cermet
Ni 50 vol%2.556(b(active TPB:
56.8 % [26])2.24(3.95 based on
active TPB)

𝑇 = 1273 K
𝑃H2 = 0.9 − 0.988 atm
𝑃H2O = 0.012 − 0.1 atma) Estimated by weight ratio of NiO and YSZ based on the data sets corrected by FIB-SEM [34].
b) Measured value by FIB-SEM.

63

Figure 3-9. Fitting curves of Eq. (3.5) to Ni/YSZ anode experiments by Kishimoto etal. [21] to determine 𝑡e . Parameters in Table 3-1 are used for calculation of analyticalresults. The dependence of anode overpotential on temperature is shown.

Figure 3-10. Fitting curves of Eq. (3.5) to Ni/YSZ anode experiments by Matsui et al.
[22] to determine 𝑡e . Parameters in Table 3-1 are used for calculation of analyticalresults. The dependence of anode overpotential on steam partial pressure at 1273 K isshown.
64

Figure 3-11. Fitting curves of Eq. (3.5) to Ni/YSZ anode experiments by Kanno et al.
[23] to determine 𝑡e . Parameters in Table 3-1 are used for calculation of analyticalresults. The dependences of anode overpotential on (a) steam partial pressure at 1073
K and (b) temperature at (𝑃H2 , 𝑃H2 O ) = (0.97, 0.03) atm are shown.

65

Figure 3-12. Fitting curves of Eq. (3.5) to Ni/YSZ anode experiments from Refs.
[24,25] to determine 𝑡e . Parameters in Table 3-1 are used for calculation of analyticalresults. The dependence of anode overpotential on steam partial pressure at 1273 K isshown. Dashed lines show anode overpotential calculated in LBM simulation by
Shikazono et al. [24].

3.5Discussions

3.5.1

Dependence on fuel compositions and temperature
The dependences of current density with oxygen activity 𝑖(𝑎O ) [Eq. (3.4)] andanode overpotential with current density 𝜂𝑎 (𝑖) [Eq. (3.5)] on hydrogen partial pressure,steam partial pressure, and temperature are discussed based on obtained fitting results.
As shown in Figs. 3-6(a) and 3-7(a), as the hydrogen partial pressure 𝑃H2 decreases,
both the experimental and the analytical current densities shift in the direction of higher

66

oxygen activity on the horizontal axis. That is, in order to obtain the same current density,a higher oxygen activity is required. In Eq. (3.6), it is clear that the value of 𝑖limit
decreases with decreasing 𝑃H2 . Following the decrease in 𝑖limit , the current density,𝑖(𝑎O ), shifts in the direction of higher oxygen activity on the horizontal axis. In the caseof 𝑃H2 ≤ 0.05 atm in Figs. 3-6(a) and 3-7(a), the experimental current densities
asymptote 𝑖limit with increasing oxygen activity 𝑎O , which are in good agreement withanalytical results based on the model.
From the analytical and experimental results under the conditions of (𝑃H2 , 𝑃H2 O ) =(0.97, 0.03), (0.07, 0.03), and (0.02, 0.03) atm in Fig. 3-6(b), it is clear that the anodeoverpotential is not strongly affected by 𝑃H2 in the low-current-density range (𝑖 ≤ 0.1
A/cm2). In the case of (𝑃H2 , 𝑃H2 O ) = (0.015, 0.01) atm, the anode overpotential around
0.1 A/cm2 is higher than those for the other three fuel composites. Moreover, in the caseof (𝑃H2 , 𝑃H2 O ) = (0.015, 0.03) atm, the calculated anode overpotential around 0.1 A/cm2
is relatively close to the anode overpotentials of (𝑃H2 , 𝑃H2 O ) = (0.97, 0.03), (0.07, 0.03),
and (0.02, 0.03) atm. Therefore, the increase in overpotential around 0.1 A/cm2 of (𝑃H2 ,𝑃H2 O ) = (0.015, 0.01) atm is a result of the decrease in humidity from 0.03 to 0.01 atm.
On the other hand, the anode overpotential increases drastically as the current density
approaches the limiting current density (=C1) in Eq. (3.6), as discussed in Chapter 2. In
the case of (𝑃H2 , 𝑃H2 O ) = (0.02, 0.03) and (0.015, 0.01) atm, 𝑖limit based on Eq. (3.6) is
0.27 and 0.20 A/cm2, respectively. At the region where the current density approaches
these values, the experimental plots follows the analytical trends. Wen et al. [16]investigated the dependence of the anode overpotential of a Ni/YSZ cermet anode on afuel composition, which clarified that an anode overpotential is independent of hydrogenconcentration while decreases with increasing humidity in hydrogen fuel. Their results

67

show the same trend as the present analytical and experimental results in the low-currentdensity range (𝑖 ≤ 0.1 A/cm2).
In order to discuss the 𝑃H2 and 𝑃H2 O dependence of anode overpotential, thecalculated variations ∆ of anode overpotential [Eq. (3.5)], 1st term, and 2nd + 3rd termsof Eq. (3.5) from standard condition at 1073 K and 0.1 A/cm2 are shown as a function of
𝑃H2 and 𝑃H2 O in Figures 3-13(a) and (b), respectively. The standard condition is set to𝑃H2 = 0.97 atm for Fig. 3-13 (a) and 𝑃H2 O = 0.01 atm for Fig. 3-13(b). From Fig. 313(a), the incremental of 1st term and decrement of 2nd + 3rd terms due to the decrease
in 𝑃H2 are balanced, which results in the constant 𝜂𝑎 over a wide range of 𝑃H2 . On the

(a)
∆𝜂𝑎

Variation fromstandard condition [V]0.3Standard condition(𝑃H2 = 0.97 atm)

0.2
0.1

1

0

-0.1

0

-0.2

0.2

0.4

0.6

0.8

1

𝐶2

3
∆𝐺𝑓° H2 O
𝑃H2 O
𝑅𝑇
=∆ −
−
ln
4𝐹
2𝐹
𝑃H2

𝑃H2O = 0.03 atm, T = 1073 K-0.3

𝐾 H2 O 𝑃H2 O 𝑖
𝐾O 𝐶1 − 𝑖2n※𝑖 = 0.1 A/cm2 in all cases.

𝑃H2 [atm](b)(c)
Variation fromstandard condition [V]0.5

Variation fromstandard condition [V]

1
𝑅𝑇
ln
2𝐹

=∆

Standard condition(𝑃H2O = 0.01 atm)

0.25
0
0

0.2

0.4

0.6

0.8

1

-0.25

-0.5

𝑃H2 = 1 - 𝑃H2O atm, T = 1073 K

0.04

Standard condition(T = 973 K)

0.02
0
-0.02

873

973

1073

1173

1273

1373

-0.04
-0.06

(𝑃H2, 𝑃H2O )=(0.97, 0.03) atm-0.08

𝑃H2O [atm]𝑇 [K]Figure 3-13. Calculated variations ∆ of anode overpotential [Eq. (3.5)], 1st term, and2nd + 3rd terms of Eq. (3.5) from standard condition as a function of (a) 𝑃H2 , (b)𝑃H2 O , and (c) T. The standard condition of (a), (b), and (c) is 𝑃H2 = 0.97 atm,
𝑃H2 O = 0.01 atm, and T = 973 K, respectively. Current density is fixed to 0.1 A/cm2
in all cases, and other calculated conditions are denoted in each graph.

68other hand, the incremental of 1st term is smaller than the decrement of 2nd + 3rd terms
due to the increase in 𝑃H2 O . Consequently 𝜂𝑎 decreases with increasing 𝑃H2 O , as shownin Fig. 3-13(b). The fitting results in Figs. 3-6(b), 3-9, 3-10, 3-11(a), and 3-12 shows thatthe model represents the 𝑃H2 O dependence of 𝜂𝑎 well in the range of 0.01 ≤ 𝑃H2 O ≤0.2 atm. At high humidity (𝑃H2 O = 0.2 − 0.4 atm) in Fig. 3-10, however, the model
predicts that the anode overpotential becomes lower with increasing humidity, which does
not agree with experimental trend. One possible explanation of this disagreement is thesurface oxidation of Ni caused by increased equilibrium 𝑃O2 with humidity at anode side
as mentioned previously [35].
The temperature dependence of 𝑖(𝑎O ) and 𝜂𝑎 (𝑖) can be also discussed based on
the model. Fig. 3-7(b) discloses that as the temperature increases, the analytical current
densities shift toward high oxygen activity on the horizontal axis. This trend is in good
agreement with experimental results by Ihara et al. [17]. The shift in the direction of thehigh oxygen activity mainly results from the change of 𝐾O . In this model, the terms of
𝐾O and 𝑎O always appear as a product, 𝐾O 𝑎O , as shown in Eqs. (2.21)–(2.28). In
addition, 𝐾O decreases with increasing temperature through Eq. (3.8), which results inthe shift of 𝑖(𝑎O ) in the direction of high oxygen activity on the horizontal axis. On theother hand, analytical curves in Fig. 3-7(b) also indicate that temperature does notstrongly affect 𝑖limit [Eq. (3.6)]. This is because the coverage of adsorbed hydrogen in
Area 1, 𝜃H(1) , decreases with increasing temperature, while anodic reaction rate
constants, 𝑘𝑎𝐼 and 𝑘𝑎𝐼𝐼 increase through Arrhenius-type expression [Eq. (3.9)].
As shown in Figs. 3-9 and 3-11(b), the analytical results of anode overpotential
decrease with increasing temperature, which agrees well with the experimental results.
The calculated variations ∆ of anode overpotential [Eq. (3.5)], 1st term, and 2nd + 3rd

69

terms of Eq. (3.5) from standard condition (𝑇 = 973 K) at 0.1 A/cm2 are shown as afunction of 𝑇 in Figures 3-13(c). From this figure, both 1st term and 2nd + 3rd terms
decrease with increasing temperature, which is followed by the decrease in anodeoverpotential.

3.5.2 Effective anode thickness
Figure 3-14 summarizes effective anode thickness estimated by present model withrespect to temperature, which is replotted from Table 3-2. From Fig. 3-14, a general trend
is seen in six anodes: 𝑡eincreases with temperature. As Miyawaki et al. pointed out[36], effective anode thickness is dominated by the balance between electrochemical
reaction rate at the TPB and oxide ion conductivity in the YSZ phase, both of which
increase with temperature. Fig. 3-14 indicates that when temperature increases, theenhancement of oxide ion conductivity is larger than that of electrochemical reaction rate,
resulting in an increase in the effective anode thickness. The same trend was reported in
the numerical simulation by Miyawaki et al. [36].
Although the trend of increased 𝑡equantitative discussion of 𝑡efactorwith temperature is observed in Fig. 3-14,

is still difficult because it strongly depends on frequency, that is, what kind of Ni-patterned anode experiment is selected as a basic data.

Here, the analytical results based on our model are compared with LBM simulation by
Shikazono et al. [24]. This is because in their work, exchange current density per unit
TPB length for Butler-Volmer equation were obtained from Ni-patterned anodeexperiment by B.de Boer [20], which is the same one used in this study as shown in Fig.
3-8. In addition, active TPB ratio, 56.8%, is also presented in their microstructure [26],which has continuous networks of Ni from TPB to current collector, of YSZ to electrolyte,

70This study
Ihara et al. (2001) [17]Kishimoto et al. (2011) [21]Matsui et al. (2010) [22]Kanno et al. (2011) [23]Shikazono et al. (2010) [24] andKishimoto et al. (2012) [25]Linear fit

Effective anode thickness [µm]

3
2.5
2
1.5
1
0.5
923

1023

1123

1223

1323

Temperature [K]Figure 3-14. Correlation between temperature and effective anode thickness estimatedby the fitting of present model to experimental results. Error bar shows the temperature
range and plot represents the average temperature in each experiment. The data is
replotted from Table 3-2.

and of pore to inlet gas phase. This can lead to quantitatively more precise value of 𝑡e ,3.95µm. The comparison of anode overpotentials at 1273 K obtained by experiments[24,25], current model, and LBM simulation from Shikazono et al [24] is shown in Fig.
3-12. The LBM simulation overestimates the anode overpotential at a high humidity (10%
H2O). The same trends are observed in other simulations at practical anode microstructure[21,23,25]. In those works, it was mentioned that the dependence of exchange current
density on gas compositions assumed in the simulations possibly causes the discrepancy.
On the other hand, dependence on steam partial pressure is well reproduced by the present

71Ionic current density 𝑖ion [A/cm2]

𝑖ion (𝑧) by species territory adsorption model0-0.1

𝑖ion(𝑧) at 1.2% H2O by LBM [24]

-0.2
-0.3

YSZ

Ni/YSZ

Current
collector

20

25

-0.4
-0.5

𝑡e
= 3.95

-0.6

𝑧

-0.7
0

5

10

15

30

Position 𝑧 [µm]Figure 3-15. Ionic current density distributions at 1273 K in anode thickness direction𝑧, 𝑖ion (𝑧), estimated by the model and calculated by the LBM simulation [24]. The
distribution by the model is based on the assumption that all active TPBs at 𝑧 ≤ 𝑡econtributes electrochemical reaction uniformly while the reaction does not occur inother area.
model. As shown here, if the same Ni-patterned anode experiment is selected as a basic
data, the present model can predict more precise dependence of anode overpotential on
steam partial pressure than that by Butler-Volmer equation with empirical exchange
current density.
Figure 3-15 shows ionic current density distributions at 1273 K in anode thickness
direction 𝑧, 𝑖ion (𝑧), estimated by the model and calculated by the LBM at 1.2% H2O[24]. Under the condition, experimental results are in good agreement with thosepredicted by LBM simulations in Fig. 3-12. Here, 𝑖ion (𝑧) estimated by the model islinear because the distribution is based on the assumption that all active TPBs at 𝑧 ≤ 𝑡e(= 3.95µm) contributes electrochemical reaction uniformly while the reaction does not72

occur in other area. In Fig. 3-15, the LBM result is consistent with the linear profile bypresent model at 𝑧 ≤ 1.5 µm. On the other hand, |𝑖ion (𝑧)| by the LBM is larger thanthat by present model at 𝑧 ≥ 1.5 µm. This indicates that in the LBM, all active TPBs at𝑧 ≤ 1.5 µm uniformly contribute electrochemical reaction while the reaction at 𝑧 ≥ 1.5µm is not uniform. In order to predict an non-uniform ionic current density distribution
in porous anode, numerical simulation, such as LBM, needs to be conducted instead ofevaluation of 𝑡ethrough fitting. The above discussion indicates that the introduction ofpresent model into numerical simulation instead of Butler-Volmer equation can give moreaccurate prediction of anode polarization. One proposed scheme is as follows. At first,
oxygen chemical potential distribution 𝜇O (𝒓) is calculated by numerical simulation [24,37]. Here, 𝒓 shows a position vector in an electrode. Then, a local oxygen activity𝑎O (𝒓) in an electrode is obtained as follows [38]  (r )  O 
aO (r )  exp  O

RT



(3.13)

where 𝜇O0 is 𝜇O of 1 atm O2 gas. Finally, local charge-transfer current density 𝑖(𝒓)[A/cm3] is obtained from 𝑎O (𝒓) and Eq. (3.4) divided by 𝑡e .

3.5.3 Sensitivity analysis
In this section, the effect of 𝜃H2 O(2) and 𝜃O(2) on calculated anode overpotential
was discussed through a sensitivity analysis because ∆𝐻 and ∆for H2O adsorption on

YSZ (described as ∆𝐻H2 O(2) and ∆ H2 O(2) , respectively) were assumed to be the sameas those on the Ni(111) surface, and for O adsorption on YSZ (∆𝐻O(2) and ∆ O(2) ) were
determined through the fitting to the experimental results, as shown in Section 3.4. The
effect ∆𝐻H2 O(2) and ∆𝐻O(2) values on anode overpotential and coverages adsorbed

73

species on YSZ (𝜃O(2) , 𝜃H2 O(2) , 𝜃𝑉(2) ) were investigated under the condition of (𝑃H2 ,𝑃H2 O ) = (0.97, 0.03) atm at 1073 K.
Figure 3-16(a) shows the analytical results of anode overpotential with current
density at ∆𝐻H2 O(2) = 100, -18, and -100 kJ/mol. Anode overpotential does not vary
when ∆𝐻H2 O(2) is increased from -18 to 100. On the other hand, anode overpotential

Figure 3-16. (a) Analytical results of anode overpotential with current density at∆𝐻H2 O(2) = 100, -18, and -100 kJ/mol under the conditions of (𝑃H2 , 𝑃H2 O ) = (0.97,
0.03) atm and T = 1073 K. Experimental result is the same as in Fig. 3-6(b). (b)-(d)The corresponding calculated coverages of adsorbed species on YSZ as a function ofoxygen activity at (b) ∆𝐻H2 O(2) = 100, (c) -18, and (d) -100 kJ/mol. The analyticalresult of current density with oxygen activity is also shown by dotted line.

74

slightly increases when ∆𝐻H2 O(2) is decreased from -18 to -100. Figures 3-16(b)–(d)show the coverages of adsorbed species on YSZ and the current density as a function of𝑎O at ∆𝐻H2 O(2) = 100, -18, and -100 kJ/mol, respectively. Even though 𝜃H2 O(2)increases from 10-11 to 10-1 with decreasing enthalpy ∆𝐻H2 O(2) from 100 to -100 kJ/mol,
both any other coverage on YSZ and the current density do not change significantly. As

Figure 3-17. (a) Analytical results of anode overpotential with current density at∆𝐻O(2) = -188, -171, and -154 kJ/mol under the conditions of (𝑃H2 , 𝑃H2 O ) = (0.97,
0.03) atm and T = 1073 K. Experimental result is the same as in Fig. 3-6(b). (b)-(d)The corresponding calculated coverages of adsorbed species on YSZ as a function ofoxygen activity at (b) ∆𝐻O(2) = -188, (c) -171, and (d) -154 kJ/mol. The analyticalresult of current density with oxygen activity is also shown by dotted line.

75

vacancy site is dominant on YSZ, an increase in coverage 𝜃H2 O(2) does not affect 𝜃O(2) ,resulting in the weak impact of ∆𝐻H2 O(2) or 𝜃H2 O(2) on anode overpotential and current
density.
The impact of ∆𝐻O(2) on the analytical results of anode overpotential is shown in
Figure 3-17(a). From this figure, it is disclosed that only 10% change of ∆𝐻O(2) fromthe fitted value (from -171 to -188 or -154 kJ/mol) causes 2-3 times variation of anodeoverpotential. Figures 3-17(b)–(d) show the coverages of adsorbed species on YSZ and
the current density as a function of 𝑎O at ∆𝐻O(2) = -188, -171, and -154 kJ/mol,
respectively. As ∆𝐻O(2) increases from -188 to -154 kJ/mol, 𝜃O(2) decreases in twoorders of magnitude, resulting in one order of magnitude decrease of current density. As
shown in Eq. (2.42), anodic current is proportional to 𝜃O(2) while independent of
𝜃H2 O(2) in this model. Therefore, anode overpotential and current density are strongly
affected by ∆𝐻O(2) and almost independent of ∆𝐻H2 O(2) at the region where anodic
current is dominant, as shown in Figs. 3-16 and 3-17.

3.5.4 Insights into oxygen migration process
At the end of this chapter, an oxygen migration process is discussed based on themodel. From the fitting process in the section 3.4, ∆𝐻O(2) should be a large negativevalue; -171 kJ/mol. This means that oxygen migration from YSZ bulk to its surface near
the TPB is an exothermic reaction. Similar trend was reported in DFT study by Cucinotta
et al. [13]. Their calculation indicates that by filling the vacancy at Ni/YSZ interface withoxygen atom migrated from YSZ bulk, the potential energy of the reaction systemdecreases by about 81.9 kJ/mol. Although this energy gap is smaller than fitted ∆𝐻O(2)value obtained here, qualitative trend is consistent.

76

Alternatively, it could be interpreted that an oxygen atom supplied from YSZ bulk
is adsorbed on the interface between Ni and YSZ as shown in path (ii) of Fig. 3-5 since
the standard enthalpy of formation of NiO, -239.7 kJ/mol [39] is relatively close to thefitted ∆𝐻O(2) . The large negative value of ∆𝐻O(2) is possibly attributed to the enthalpyof chemical bond formation between oxygen atom and Ni surface. Most of recent DFT
calculations of hydrogen oxidation at Ni/YSZ anode [12-15] concluded that energeticallyfavored path involves the reaction between hydrogen atom on Ni and oxygen atom boundto both Ni and YSZ, which is consistent with reaction path (ii) of Fig. 3-5.
As discussed in the sensitivity analysis in Fig. 3-17, parameters related to the oxygen
migration process and the oxygen coverage on YSZ have a great impact on current density
and anode overpotential. This result indicates that the dynamics of oxygen atom in thebulk and on the surface near the TPB, which is discussed here, is a key process for theenhancement of fuel oxidations and the improvement of anode performance. In order tounderstand the reaction mechanism of hydrogen oxidation at the anode and obtain new
guidelines for the advanced SOFC anode design with higher electrochemical performance,
precise dynamics of oxygen atom near the TPB should be further investigated andclarified.

3.6

Summary
The quantitative validation of the species territory adsorption model for Ni/YSZ

anode was discussed based on the comparison to measured and reported experimental
results. By introducing referenced thermodynamic and kinetic parameters predicted by
DFT calculations, the model can predict anode overpotential using unknown values ofquantities of state for oxygen migration process in YSZ near a TPB, frequency factor for77hydrogen oxidation, and effective anode thickness. The former two were determinedthrough careful fitting process between the model and experimental results of Ni/YSZ
cermet and Ni-patterned anodes. This makes it possible to estimate effective anode
thickness based on the model. The estimated effective thicknesses for six Ni/YSZ anodes
used in this study and several references show positive correlation with temperature. In
addition, the comparison between results obtained by proposed model and by a publishednumerical simulation indicates that if the same Ni-patterned anode experiment is selected
as a basic data, the present model can predict more precise dependence of anodeoverpotential on steam partial pressure than that by Butler-Volmer equation with
empirical exchange current density. This suggests that the introduction of present model
into numerical simulation instead of Butler-Volmer equation can give more accurate
prediction of anode polarization. Moreover, the sensitivity analysis showed that the model
parameters related to the oxygen migration process and the oxygen coverage on YSZ havea great impact on current density and anode overpotential. This result indicates that the
dynamics of oxygen atom in the bulk and on the surface near the TPB is a key process forthe enhancement of fuel oxidations and the improvement of anode performance.

78References[1] J. Hanna, W.Y. Lee, Y. Shi, A.F. Ghoniem, Prog. Energy Combust. Sci. 40 (2014) 74–
111.
[2] R.J. Gorte, J.M. Vohs, Annu. Rev. Chem. Biomol. Eng. 2 (2011) 9–30.
[3] A. Atkinson, S. Barnett, R.J. Gorte, J.T.S. Irvine, A.J. Mcevoy, M. Mogensen, S.C.
Singhal, J. Vohs, Nat. Mater. 3 (2004) 17–27.
[4] M. Brown, S. Primdahl, M. Mogensen, J. Electrochem. Soc. 147 (2) (2000) 475–485.
[5] S.P. Jiang, S.P.S. Badwal, J. Electrochem. Soc. 144 (11) (1997) 3777–3784.
[6] J. Mizusaki, H. Tagawa, T. Saito, K. Kamitani, T. Yamamura, K. Hirano, S. Ehara, T.
Takagi, T. Hikita, M. Ippommatsu, S. Nakagawa, K. Hashimoto, J. Electrochem. Soc.
141 (8) (1994) 2129–2134.
[7] J. Mizusaki, H. Tagawa, T. Saito, T. Yamamura, K. Kamitani, K. Hirano, S. Ehara, T.
Takagi, T. Hikita, M. Ippommatsu, S. Nakagawa, K. Hashimoto, Solid State Ionics
70/71 (1994) 52–58.
[8] A. Bieberle, L.P. Meier, L.J. Gauckler, J. Electrochem. Soc. 148 (6) (2001) A646–
A656.
[9] M. Vogler, A. B-Hütter, L. Gauckler, J. Warnatz, W.G. Bessler, J. Electrochem. Soc.
156 (5) (2009) B663–B672.
[10] D.G. Goodwin, H. Zhu, A.M. Colclasure, R.J. Kee, J. Electrochem. Soc. 156 (9)(2009) B1004–B1021.
[11] W. Yao, E. Croiset, J. Power Sources 248 (2014) 777–788.
[12] M. Shishkin, T. Ziegler, J. Phys. Chem. C 114 (2010) 11209–11214.
[13] C.S. Cucinotta, M. Bernasconi, M. Parrinello, Phys, Rev. Lett. 107 (2011) 206103.
[14] S.C. Ammal, A. Heyden, J. Phys. Chem. Lett. 3 (2012) 2767–2772.

79

[15] S. Liu, T. Ishimoto, D.S. Monder, M. Koyama, J. Phys. Chem. C 119 (2015) 27603–
27608.
[16] C. Wen, R. Kato, H. Fukunaga, H. Ishitani, K. Yamada, J. Electrochem. Soc. 147 (6)(2000) 2076–2080.
[17] M. Ihara, T Kusano, C. Yokoyama, J. Electrochem. Soc. 148 (3) (2001) A209–A219.
[18] D. Mogensen, J.-D. Grunwaldt, P.V. Hendriksen, K. Dam-Johansen, J.U. Nielsen, J.
Power Sources 196 (2011) 25–38.
[19] S. Liu, T. Ishimoto, M. Koyama, Appl. Surf. Sci. 333 (2015) 86–91.
[20] B.de Boer, Ph.D. Thesis, University of Twente, The Netherlands (1998).
[21] M. Kishimoto, H. Iwai, M. Saito, H. Yoshida, J. Power Sources 196 (2011) 4555–
4563.
[22] T. Matsui, R. Kishida, J.Y. Kim, H. Muroyama, K. Eguchi, J. Electrochem. Soc. 157(5) (2010) B776–B781.
[23] D. Kanno, N. Shikazono, N. Takagi, K. Matsuzaki, N. Kasagi, Electrochimica Acta
56 (2011) 4015–4021.
[24] N. Shikazono, D. Kanno, K. Matsuzaki, H. Teshima, S. Sumino, N. Kasagi, J.
Electrochem. Soc. 157 (5) (2010) B665–B672.
[25] M. Kishimoto, H. Iwai, M. Saito, H. Yoshida, J. Electrochem. Soc. 159 (3) (2012)
B315–B323.
[26] H. Iwai, N. Shikazono, T. Matsui, H. Teshima, M. Kishimoto, R. Kishida, D. Hayashi,
K. Matsuzaki, D. Kanno, M. Saito, H. Muroyama, K. Eguchi, N. Kasagi, H. Yoshida,
J. Power Sources 195 (2010) 955–961.
[27] S. Uemura, D. Fukabori, S. Tsushima, S. Hirai, Transactions of the JSME, Ser. B 78
(785) (2012) 74–82 (in Japanese).

80[28] E. Siebert, A. Hammoucha, M. Kleitz, Electrochim. Acta 40 (11) (1995) 1741–1753.
[29] M. Shishkin, T. Ziegler, J. Phys. Chem. C 113 (2009) 21667–21678.
[30] D.W. Blaylock, T. Ogura, W.H. Green, G.J.O. Beran, J. Phys. Chem. C 113 (2009)
4898–4908.
[31] M. Shishkin, T. Ziegler, Phys. Chem. Chem. Phys. 16 (2014) 1798–1808.
[32] S. Primdahl, M. Mogensen, J. Electrochem. Soc. 146 (8) (1999) 2827–2833.
[33] J.H. Nam, D.H. Jeon, Electrochim. Acta 51 (2006) 3446–3460.
[34] J.R. Wilson, J.S. Cronin, S.A. Barnett, Scr. Mater. 65 (2011) 67–72.
[35] K. Eguchi, Y. Kunisa, K. Adachi, H. Arai, J. Electrochem. Soc. 143 (11) (1996) 3699–
3703.
[36] K. Miyawaki, M. Kishimoto, H. Iwai, M. Saito, H. Yoshida, J. Power Sources 267(2014) 503–514.
[37] K. Matsuzaki, N. Shikazono, N. Kasagi, J. Power Sources 196 (2011) 3073–3082.
[38] J. Mizusaki, K. Amano, S. Yamauchi, K. Fueki, Solid State Ionics 22 (1987) 313–
322
[39] S. Seki (Ed.), Kagaku Binran-Kiso II, second ed. Handbook of Chemistry-basic II(1975) pp. 962, Maruzen, Tokyo (in Japanese).

81

Chapter 4

Imaging of microstructure-scaled active sites in porouscomposite cathode4.1

Introduction
Porous composite electrodes are widely used for state-of-the-art SOFCs, such as

Ni/YSZ for anodes or LSM/YSZ for cathodes. These electrodes have micro/nano-scalecomplex structures consisting of electron conductors, oxide ion conductors, and porephases, where chemical species are transported and accompanied by electrochemical
reactions at the TPB. The distributions of active reaction sites and the transport paths ofions and electrons greatly affect the electrode performance, which has been intensively
investigated by numerical modeling and simulations [1-5]. However, experimental
information about active reaction site distribution or oxide ion paths in the microstructureof the composite electrode has not been reported so far. Imaging active sites in composite
electrodes can verify numerical results and attain new guidelines to optimize its
microstructures for further improvement of SOFC performance and stability. In addition,oxygen migration process near the reaction site has not been well understood [6] though
the process strongly affects electrochemical performance of an anode, as discussed in
Chapter 3. Tracking oxide ion paths near the TPB of composite electrodes can givevaluable information related to the detailed reaction mechanisms. Therefore, an imaging
technique of active sites and oxide ion flows in porous composite electrodes should be82

realized and developed in microstructure scale.
Atomic labeling using oxygen isotope is a powerful tool to visualize active sites andoxide ion flows in SOFC materials, which has been mainly applied to thin film electrodes
with well-defined geometries at low temperatures (573-973 K) to clearly distinguishoxygen incorporation sites from other parts [7-9]. Oxygen isotope exchange using Pt
electrode on YSZ electrolyte under cathodic polarization was conducted at 973 K by
Kawada et al. [7], showing that Pt/YSZ/gas TPBs are active sites. In the case of LSM/YSZ
system, Horita et al. [8] showed that both TPB and LSM bulk paths are active. In addition,effective TPB width of Pt thin film cathode on YSZ was investigated at about 600 K by
Fleig et al. [9]. In the case of composite electrodes operated at a practical temperature(~1073 K), however, it seems hard to identify active sites in the zirconia phase because
the incorporated isotope diffuses quickly into the whole area of YSZ or ScSZ, forming a
micron/submicron-scaled percolation structure and resulting in a uniform concentrationof 18O. Although overall oxide ion flows from cathode to anode sides in a practical SOFC
was visualized using a 18O labeling by Horita et al. [10], active reaction sites have notbeen observed in an electrode particle scale so far.
In this study, the LSM/ScSZ porous cathode is selected as a target for active sites
imaging. Although lanthanum cobaltite and ferrite cathodes, such as (La,Sr)CoO3 (LSC)or (La,Sr)(Co,Fe)O3 (LSCF), are more active for oxygen reduction, LSM-based cathodes
are the most practical because LSM is more thermodynamically stable than mixed
conductors containing cobalt or iron [5,11,12]. In addition, a thermal expansion match
between LSM and YSZ makes it easier to fabricate a wide variety of cathodemicrostructures and cell geometries [12]. In the LSM/ScSZ (YSZ) system, both the TPB
between the LSM-ScSZ and gas phases, and the double phase boundary (DPB) between

83,

DPB path
TPB path
LSM,

TPB path
DPB path

ScSZ,

Figure 4-1. Two oxygen reduction pathways at the LSM/ScSZ cathode [15]. Oxygen
atoms are incorporated from the gas phases into the ScSZ bulk in the TPB path while
into the LSM bulk in the DPB path.

the LSM and gas phases work as active sites for oxygen reduction [13-16]. Figure 4-1
shows a schematic of two oxygen reduction pathways in the LSM/ScSZ system given in
kinetic study of oxygen vacancy formation of LSM by Jiang et al. [15]. At a low current
density, oxygen reduction mainly proceeds at the TPB denoted by a TPB path.
1O2  2e-  VO,ScSZ  OO,ScSZ
2Here, 𝑉O,∙∙ c

and O×O, c(4.1)

represent an oxygen vacancy and O2− in the ScSZ bulk,

respectively. At a high current density, the remaining electrons are provided to theinterface between LSM and ScSZ because not all the electrons can be consumed at the
TPB. This is followed by the partial reduction of Mn3+ to Mn2+ accompanied by thegeneration of oxygen vacancies in the LSM bulk, as follows:

OO,LSM  2e-  VO,ScSZ  2Mn  OO,ScSZ  VO,LSM  2Mn

84

(4.2)

×
∙∙
2−
Here, OO,L
M and 𝑉O,L M show the oxide ion, O , and an oxygen vacancy in the LSM

bulk, respectively. Moreover, Mn∙ represents a normal Mn3+ ion, while Mn× represents a
reduced state, e.g. Mn2+. The generated oxygen vacancy diffuses to the LSM surface andrecombines with oxygen gas (DPB path in Fig. 1) with the re-oxidation of Mn2+ to Mn3+,
as follows:
1
O2  VO,LSM  2Mn  OO,LSM  2Mn
2

(4.3)

This means that with an increasing charge transfer current, oxygen reduction sites are
expanded from a TPB to a DPB, and oxygen diffusion is promoted into the LSM bulk.
Indeed, the enhanced 18O diffusion into the LSM bulk with increasing cathodic
polarization has been confirmed by several isotope exchange experiments using thin film
cathodes [13,17]. The oxygen tracer diffusion coefficient of LSM is seven orders ofmagnitude smaller than that of ScSZ [18,19]; thus, the oxygen isotope incorporated into
LSM diffuses only about 10 nm during 1 min annealing in 18O2 at 1073 K, and is expected
to remain inside the same particle (the concentration of 18O depends strongly on theactivity of oxygen reduction). Consequently, the isotope oxygen inside the LSM works
as an active site ‘detector’.
In this chapter, visualization technique of active reaction sites in SOFC porous
electrodes with microstructure scale is developed. In order to quench a reaction, a SOFC
power generation equipment with a nozzle for direct helium gas impinging jet to the cellis prepared, and its cooling performance is evaluated. Using constructed quench systemand oxygen isotope labeling, active sites for oxygen reduction reaction in LSM/ScSZ
porous cathode are visualized in microstructure scale. An electrolyte-supported cell isoperated in 18O2 at 1073 K and subsequently quenched to a room temperature. Then, the18O distribution in cross section of the cathode is obtained by secondary ion mass85

spectroscopy (SIMS) with a spatial resolution of 50 nm. Finally, the active sites
distribution is discussed based on the obtained 18O concentration images.

4.2

Experimental section

4.2.1

Power generation equipment with quench system

In order to quench a reaction in a SOFC cell during isotope exchange experiment, apower generation equipment with a nozzle for a helium impinging jet was prepared. As
shown in Figure 4-2(a), the flow system includes 18O2 supply and recirculation lines atcathode side and helium lines at both anode and cathode sides. 4-way and 6-way valves
are used to change gas atmospheres quickly for anode and cathode sides, respectively.
The 18O2 recirculation line is used when long-time (> 3 min) 18O2 anneal is needed in anexperiment. Figure 4-2(b) shows a details of the quench system. Inside an electric furnace,a single cell is fixed with ceramic tubes using a glass seal. A Pt wire attached to the cellis used for electrochemical measurement. Inside the ceramic tubes, nozzles with adiameter of 1 mm, which are covered by a water cooling jacket and a thermal insulator,
are set at both anode and cathode sides. In this equipment, an inside of the nozzle can be
kept at a room temperature while the SOFC cell is operated at 1073 K (The detailed
thermal design of the developed quench system is presented in Appendix D). The operated
cell is abruptly cooled by supplying helium gas of 10 L/min, which is equivalent to a flow
velocity of 213 m/s at an outlet of the nozzle. The impinging jet and high thermal
conductivity of He, which is one order of magnitude larger than that of typical gases suchas Air, N2, or Ar [20], enhance a heat transfer, resulting in a high cooling rate. A
photograph of the nozzle is shown in Figure 4-2(c). The cooling performance of theequipment was experimentally evaluated and discussed. The details of the experiment are

86

(a)

Electric furnace
Oxidant

6-way valve

Fuel

SOFC

Exhaust(oxidant side)

Exhaust
Mass
flow
meter

18O
2

FilterPump

Recirculation
system

4-way valve

Exhaust(fuel side)
ExhaustValve
3-way valve

ExhaustMass flow
controller

Exhaust

O2 He

Flow
meter
H2 Ar

He

(c)

(b)
Electric furnace

NozzlePt wireNozzleWater
jacketHeat insulator

Glass seal

Heat insulator

He gas

SOFC
cell

Ceramic tube

Figure 4-2. Power generation equipment with quench system for isotope exchange
experiment. (a) Schematic of a flow line for the SOFC power generation experimentin 18O2 atmosphere. The system is equipped with a 18O2 recirculation pump and He
flow line. (b) Detailed schematic of the quench system inside electric furnace. A nozzle
for helium impinging jet is covered by water cooling jacket and heat insulator. (c)Photograph of the nozzle for quenching.

presented with the results and discussion in section 4.3.

4.2.2 Cell fabrication
As shown in Figure 4-3(a), an electrolyte-supported cell was used in this work. For
the electrolyte, a YSZ (8 mol% Y2O3-stabilized ZrO2) disk with a diameter of 20 mm andthickness of 300 µm was used. To manufacture the anode, a mixture of NiO, YSZ (weight

87

X

(a)
Reference electrode
Thermocouple

B

A
e-

e-

X’

C

Electric lead
(Pt wire)

Current
collector(Silver paste)
Ni/YSZ anodeC

X

LSM/ScSZ cathode

Electric leadX’YSZ electrolyte(b)CathodeElectrolyte

Figure 4-3. (a) Electrolyte-supported cell with working and reference electrodes usedin this study. SIMS images were obtained from sections A, B, and C. In the middle
figure, area of cathode working and attached current collector (silver paste) is
described by C and, respectively. (b) SEM image of the cross section of
LSM/ScSZ cathode.

ratio of NiO:YSZ=66:34), α-terpineol, ethyl cellulose, a dispersant, and a plasticizer was
prepared and coated onto one side of the disk. The disk was dried at 90 ℃ for 12 h andsintered at 1300 ℃ for 4 h in an ambient atmosphere. The cathode was fabricated using
a composite powder of LSM (La0.8Sr0.2MnO3-δ) and ScSZ (10 mol% Sc2O3-1 mol% CeO2ZrO2) at a weight ratio of 50:50, and the same admixture for the anode paste was used.
The paste was coated onto the other side, dried at 90 ℃ for 12 h, and sintered at 1200 ℃

88

for 4 h in an ambient atmosphere. Both the anode and cathode were separated into twoparts to prepare reference electrodes, as shown in Fig. 4-3(a). The thicknesses of thefabricated anode and cathode were about 20 µm and 25 µm, respectively. The SEM imageof the cross section of the cathode is shown in Figure 4-3(b). Pt wire was attached toworking electrodes as an electric lead using a current collector of silver paste (Heraeus,
C8728). In the middle of Fig. 4-3(a), area of cathode working and attached current
collector (silver paste) is described byCandcovered by a current collector was about 50 % (, respectively. The electrode area
⁄ C

= 0.5) in this study. A K-type

thermocouple was also attached to the anode reference using silver paste to monitor thecell temperature.

4.2.3

Power generation in 18O2 and quench experiment

Initially, the cell was operated in 50% H2 and 50% Ar for the anode side and in 100%
normal O2 for the cathode side at 1073 K for 10 min under a constant current density of
0.14 A/cm2. Then, the normal O2 was switched to 18O2 (>97.5%, Center of Molecular
Research), and the cell was operated for 3 min. Finally, the cell was abruptly quenched toa room temperature by the helium impinging jet of 10 L/min at both anode and cathodesides. Since fuel and oxidant were also supplied through water-cooled nozzles in thisexperiment, high flow rate causes a decrease in temperature during fuel cell operation.
Therefore, the total flow rate of each side was fixed to relatively low value, 30 mL/min.
The amount of supplied H2 and O2 seems to be sufficient for the power generation because
fuel and oxygen utilization during operation at 0.14 A/cm2 is 2.3 % and 0.6 %,respectively.

89

4.2.4 SIMS analysis
The 18O distribution in a cross section of the quenched cathode was obtained bysecondary ion mass spectroscopy (SIMS) with a spatial resolution of 50 nm (CAMECA,
NanoSIMS 50L). Before the SIMS analysis, pores of the sample were infiltrated with an
epoxy resin; then, the cross section of the cathode was polished using a cross section
polisher (JEOL, SM-09010CP) to obtain a smooth surface. A focused Cs+ primary ion
beam (beam diameter: ca. 100 nm) was scanned on the polished surfaces and secondary
ions were detected by a double-focusing magnetic sector mass spectrometer. Here, thedistributions of four secondary ions (16O-, 18O-, 55Mn16O-, and 90Zr16O-) were analysed.

4.3

Results and discussion

4.3.1

Evaluation of cooling performance
Cooling performance of the developed system was evaluated using two YSZ disks asshown in Figure 4-4(a). A K-type thermocouple with a diameter of 0.127 mm was fixed
between two YSZ electrolyte disks using silica glue. This sample was set to the equipment
described in Fig. 4-2(b), a temperature was monitored during a quenching, and the results
were compared with an analytical solution of heat conduction equation. YSZ plane wallwith a thickness of 600 µm was assumed for the calculation of heat conduction as shownin Figure 4-4(b). Both surfaces of the wall were cooled by a helium impinging jet, andthe temperature change of the center (point A) was calculated based on both local Nusselt
number at stagnation point, 𝑁𝑢𝑚𝑎𝑥 , and average Nusselt number in the region with adiameter of 20 mm, 𝑁𝑢𝑎𝑣𝑒 . 𝑁𝑢𝑚𝑎𝑥 is calculated as follows [21].

Numax  5.97Pr 0.5 ReD0.5  H D 

0.1

(4.4)

90

(a)

(b)

600 µmYSZ plane𝐷

φ20 mmThermocouple(φ0.127 mm)

Nozzle𝑉He

He gasA

Stagnation
point

Silica glue
YSZ disc𝐻

0

300 µm(c)

QuenchTemperature [oC]

1000

ExperimentAnal., 𝑁𝑢𝑚𝑎𝑥
Anal., 𝑁𝑢𝑎𝑣𝑒

800
600
400
200
0
-1

0

1

2

3

4

5

Elapsed time [s]Figure 4-4. Evaluation of cooling performance. (a) Thermocouple between two YSZelectrolytes attached by silica glue for temperature measurement. (b) Assumed
geometry for calculation of heat conduction equation. 𝑉He is a flow velocity ofejected helium. (c) Experimental and analytical results of temperature change at thecenter of electrolyte [point A in (b)] during quenching using He impinging jet. Twoanalytical results based on average and local Nusselt number are shown.

Here, 𝐻 is a distance between the nozzle and wall (= 12 mm), and 𝐷 is a diameter ofthe nozzle (= 1 mm). 𝑅𝑒𝐷 is calculated by the representative length 𝐷 and the velocity
of ejected helium 𝑉He (= 213 m/s). 𝑁𝑢𝑎𝑣𝑒 is obtained by following formula [21].

91DNuave  r

1  1.1Dr

H
D
1  0.1  6 
D
r

0.5

 2 ReD

0.5

 ReD 0.55 
0.42
1 
  Pr
200 


(4.5)

where 𝑟 is a radius of the region for the average (=10 mm). As a result, 𝑁𝑢𝑚𝑎𝑥 = 160
and 𝑁𝑢𝑎𝑣𝑒 = 6.77 are obtained. Analytical lines in Figure 4-4(c) are exact solutions of
1-dimensional unsteady-state heat conduction equation for plane wall under the boundary
condition of the third kind with above Nusselt numbers [22].
In the experiment, one side of the sample was exposed to 50% H2-50% Ar andanother to pure O2 at 830 ℃ for a few minutes, subsequently the sample was cooled to aroom temperature by changing the gas to helium of 10 L/min. Fig. 4-4(c) shows
experimental and analytical results of temperature change during quenching. At 𝑡 = 0
sec., gas atmosphere was quickly changed to helium. As shown in Fig. 4-4(c), thetemperature of YSZ electrolyte could be decreased from 830 to 150 oC within 1.5 sec.,
which was in good agreement with analytical results based on the average Nusselt number
𝑁𝑢𝑎𝑣𝑒 . The cooling rate obtained here (1.5 sec.) is much faster than the previous ones (ca.
20 sec. ~ several minutes) by blowing inert gas to a wall of a reactor tube [7,8,13,17]. The
analytical results based on 𝑁𝑢𝑚𝑎𝑥 predict that it takes only 0.2 sec. to decrease thetemperature from 830 to 150 oC, which is much faster than experimental results.
Based on the obtained temperature profiles in Fig. 4-4(c), diffusion length of oxygen
atom during quenching was estimated. As shown in Figure 4-5(a), 1-dimensional semiinfinite solid of YSZ is assumed and relative 18O concentration profile is obtained by solving
a diffusion equation numerically. Before the quench, 18O is assumed to exist only near the
TPB (x = 0), which is denoted by ‘Initial’ in Figure 4-5(b). There is no 18O flux at x = 0 andan oxygen diffusivity in YSZ bulk 𝐷bulk [m2/s] at each temperature is calculated by

92

(a)

TPB

18O

Diffusion

YSZ

Relative concentration of
isotope oxygen 18O [-](b)
1

Initial (t = 0 s)
t = 5 s, T = Exp.
t =5 s, T = Anal. (𝑁𝑢𝑚𝑎𝑥)t = 5s, T = Anal. (𝑁𝑢𝑎𝑣𝑒 )

0.8
0.6
0.4
0.2
0
0

1

2

3

4

5

6

Distance from TPB

[µm]

7

8

Figure 4-5. (a) Schematic of 18O diffusion in 1-dimensional semi-infinite solid of YSZ.
(b) Numerical results of relative 18O concentration profile in YSZ bulk in 5 sec. after
quench has been started.

following experimental relation [23].

Dbulk  8.0 107 exp  1.11eV kBT (4.6)

Fig. 4-5(b) shows 18O concentration profile (t = 5 sec.) after the sample is cooled enoughin Fig. 4-4(c). Based on the experimental temperature profile, 18O diffuses maximum 4
μm from TPB and an obvious concentration difference is observed between locations at
x = 0 and 2-3 μm. This indicates that the quench can suppress 18O diffusion length withina scale of 2-3 YSZ particles with diameter of 1 μm. Fig. 4-5(b) also indicates thatquenching with 𝑁𝑢𝑚𝑎𝑥 can give an obvious 18O concentration difference between
locations at x = 0 and 1 μm.

4.3.2 Electrochemical performance and monitored temperatureFirst, the initial I-V characteristics and electrochemical impedance of the cell usedin the isotope exchange were measured at 1073 K, as shown in Figures 4-6(a) and (b),respectively. The impedance spectra were measured between anode working and cathodeworking at 0.14 A/cm2. The cell showed a maximum power density (𝑃max ) of 0.085

93

(a)

(b)
0.1
0.08

1
0.8

0.06

0.6

0.04

0.4

0.02

0.2

0.4
0.3

-Im(Z) [Ω•cm2]

1.2

Power density [W cm-2]
Power density [W/cm2]

voltage
Terminalvoltage[V][V]
Terminal

1.4

𝑅ohm

0.2
0.1

0
-0.1 1.5

2

2.5

-0.2

0
0

4

𝑖 = 0.14 A/cm2

0.1

0.2

0.3

-0.4

0.4

Re(Z) [Ω•cm2]

Current density [A/cm2]

(d)

(c)
Normal O2

18O
2

Quench𝑖 = 0.14 A/cm2

0.8

1073

0.6
0.4

0.2
0
0

200

400

Power
generation Quench
1273

1

Temperature [K]Terminal voltage [V]

3.5

-0.3

0

Terminal voltage [V]

3

600

800

1000

873

673
473
273

Elapsed time [s]

-2

0

2

4

6

8

Elapsed time [s]Figure 4-6. (a) Initial performance of the cell used in the isotope exchange at 1073 K.
Mixture of 50% H2 – 50% Ar and pure oxygen were supplied as a fuel and oxidant,
respectively. (b) Impedance spectra at 0.14 A/cm2 measured between anode working
and cathode working. (c) Terminal voltage versus elapsed time with a constant current
density of 0.14 A/cm2. (d) Temperature change of the cell during quenching measured
by the thermocouple in Fig. 4-3(a).

W/cm2 and overall ohmic resistance (𝑅ohm ) of 2.16 Ω•cm2, which is larger than the value
estimated for 𝑅ohm from the ionic conductivity [24] and thickness of the YSZ electrolyte(1.50 Ω•cm2). This comes from the small contact area between the electrode and current
collector [25], and is discussed later. While a constant current density of 0.14 A/cm2 wasapplied, the cell showed an almost stable terminal voltage of about 0.56 V until quenching
reaction as shown in Figure 4-6(c). In the quenching process, the temperature of the cellmeasured by the thermocouple in Fig. 4-3(a) decreased from 1073 K to 673 K in 1 sec.,94

as shown in Figure 4-6(d). This rapid cooling makes it possible to keep the electrode inan operational state by suppressing the diffusion length of the oxide ion within about 3µm in ScSZ [19] and 1 nm in LSM [18]. The cooling rate observed here was a little bit
smaller than the rate in the quench performance test [Fig. 4-4(c)], which maybe resulted
from the difference of the position of thermocouples in Figs. 4-3(a) and 4-4(a).

4.3.3 Secondary ion mappings
In this study, SIMS images at the interface between the cathode and electrolyte weretaken from different three sections A, B, and C in Fig. 4-3(a). Section A is a part of cathodereference and represents OCV (non-biased) condition while both sections B and C areplaced in cathode working (biased condition). Since several studies suggested an
inhomogeneous current density distribution induced by non-uniform contact between
cathode and current collector [25,26], SIMS images at section B (biased, far area fromcurrent collector) and C (biased, directly under the contact area of the current collector)
were collected here. Figures 4-7, 4-8, and 4-9 show the secondary ion mappings at
sections A, B, and C, respectively. In these figures, (a) shows a phase mapping of LSM
and zirconia based on the intensity of Mn16O- and Zr16O-, and (b) shows an 18O
concentration (= 𝑐18O ) mapping represented by I(18O-)/[I(16O-) + I(18O-)]. Here, I(16O-)
and I(18O-) indicate the SIMS signal intensity of each ion. Obtained 𝑐18O value means aratio of the number of 18O atom to the total number of oxygen atom in arbitrary volume.
Prior to the calculation of 𝑐18O image, binarization processing is performed on the 16Oimage to remove all signal from pore phases. From the phase mapping images, the LSM,
zirconia (ScSZ, YSZ), and pore phases can be distinguished clearly in microstructure
scale.

95

Section A (non-biased)(a)Electrolyte
Cathode(b)
Red: Mn16OLight blue: Zr16OBlack: Pore

Electrolyte

c18O

Cathode

Ⅰ

Ⅰ

1

1

Figure 4-7. Secondary ion mappings of the interface between the LSM/ScSZ cathodeand YSZ electrolyte obtained from section A (non-biased) in Fig. 4-3(a). (a) Phasemapping of each material. Red and light blue represent Mn16O- (LSM) and Zr16O(ScSZ, YSZ), respectively. The black regions show the pore phases. (b) Oxygenisotope concentration (= 𝑐18O ) mapping represented by I(18O-)/[I(16O-) + I(18O-)].

As shown in Fig. 4-7(b), 18O is uniformly distributed in the ScSZ phase with 𝑐18O ≈0.25, while an almost natural value of

𝑐18O = 0.002 is observed inside the LSM bulk

under no current condition. 18O exchanges with lattice oxygen of ScSZ surface (surface
exchange) and diffuses to inside ScSZ bulk (tracer diffusion) under non-biased condition
while does not diffuse to inside LSM bulk due to a low oxygen tracer diffusivity of LSM[18].
In SIMS image at section B shown in Fig. 4-8(b), 18O is distributed only inside the
ScSZ bulk with 𝑐18O ≈ 0.25 as in the case with non-biased condition (section A) though96Section B (biased, far from the current collector)
(a)

(b)

Red: Mn16OLight blue: Zr16OElectrolyte
Cathode Black: Pore

Electrolyte
Cathodec18OFigure 4-8. Secondary ion mappings of the interface between the LSM/ScSZ cathodeand YSZ electrolyte obtained from section B (0.14 A/cm2-biased, far area from thecurrent collector) in Fig. 4-3(a). (a) Phase mapping of each material. Red and light
blue represent Mn16O- (LSM) and Zr16O- (ScSZ, YSZ), respectively. The black regions
show the pore phases. (b) Oxygen isotope concentration (= 𝑐18O ) mapping representedby I(18O-)/[I(16O-) + I(18O-)].

section B is a part of cathode working. This means that a cathode area far from a current
collector is almost inactive. The correlation between this result and electrochemical
impedance spectra is discussed in section 4.3.4.
At section C shown in Fig. 4-9(c), an almost uniform 18O distribution in ScSZ witha considerably higher 𝑐18O ≈ 0.55 compared to that in section A or B is observed. By
supplying a current, the 18O concentration in ScSZ becomes higher because ofincorporated oxygen by the electrochemical reaction. However, the TPB where 18O is

97

Section C (biased, near the current collector)(a)(b)
Red: Mn16OLight blue: Zr16OBlack: Pore

Electrolyte
CathodeElectrolyte

3

3
Ⅲ

Ⅲ

Ⅱ
4

c18O

Cathode

Ⅱ
4

5

5

Ⅳ

Ⅳ

2

2

Figure 4-9. Secondary ion mappings of the interface between the LSM/ScSZ cathodeand YSZ electrolyte obtained from section C (0.14 A/cm2-biased, directly under thecontact area of the current collector) in Fig. 4-3(a). (a) Phase mapping of each material.
Red and light blue represent Mn16O- (LSM) and Zr16O- (ScSZ, YSZ), respectively. The
black regions show the pore phases. (b) Oxygen isotope concentration ( = 𝑐18O )mapping represented by I(18O-)/[I(16O-) + I(18O-)]. The high resolution images in Fig.
4-12 were taken at the area surrounded by dashed lines.

incorporated could not be distinguished because of the fast tracer diffusion inside ScSZ
[19]. In contrast, we can observe a non-uniform 18O concentration image inside the LSM
at section C, and the details are discussed in section 4.3.5.

4.3.4 Effect of contact area between cathode and current collector
As shown in Fig. 4-8(b), the SIMS image at section B indicates that the area far fromthe current collector is not active. In order to explore this result, the effect of a contact

98

(a)

(b)

Cell A

Cathodereference

Cell B

Cathode working
YSZ electrolyte
Silver paste
Lead wire (Pt)
20 mm

(c)

(d)
0.3

𝑅ohm

Cell A
Cell B-Im(Z) [Ω•cm2]

0.5
0
1

2

3

-0.5

4

𝑅 ol,cCell A
Cell B

0.15

5-Im(Z) [Ω•cm2]

1

0
1

1.2

1.4

1.6

1.8

2

-0.15
-0.3

-1

Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2]

Figure 4-10. (a,b) Photographs of cathode side of (a) cell A and (b) cell B used in
power generation experiment to investigate the effect of contact area between cathodeand current collector on the electrochemical performance. (c,d) Impedance spectra ofcell A and B under OCV condition at 1073 K measured between (c) anode working
and cathode working and (d) cathode working and cathode reference.

area between cathode and current collector on the electrochemical performance wasinvestigated using conventional power generation equipment shown in Fig. 3-3 in Chapter
3. The same single cells as used in the isotope exchange experiment were prepared. The
electrochemical measurements were conducted at 1073 K. As a fuel and oxidant, 3%humidified hydrogen and pure oxygen were supplied, respectively. Total flow rate ofanode and cathode side is 200 mL/min and 60 mL/min, respectively. Current wascollected by pressing Au mesh for anode side, and by attaching Ag paste for cathode side.
In this experiment, the impedance spectra of two cells, cell A and B, with different ratio99

Table 4-1. The effect of contact area between cathode and current collector on overallohmic resistance and cathode polarization resistance under OCV condition at 1073 K.
Cell

Raito of cathode area covered by current
collector (Ag paste),/ C [%]Overall ohmic resistance𝑅ohm [Ω•cm2]

Cathode polarization resistance𝑅 ol,c [Ω•cm2]

Cell A

76.5

2.04

0.43

Cell B

89.3

1.59

0.30

of cathode area covered by Ag paste (⁄ C ) were collected. Photographs of two cells

are shown in Figures 4-10(a) and (b). The overall ohmic resistance Rohm was obtained
from impedance spectra at OCV measured between anode working and cathode working
as shown in Figure 4-10(c), and the cathode polarization resistance Rpol,c was measured
between cathode working and cathode reference in Figure 4-10(d).

⁄ C , 𝑅ohm , and𝑅 ol,c of two cells are summarized in Table 4-1.
From Table 4-1, both 𝑅ohm and 𝑅 ol,c decrease with increasingcase of cell B (⁄ C⁄ C . In the= 89.3%), measured 𝑅ohm = 1.59 Ω•cm2 is relatively close to

the estimated value of 300µm-thickness YSZ, 1.5 Ω•cm2 [24]. These results indicate thata cathode area far from a current collector does not contribute to the electrochemical
reaction and oxide ion/electron conduction, which support the SIMS observation resultsin Fig. 4-8. Several former works also show that cathode polarization increases withdecreasing a contact area between cathode and current collector [25,26].

4.3.5 Line profile analysis of 18O concentration mappings
As shown in Fig. 4-9(b), the non-uniform distribution of 18O concentration wasobserved inside the LSM at section C. 𝑐18O profiles inside several LSM particles
denoted by lines 2 to 5 in Fig. 4-9 are shown in Figure 4-11. As a comparison, a 𝑐18O
profile of the LSM at OCV condition, which is indicated by line 1 in Fig. 4-7, is also100Line 1 (OCV, Section A)
Line 2 (Biased, Section C)
Line 3 (Biased, Section C)
Line 4 (Biased, Section C)
Line 5 (Biased, Section C)
Fitting by Eq. (4.8)
LSM/gas interface

The other LSM/gas interface

0.2

𝑐18O [-]

0.15
0.1
0.05
0
0

0.2

0.4

Position

0.6

0.8

1

[µm]

Figure 4-11. 𝑐18O line profiles inside LSM particles denoted by line 1 in Fig. 4-7 andlines 2 to 5 in Fig. 4-9. Positive direction in position x corresponds to each arrow
direction in Figs. 4-7 and 4-9. Fitting curves of Eq. (4.8) to the profiles of line 1 and 5
are also shown.

shown. From Fig. 4-11, typical monotonically decreasing diffusion profiles are observedin line 1 and 5. On the other hand, 𝑐18O profiles near the cathode/electrolyte interface(lines 2 to 4) have a maximum value inside a LSM bulk, not at a surface. This can beclearly observed in high-resolution SIMS images shown in Figure 4-12. Fig. 4-12 was101

taken at the area surrounded by dashed lines in Fig. 4-9 with a beam diameter of ca. 50
nm. The phase mapping and 18O concentration are not exactly corresponds to that in Fig.
4-9 because the measured plane in Fig. 4-12 was deeper than that of Fig. 4-9. The original
surface in Fig. 4-9 was a little bit removed by high-intensity primary ions, which wasemitted by changing the SIMS equipment from low to high-resolution modes. LSM
particles denoted by circles in Fig. 4-12 show higher 𝑐18O inside the bulk than that on

Section C (high resolution)
(a)

(b)

Electrolyte
CathodeRed: Mn16OLight blue: Zr16OBlack: Pore

Electrolyte
Cathodec18OFigure 4-12. High-resolution secondary ion mappings of the interface between the
LSM/ScSZ cathode and YSZ electrolyte obtained from the area surrounded by dashedlines in Fig. 4-9. (a) Phase mapping of each material. Red and light blue represent
Mn16O- (LSM) and Zr16O- (ScSZ, YSZ), respectively. The black regions show the porephases. (b) Oxygen isotope concentration ( = 𝑐18O ) mapping represented by
I(18O-)/[I(16O-) + I(18O-)]. The measured plane is deeper than that of Fig. 4-9 because
the original surface was a little bit removed by high-intensity primary ions, which wasemitted by changing the SIMS equipment from low to high-resolution modes.

102the surfaces. Such a “uphill” diffusion profile under cathodically-biased condition has
been recently reported in oxygen isotope exchange experiment using a LSM thin film on
a YSZ electrolyte by Huber et al. [17,27]. In their work, an uphill diffusion profile resultsfrom a combination of oxygen vacancy concentration distribution induced by polarizationand fast grain boundary diffusion in the LSM layer. It was also shown that this uphill
diffusion profile appears and enhanced at higher overpotential [17,27]. In Fig. 4-9(b),uphill diffusion profiles are observed at the region where distance fromelectrolyte/cathode interface (d) is shorter than 3.8 µm, indicating that local
overpotentials are higher and charge transfer reactions are more enhanced at the regionof d < 3.8 µm than those at other regions. This result qualitatively shows that reaction
sites near the cathode/electrolyte interface are more electrochemically active than thoseat other regions. Some previous study showed that cathode polarization resistancedecreases with increasing LSM/YSZ layer thickness t at t < ~ 2-6 µm while becomes
constant value at t > ~ 2-6 µm [28,29], indicating the existence of active regions near thecathode/electrolyte interface. In addition, several numerical simulations [2,4,5,30]
showed that local charge transfer current densities increase when the position approaches
from cathode top surface to cathode/electrolyte interface. These works are qualitatively
consistent with the SIMS result obtained here. This is the first experimental work tovisualize active sites in an SOFC porous electrode in microstructure scale.
In the OCV (section A) and the region at d > 3.8 µm of section C, 𝑐18O profiles in
LSM particles can be analysed by assuming diffusion in a semi-infinite media because
𝑐18O drops to an almost natural value, 0.002, around the center of each particle as shownin lines 1 and 5 in Fig. 4-11. At the gas/LSM interface, the rate of isotope exchange isassumed to be proportional to the isotope concentration difference between gas and solid103phases. This boundary condition is descried as follows

 D

c18O
g
s
 k  c18O
 c18Ox x 0





(4.7)

where D* is the oxygen tracer diffusion coefficient, k* is the surface exchange coefficient,
𝑐18O is the 18O fraction at the surface, and 𝑐18O (= 97.5 %) is the isotope enrichment of
the gas. The analytical solution of 1-dimentional diffusion equation for a semi-infinite
media under the boundary condition (4.7) is given as follows [31].
bg
 x
 x 
 k  x k *2t 
c18O  c18O
t 


erfc

exp


erfc

k






g
bg



c18O
 c18OD D D2 D t 
2 D t(4.8)

bHere, 𝑐18O (= 0.2 %) is the natural isotope background level of 18O and t (= 188 s) is thetime of the isotope anneal. 𝑐18O profiles can be well fitted to Eq. (4.8) as shown in lines
1 and 5 of Fig. 4-11, and D* and k* values can be determined.
Both in the case of section A and C, D* and k* are determined at 15 measured points
and plotted against d as shown in Figures 4-13(a) and (b). Here d is defined as a relative
position of each point (LSM/gas interface at each measured line profile) fromelectrolyte/cathode interface. All measured points, an example of fitted graph, andobtained D* and k* values are shown in Appendix E. At the OCV, averaged D* = 1.21 ×
10-13 cm2/s is within the range of reported order of magnitude of D* in LSM bulk at 1073
K, 10-15 to 10-13 cm2/s [18,32,33]. Averaged k* = 1.17 × 10-9 cm/s obtained here isrelatively close to 2.67 × 10-9 cm/s by Fearn et al. [33]. From Figs. 4-13(a) and (b), bothaveraged D* (3.24 × 10-13 cm2/s) and k* (5.91 × 10-9 cm/s) at section C are clearly higher
than those at section A, indicating that under biased condition, both LSM bulk diffusionand surface exchange reaction are enhanced compared to non-biased condition. The
enhanced k* under biased condition also seems to be attributed to the increased oxygen
vacancies in LSM, as is the case with enhanced D* mentioned in Fig. 4-1. Previous

104

(a)
Oxygen tracer diffusion
coefficient D* [cm2 s-1]

-1210
1.0E-12

OCV, Section A
Averaged D* (OCV)
Biased, Section C
Averaged D* (biased)-13
1.0E-13
10

Uphill diffusion-14
1.0E-14
10

0

5

10

15

Distance from cathode/electrolyte interface d [µm](b)-71.00E-07

Surface exchange
coefficient k* [cm s-1]

10OCV, Section A
Averaged k* (OCV)
Biased, Section C
Averaged k* (biased)

Uphill diffusion
10-8

1.00E-08-9
1.00E-09

10

10-10

1.00E-10

0

5

10

15

Distance from cathode/electrolyte interface d [µm]Figure 4-13. (a) Oxygen tracer diffusion coefficient D* and (b) surface exchange
coefficient k* of LSM particles are plotted against distance from cathode/electrolyte
interface (𝑑) in the case of sections A and C. Each averaged value of 15 measured
points is also shown. For section C, D* and k* are not obtained at d < 3.8 µm as uphill
diffusion profiles are observed in this region.

experimental and numerical studies [34,35] pointed out that a higher oxygen vacancy
concentration in cathode materials such as LSM or LSCF resulted in a higher surface

105exchange rate (higher k*) because the reaction seems to occur at the surface oxygen
vacancy. In this case, increased bulk and surface oxygen vacancies of LSM induced byoverpotential are followed by the enhanced D* and k*, respectively. In this experimental
condition, however, obvious dependence of D* and k* on d was not observed in the rangeof 3.8 < d < 13 µm at section C.

4.3.6 Grain boundary diffusion and inactive LSM particles
Some other valuable information related to the oxygen transport mechanism and/or
active site distribution can be also obtained from the SIMS signal in several LSM particles.
Figures 4-14(a) and (b) show magnified phase and 𝑐18O mappings of LSM particles
denoted by spot I in Fig. 4-7 (OCV) and spot II in Fig. 4-9 (biased), respectively. Grainboundary diffusion inside LSM bulk is observed in these spots, and the line profile ofboth spots (Figure 4-14(c)) indicate that grain boundary diffusion is enhanced at biased
condition (spot II) compared to at OCV (spot I). In addition, LSM particles in spots III
and IV at Fig. 4-9 show no 18O diffusion inside their bulk though these locations are close
to the electrolyte/cathode interface. This means that these particles are inactive (or at least
less active) than others, which possibly results from an insufficient network of LSM
particles in the microstructure. The reported 3D-microstructure analysis by FIB-SEM[36] shows that in the conventional LSM-YSZ composite (LSM:YSZ = 50:50 wt%), thepore and YSZ phase networks are entirely connected (> 99 vol%), while 10-20 vol% of
the LSM particles are isolated. The combination of active sites imaging conducted here
and 3D-microstructure observations by FIB-SEM can give further understanding of thephenomena inside the LSM/ScSZ porous cathode.

106

(a) Spot Ⅰ in Section A(b) Spot Ⅱ in Section C
1µm

1µm

𝑐18O [-]

(c)

0.08

Spot Ⅱ

0.04

Spot Ⅰ

0

0

0.3

0.6

[µm]
Figure 4-14. Grain boundary diffusion in LSM. (a,b) Magnified phase and 𝑐18O
mappings of LSM particles denoted by (a) spot I in Fig. 4-7 (OCV) and (b) spot II in

Fig. 4-9 (biased). (c) 𝑐18O line profiles denoted by arrows in (a) and (b)4.4

Summary
Imaging technique of active reaction sites in SOFC porous electrodes was developedin microstructure scale. A power generation equipment with a nozzle for direct helium
gas impinging jet to the cell was newly prepared to quench an SOFC reaction. The quench
performance test showed that the temperature of YSZ electrolyte could be decreased from
830 to 150 oC within 1.5 sec, which was in good agreement with analytical results basedon the average Nusselt number of impinging jet heat transfer. Using constructed quench
system and oxygen isotope labeling, active sites for oxygen reduction reaction in
LSM/ScSZ porous cathode were visualized. From the 18O concentration mappings of the107quenched cathode obtained by SIMS, it was disclosed that cathode area far from a current
collector does not contribute to the electrochemical reaction and oxide ion/electron
conduction. This result was also supported by the dependence of electrochemical
performance on contact area between cathode and Ag paste current collector. In addition,
the expansion of the oxygen reduction sites from a TPB to a DPB enables us to identify
those positions in electrode particle scale by slow oxygen tracer diffusion in the LSM
bulk. Enhanced 18O concentration and uphill diffusion profiles inside LSM observed only
near the cathode/electrolyte interface indicates that reaction sites near thecathode/electrolyte interface are more electrochemically active than those at other regions.
This is the first experimental work to visualize active sites in an SOFC porous electrodein microstructure scale. Finally, an oxygen tracer diffusion coefficient and a surface
exchange coefficient of each LSM particle were quantified from 𝑐18O line profiles,
which were enhanced at current-biased condition compared to those at OCV.

108

References[1] P. Costamagna, P. Costa, V. Antonucci, Electrochim. Acta 43 (1998) 375–394.
[2] J. H. Nam, D. H. Jeon, Electrochim. Acta 51 (2006) 3446–3460.
[3] N. Shikazono, D. Kanno, K. Matsuzaki, H. Teshima, S. Sumino, N. Kasagi, J.
Electrochem. Soc. 157 (2010) B665–B672.
[4] K. Miyoshi, T. Miyamae, H. Iwai, M. Saito, M. Kishimoto, H. Yoshida, J. Power
Sources 315 (2016) 63–39.
[5] A. Banerjee, O. Deutschmann, J. Catal. 346 (2017) 30–49.
[6] M. Shishkin, T. Ziegler, J. Phys. Chem. C 113 (2009) 21667–21678.
[7] T. Kawada, T. Horita, N. Sakai, H. Yokokawa, M. Dokiya, J. Mizusaki, Solid State
Ionics 131 (2000) 199–210.
[8] T. Horita, K. Yamaji, N. Sakai, Y. Xiong, T. Kato, H. Yokokawa, T. Kawada, J.
Power Sources 106 (2002) 224–230.
[9] J. Fleig, A. Schintlmeister, A.K. Opitz, H. Hutter, Scripta Mater. 65 (2011) 78–83.
[10] T. Horita, T. Shimonosono, H. Kishimoto, K. Yamaji, M.E. Brito, Y. Hori, H.
Yokokawa, Electrochem. Solid-State Lett. 13 (12) (2010) B135–B138.
[11] C. Sun, R. Hui, J. Roller, J. Solid State Electrochem. 14 (2010) 1125–1144.
[12] S.B. Adler, Chem. Rev. 104 (2004) 4791–4843.
[13] T. Horita, K. Yamaji, N. Sakai, H. Yokokawa, T. Kawada, T. Kato, Solid State Ionics
127 (2000) 55–65.
[14] A.K. Opitz, M. Kubicek, S. Huber, T. Huber, G. Holzlechner, H. Hutter, J. Fleig, J.
Mater. Res. 28 (2013) 2085–2105.
[15] Y. Jiang, S. Wang, Y. Zhang, J. Yan, W. Li, J. Electrochem. Soc. 145 (1998) 373–378.
[16] R. Radhakrishnan, A.V. Virkar, S.C. Singhal, J. Electrochem. Soc. 152 (2005) A210–

109

A218.
[17] T.M. Huber, E. Navickas, G. Friedbacher, H. Hutter, J. Fleig, ChemElectroChem 2(2015) 1487–1494.
[18] I. Yasuda, K. Ogasawara, M. Hishinuma, T. Kawada, M. Dokiya, Solid State Ionics
86-88 (1996) 1197–1201.
[19] E.S. Raj, A. Atkinson, J.A. Kilner, Solid State Ionics 180 (2009) 952–955.
[20] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, second ed., John
Wiley & Sons, Inc., (2007).
[21] The Japan Society of Mechanical Engineers, JSME Data Book: Heat Transfer 5th
Edition, pp. 39, Maruzen (2009). (in Japanese)[22] The Japan Society of Mechanical Engineers, JSME Textbook Series, Heat Transfer,
pp. 45, Maruzen (2005). (in Japanese)[23] G. Knöner, K. Relmann, R. Röwer, U. Södervall, H-E. Schaefer, PNAS 100, 7 (2003)
3870–3873.
[24] K.C. Wincewicz, J.S. Cooper, J. Power Sources 140 (2005) 280–296.
[25] S.P. Jiang, J.G. Love, L. Apateanu, Solid State Ionics 160 (2003) 15–26.
[26] K. Sasaki, J.-P. Wurth, R. Gschwend, M. Gödickemeier, L.J. Gauckler, J.
Electrochem. Soc. 143 (2) (1996) 530–543.
[27] T.M. Huber, E. Navickas, K. Sasaki, B. Yildiz, H. Tuller, G. Friedbacher, H. Hutter,
J. Fleig, J. Electrochem. Soc. 164 (7) (2017) F809–F814.
[28] M. Juhl, S. Primdahl, C. Manon, M. Mogensen, J. Power Sources 61 (1996) 173–
181.
[29] E.P. Murray, T. Tsai, S.A. Barnett, Solid State Ionics 110 (1998) 235–243.
[30] K. Miyoshi, H. Iwai, M. Kishimoto, M. Saito, H. Yoshida, J. Power Sources 326110(2016) 331–340.
[31] J. Crank, The Mathematics of Diffusion, Oxford University Press, Oxford, 1975.
[32] R.A. De Souza, J.A. Kilner, J.F. Walker, Mater. Lett. 43 (2000) 43–52.
[33] S. Fearn, J.C.H. Rossiny, J.A. Kilner, J.R.G. Evans, Solid State Ionics 211 (2012)
51–57.
[34] Y-L. Huang, C. Pellegrinelli, E.D. Wachsman, ACS Catal. 6 (2016) 6025–6032.
[35] L. Wang, R. Merkle, Y.A. Mastrikov, E.A. Kotomin, J. Maier, J. Mater. Res. 27, 15(2012) 2000–2008.
[36] J.R. Wilson, A.T. Duong, M. Gameiro, H-Y. Chen, K. Thornton, D.R. Mumm, S.A.
Barrnet, Electrochem. Commun. 11 (2009) 1052–1056.

111

Chapter 5

Analysis method of oxide ion flux at cathode/electrolyte
interface through oxygen isotope labeling

5.1

Introduction
In Chapter 4, active sites of LSM/ScSZ cathode were identified in microstructure

scale based on the 18O diffusion into LSM induced by overpotential. However, thequantitative discussion of the reaction rate or oxide ion flux incorporated to the cathodeis difficult only from the information in LSM because most flux is directly incorporated
from a zirconia surface (YSZ, ScSZ) near the TPB (Fig. 4-1, TPB path). As shown in
Chapter 4, the fast 18O diffusion inside ScSZ resulted in a uniform 18O concentration in
the cathode microstructure scale, which is difficult to analyze by diffusion equation.
In this chapter, the oxygen isotope exchange experiment is conducted at 973 K,
100 ℃ lower than in Chapter 4, to suppress the 18O diffusion in a zirconia phase, and the18

O diffusion profile in YSZ electrolyte is analyzed. Based on the results, quantitativeoxide ion flux incorporated from the cathode/electrolyte interface is estimated.

5.2

Experimental section
In this experiment, a YSZ-electrolyte supported cell with a Ni/YSZ anode and

LSM/YSZ (LSM:YSZ = 50:50 wt%) cathode was used. The cell geometry and fabrication
process are the same as in Chapter 4, and only ScSZ in the cathode was changed to YSZ.

112

(a)

(b)
0.8

1073 K
973 K

1.2

1

𝑖 = 0.09 A/cm2

0.6-Im(Z) [Ω•cm2]

Terminal voltage [V]

1.4

0.8
0.6
0.4
0.2

T : 973 K

0.4
0.2

0
1

2

3

0
0

0.1

0.2

5

6

7

6

8

-0.4

0.3

Re(Z) [Ω•cm2]

Current density [A/cm2]

(c)

(d)

18O
2

Power
generation Quench

QuenchNormal O2

1073

1

𝑖 = 0.09 A/cm2
T : 973 K

0.8
0.6

Temperature [K]Terminal voltage [V]

4

-0.2

0.4
0.2

0
0

200

400

600

800

873
673
473

273

Elapsed time [s]

-2

0

2

4

Elapsed time [s]Figure 5-1. (a) Initial performance of the cell used in the isotope exchange at 1073 and973 K. Humidified mixture of 50% H2 – 50% Ar and pure oxygen were supplied as afuel and oxidant, respectively. (b) Impedance spectra at 0.09 A/cm2 measured between
anode working and cathode working. (c) Terminal voltage versus elapsed time with aconstant current density of 0.09 A/cm2. (d) Temperature change of the cell during
quenching measured by the thermocouple attached in anode reference (Fig. 4-3(a)).

Here, the electrode area covered by an Ag current collector was about 46.7 % (⁄ C=

0.467 in Fig. 4-3(a)) .The experimental procedure is almost the same as in Chapter 4.
Initially, the cell was operated in a mixture of 50% H2 and 50% Ar, which was humidified
by a bubbler, for the anode side and in 100% normal O2 for the cathode side at 973 K for
10 min under a constant current density of 0.09 A/cm2. Then, the normal O2 was switched
to 18O2 (>97.5%), and the cell was operated for 70 sec. Finally, the cell was abruptly
quenched to a room temperature by the helium impinging jet. The initial performance ofthe cell at 1073 and 973 K, impedance spectra at 0.09 A/cm2 measured between anode
113

(a)

(b)
Covered by Ag paste

Covered by Ag paste

CathodeElectrolyte

Section C
Polished

Anode

Ag residual

Ag residual

Section B

Unpolished

Unpolished

Polished

Epoxy
Glass plate

Figure 5-2. SEM images of the polished cross section of the cell. The position ofsections B and C are shown in (a) and (b), respectively. Most part of Ag paste waspeeled off from the cathode surface during the quench process. The sample isinfiltrated with an epoxy resin and sandwiched with two glass plates for the polishingprocess.

working and cathode working, the terminal voltage with time until quenching, andtemperature change of the cell during quenching are shown in Figures 5-1(a)–(d),respectively. The cell showed an almost stable terminal voltage of about 0.42 V at 0.09
A/cm2 until quenching reaction as shown in Fig. 5-1(c).
The 18O distribution in a cross section of the quenched cathode was obtained by
NanoSIMS 50L (CAMECA), as is the case in Chapter 4. Here, SIMS images at theinterface between the cathode and electrolyte were taken from both reference (Section A)
and working (Section B and C) electrodes. The position of section A is the same as in Fig.
4-3(a), which represents OCV (non-biased) condition. Both sections B and C are placed
directly under the contact area of the Ag paste current collector of cathode working(biased condition). As shown in Figures 5-2(a) and (b), section B is inside the area coveredby Ag paste while section C is near the edge of the paste.

114

5.3

Results and discussion

5.3.1

Secondary ion mappings
Figures 5-3 and 5-4 show the secondary ion mappings of the interface between the

LSM/YSZ cathode and YSZ electrolyte at OCV (Section A) and biased (Sections B andC) conditions, respectively. Among these, Figs. 5-3(a), 5-4(a), and 5-4(c) show phasemappings of LSM and YSZ based on the intensity of Mn16O- and Zr16O-, and Figs. 5-3(b),5-4(b), and 5-4(d) show 18O concentration ( = 𝑐18O ) mappings represented by
I(18O-)/[I(16O-) + I(18O-)]. Here, I(16O-) and I(18O-) indicate the SIMS signal intensity ofSection A (OCV)
(a)

(b)

Electrolyte
CathodeRed: Mn16OLight blue: Zr16OBlack: Pore

Electrolyte
Cathodec18OLine 1Figure 5-3. Secondary ion mappings of the interface between the LSM/YSZ cathodeand YSZ electrolyte at OCV condition obtained from section A (cathode reference).
(a) Phase mapping of each material. Red and light blue represent Mn16O- (LSM) and
Zr16O- (YSZ), respectively. The black regions show the pore phases. (b) Oxygenisotope concentration (= 𝑐18O ) mapping represented by I(18O-)/[I(16O-) + I(18O-)].

115

(a) Section B (Biased)(b) Section B (Biased)

Red: Mn16OLight blue: Zr16OElectrolyte
Cathode Black: Pore

Electrolyte

Cathodec18OLine 2(c) Section C (Biased)(d) Section C (Biased)

Line 3Figure 5-4. Secondary ion mappings of the interface between the LSM/YSZ cathodeand YSZ electrolyte at biased condition obtained from sections B (a,b) and C (c,d) in
Fig. 5-2. (a,c) Phase mapping of each material. Red and light blue represent Mn16O(LSM) and Zr16O- (YSZ), respectively. The black regions show the pore phases. (b,d)
Oxygen isotope concentration (= 𝑐18O ) mapping represented by I(18O-)/[I(16O-) +I(18O-)].

116

each ion. Prior to the calculation of 𝑐18O image, binarization processing is performed on
the 16O- image to remove all signal from pore phases. As shown in Fig. 5-3(b), 𝑐18O ≈0.04 of YSZ phases in cathode part is higher than that in the electrolyte (maximum

Section A (OCV, high resolution)(a)Electrolyte(b)Red: Mn16O16 Cathode Light blue: Zr O
Black: Pore

Electrolyte
Cathodec18OLine 4(c)𝑐18O [-]

0.06

Line 40.04∆𝑐18O ≈ 0.015

0.02
0
0

0.5

1

1.5

2

2.5

[µm]

Figure 5-5. High-resolution secondary ion mappings of the interface between the
LSM/YSZ cathode and YSZ electrolyte at OCV condition in section A (cathodereference). (a) Phase and (b) 18O concentration (𝑐18O ) mappings are shown. 𝑐18O
profile in Line 4 is also shown in (c).

117

𝑐18O ≈ 0.025 at the surface) at OCV condition. This is because the surface to volume
ratio of YSZ phase in cathode part is much larger than that in electrolyte part. At biased
condition, 𝑐18O in YSZ phase is around 0.12–0.16 at cathode or electrolyte surface,

Section B (Biased, high resolution)(a)Electrolyte(b)Red: Mn16O16 Cathode Light blue: Zr O
Black: Pore

Electrolyte
Cathodec18OLine 5(c)𝑐18O [-]

0.18

Line 50.16
0.14∆𝑐18O ≈ 0.03

0.12
0.1
0

0.5

1

1.5

2

[µm]

Figure 5-6. High-resolution secondary ion mappings of the interface between the
LSM/YSZ cathode and YSZ electrolyte at biased condition in section B (cathodeworking). (a) Phase and (b) 18O concentration (𝑐18O ) mappings are shown. 𝑐18O
profile in Line 5 is also shown in (c).

118

which is higher than that at OCV condition because of additionally-incorporated 18O by
the electrochemical reaction. Both in OCV and biased conditions, 𝑐18O in the electrolyte
gradually decrease from cathode/electrolyte interface to anode side.
Figures 5-5 and 5-6 show the high-resolution secondary ion mappings at section A(OCV) and B (biased), respectively. As is the case in Chapter 4, 18O diffusion to LSM
bulk was only observed at the region near the cathode/electrolyte interface under biased
condition. In addition, 𝑐18O in the electrolyte is uniform near the cathode/electrolyte
interface at OCV while inhomogeneous at biased condition, which may come from thenon-uniform oxide ion flux incorporated from the interface.

5.3.2

18O diffusion profile analysis in YSZ electrolyte

𝑐18O line profiles inside YSZ electrolyte denoted by Line 1 in Fig. 5-3 (OCV) andLine 2 and 3 in Fig. 5-4 (biased) are shown in Figure 5-7. In this study, polycrystalline
YSZ (8mol%Y2O3-ZrO2) was used as an electrolyte. In all cases, typical monotonicallydecreasing diffusion profiles are observed, which can be analyzed by 1-dimensional
diffusion in a semi-infinite media. As shown in Fig. 5-7, the analytical solution ofdiffusion equation (Eq. (4.8)) is well fitted to each profile, which gives oxygen tracer
diffusion coefficient D* and surface exchange coefficient k*. The D* and k* obtained
here and other references [1,2] are summarized in Table 5-1. At OCV, obtained D* = 9.70
× 10-13 m2/s and k* = 2.45 × 10-9 m/s are relatively close to those of polycrystalline YSZ(9.1mol%Y2O3) by Naito et al. [1], and within the range of summarized data sets by
Knöner et al. (single crystal, polycrystalline) [2].
When the current is applied, D* increased by a factor of only 1.2 (section B) to 1.5(section C) compared to that of OCV while k* was enhanced by one order of magnitude,

119

Cathode ElectrolyteLine 1 (OCV, Section A)
Line 2 (Biased, Section B)
Line 3 (Biased, Section C)
Fitting curves by Eq. (4.8)

0.16

0.16

𝑐18O [-]

0.12

0.12

0.08

0.08

0.04

0.04

0

0

0

5

10

15

20

25

[µm]
Figure 5-7. 𝑐18O line profiles inside YSZ electrolyte denoted by Line 1 in Fig. 5-3(OCV) and Line 2 and 3 in Fig. 5-4 (biased). Positive direction in position x
corresponds to each arrow direction in Figs. 5-3 and 5-4. Analytical solution ofdiffusion equation (Eq. (4.8)) is fitted to each profile.

as shown in Table 5-1. The weak enhancement of D* means that the enhancement of 18O
diffusion in YSZ bulk by the current is small. In a YSZ, oxide ion moves through vacancy
diffusion mechanism [3]. In a fuel cell operation, when one oxide ion is incorporated toan electrolyte form a cathode, one oxide ion is emitted to an anode accompanied by ageneration of oxygen vacancy in the electrolyte. Subsequently the generated oxygen
vacancy moves from anode to cathode side. Therefore, incorporated 18O itself does not
move along the electrochemical potential gradient of oxide ion, ∇𝜇̃O2 (see Appendix
B), but moves along the 18O concentration gradient ∇𝑐18O .
On the other hand, the one order enhancement of apparent k* indicates that 18O flux

120

Table 5-1. D* and k* of YSZ electrolyte at 973 K obtained in this study and otherreferences. All literature values were measured at non-biased condition.
Measurement

SampleSection A (OCV)

8mol%Y2O3-ZrO2
Polycrystalline(with LSM/YSZ cathode)

Section B (Biased)
Section C (Biased)

D* [m2/s]

k* [m/s]

9.70 × 10-13

2.45 × 10-9

1.15 × 10-12

1.50 × 10-8

1.45 × 10-12

2.08 × 10-8

Naito et al. [1]9.1mol%Y2O3-ZrO2
Polycrystalline

4.0 × 10-13

1.4 × 10-9

Knöner et al. [2]2.8–16mol%Y2O3-ZrO2
Single crystal, Polycrystalline

2.1 × 10-13– 4.0 × 10-12

2.0 × 10-11– 2.8 × 10-8

incorporated from the cathode/electrolyte interface to the electrolyte is greatly increased
by applying the current. The detail of the 18O flux is quantitatively discussed in the next
section.

5.3.3 Oxide ion flux incorporated from the cathode/electrolyte interface
ex(C/E)As shown in Figure 5-8(a), three kinds of 18O fluxes, 𝐽18O

c(C/E)

ex(C/E)

contribute to a total 18O flux at the cathode/electrolyte interface. 𝐽18O
ion(C/E)

a 16O/18O exchange at a free electrolyte surface and 𝐽18O

ion(C/E), 𝐽18O , and 𝐽18O

is a 18O flux by

is an isotope oxide ion(18O2-) flux by an electrochemical reaction at a LSM/YSZ/gas TPB on the electrolyte
surface. In addition, 𝑐18O of YSZ phase in the cathode is generally higher than that of
the electrolyte due to the higher surface to volume ratio of YSZ phase in the cathode, asc(C/E)

mentioned previously (section 5.3.1). 𝐽18O

is a 18O flux by the 𝑐18O difference ofex(C/E)YSZ phase between cathode and electrolyte part. Here 𝐽18O
ion(C/E)

OCV and biased conditions while 𝐽18O

c(C/E)and 𝐽18O

flow at both

exists only at biased. Therefore, the total 18O

flux incorporated from the cathode/electrolyte interface to the electrolyte at OCV andOCV(C/E)

biased conditions, 𝐽18O

Bia ed(C/E)

and 𝐽18O

121

are described as follows.

(a)

(b)
Cathode Electrolyte

𝑐18O

YSZ

18O
2

ex(C/E)

𝐽18O

16O
2

Bia ed(C/E)

𝐽18O

c(C/E)

Biased

𝐽18O
e-

OCV
ion(C/E)

LSM

𝐽18O

OCV(C/E)

𝐽18O

18O
2

c18O

Cathode Electrolyte

Low

High

Figure 5-8. (a) Three kinds of 18O fluxes incorporated from the cathode/electrolyte
ex(C/E)c(C/E)

interface to the electrolyte. 𝐽18O
and 𝐽18O
flow at both OCV and biased
ion(C/E)
conditions while 𝐽18O
exists only at biased. (b) The relationship between 𝑐18O
profile and total 18O flux incorporated from the cathode/electrolyte interface to theelectrolyte

OCV(C/E)
ex(C/E)c(C/E)J18O
 J18O J18O(5.1)

Biased(C/E)
ex(C/E)c(C/E)
ion(C/E)
J18O
 J18O J18O J18O(5.2)

OCV(C/E)As shown in Figure 5-8(b), 𝐽18O

Bia ed(C/E)

and 𝐽18O[mol/(m2•s)] corresponds to a

𝑐18O gradient at cathode/electrolyte interface ( = 0), which can be described as follows.
OCV(C/E)
18O

J

 C

Biased(C/E)
18O

J

YSZ
O

 C


OCV

D

YSZ
O

 c18O  x x 0 

BiasedDOCV c18O  x x 0 

(5.3)
Biased

(5.4)

∗
∗
2
Here 𝐷OCV
and 𝐷Biaed [m /s] represents the oxygen tracer diffusion coefficient at

OCV and biased condition, respectively. 𝐶O

122[mol/m3] is an absolute concentration ofO
Zr

YSZ unit cell
• 8.3mol%Y2O3-ZrO2• Fluorite structure• Lattice constant: 5.135• Zr site: 4, O site: 8• Zr : Y : O : VO = 10 : 2 : 23 : 1• 𝐶O = 9.41 × 104 mol/m3

Figure 5-9. Fluorite structure of zirconia and information of YSZ unit cell to calculate
𝐶O . Lattice constant is refereed from Hayashi et al [4]. VO represents an oxygen
vacancy in the lattice. The illustration of the structure was created using the VESTA
package of Momma and Izumi [5].

total oxygen atom in a YSZ bulk, which is calculated based on the lattice structure as
Bia ed(C/E)

shown in Figure 5-9. The calculated 𝐽18O
OCV(C/E)

𝐽18O

is one order of magnitude larger thanas summarized in Table 5-2.
OCV(C/E)At OCV, 𝐽18O∗
is also described by the surface exchange coefficient 𝑘OCV[m/s] as follows:
OCV(C/E)
ex(C/E)c(C/E)
gas
c18O
J18O
 J18O J18O COYSZ kOCV
 c18O x 0 

OCV

(5.5)

a

where 𝑐18O is a relative 18O concentration in gas phase (= 0.975) In the above expression,ex(C/E)it seems to be difficult to separate the contribution from 𝐽18O
ion(C/E)

Therefore, in order to calculate 𝐽18O

c(C/E)

precisely.

c(C/E)

at biased

and 𝐽18O

ex(C/E)in Eq. (5.2), 𝐽18O

𝐽18O

condition is roughly estimated below.
Both in OCV and biased condition, surface exchange coefficient on free YSZ surface,ex(C/E)

which determines 𝐽18O

c(C/E), should be the same. In addition, 𝐽18O

at OCV is not morethan 2.18 × 10-4 mol/(m2•s) from Eq. (5.5) and Table 5-2. As shown in Fig. 5-8(a), thec(C/E)

driving force of 𝐽18O

is the difference of 𝑐18O ( ∆𝑐18O ) between cathode and123

Table 5-2. 18O flux incorporated from the cathode/electrolyte
interface to the electrolyte estimated by diffusion profiles. Total
18 2O flux at given current density is also shown.

Flux

Value [mol/(m2•s)]

𝐽18O

OCV(C/E)

2.18 × 10-4

𝐽18O

Bia ed(C/E)

1.21 × 10-3 (Section B)
1.63 × 10-3 (Section C)

ion(C/E)

1.01 × 10-3 (Section B)
1.43 × 10-3 (Section C)

𝐽18O

a

ion(all)

4.58 × 10-3 (𝑖 = 0.09 A/cm2, 𝑐18O = 0.975)

𝐽18O

electrolyte part. From 𝑐18O line profiles in Figs. 5-5(c) and 5-6(c), ∆𝑐18O at OCV (≈c(C/E)

0.015) and biased condition (≈ 0.03) is the same order of magnitude. Therefore, 𝐽18O

at biased condition is also estimated to be less than or equal to 10-4 order of magnitude.
Bia ed(C/E)

Because 𝐽18O

ex(C/E)is 10-3 order of magnitude, rough estimation of 𝐽18O

ion(C/E)

at biased condition (10-4 order of magnitude) does not strongly affect 𝐽18O
ex(C/E)

Based on the above discussion, sum of 𝐽18O

c(C/E)and 𝐽18O

c(C/E)

𝐽18O.

at biased condition was∗approximately estimated using 𝑘OCV
as follows.
ex(C/E)c(C/E)
 J18O
 J18O

Biasedgasc18O COYSZ kOCV
 c18O x 0 

Biasedion(C/E)

Substitution of Eqs. (5.4) and (5.6) into Eq. (5.2) gives 𝐽18O

(5.6)
, which are summarizedion(all)in Table 5-2. The total 18O2- flux incorporated from whole cathode 𝐽18O

at givencurrent density 𝑖 [A/m2] is also shown in this table.
ion(all)gas
J18O
 c18O

i
2F

(5.7)

Under the assumption that whole cathode area contributes to the electrochemical reaction
equivalently, the results in Table 5-2 indicate that 22% (section B) ~ 31% (section C) of

124

the overall electrochemical reaction (oxide ion incorporations to YSZ phase) occurs at thecathode/electrolyte interface, while the remaining 69~78% of those proceeds inside theporous cathode.
In 3-dimensional numerical simulation of LSM/YSZ porous cathode (LSM:YSZ =50:50 wt%) based on the actual microstructure by Miyoshi et al [6], charge transfer
current distribution in the cathode thickness direction was calculated at 850 ℃. In theirresult, 22.5% of the overall electrochemical reaction occurs at the region within 1.25 µm
from the cathode/electrolyte interface, which is relatively close to the scale of one LSM
particle on the electrolyte as shown in Fig. 5-6.

5.4

Summary
Oxygen isotope exchange and quench experiment was conducted at 973 K using theelectrolyte-supported cell under fuel cell operation condition. From the analysis of 18O
diffusion profiles in YSZ electrolyte, it was disclosed that by applying a current, oxygen
tracer diffusion coefficient D* increased by a factor of only 1.2–1.5 while surface
exchange coefficient k* was enhanced by one order of magnitude. The greatly enhanced
k* comes from oxide ion flux incorporated from the cathode/electrolyte interface to theelectrolyte. Based on the 18O profiles, quantitative oxide ion flux incorporated from thecathode/electrolyte interface was estimated. The results indicated that 22~31% of theoverall electrochemical reaction occurs at the cathode/electrolyte interface, while theremaining 69~78% of those proceeds inside the porous cathode.

125References[1] H. Naito, N. Sakai, T. Otake, H. Yugami, H. Yokokawa, Solid State Ionics 135 (2000)
669–673.
[2] G. Knöner, K. Reimann, R. Röwer, U. Södervall, H-E. Schaefer, PNAS 100 (7) (2003)
3870–3873.
[3] 田 川博 章，固体酸化物燃料電池と地球環境，アグ ネ承風社 (1998). (inJapanese)[4] H. Hayashi, T. Saitou, N. Maruyama, H. Inaba, K. Kawamura, M. Mori, Solid State
Ionics 176 (2005) 613–619.
[5] K. Momma, F. Izumi, J. Appl. Crystallogr. 41 (2008) 653–658.
[6] K. Miyoshi, T. Miyamae, H. Iwai, M. Saito, M. Kishimoto, H. Yoshida, J. Power
Sources 315 (2016) 63–69.

126

Chapter 6

Conclusions

6.1

Key findings and contributions
In this thesis, toward construction of the detailed reaction kinetics and dynamics on

SOFC porous electrodes, analytical reaction model was constructed and active sites
imaging was conducted for more accurate understanding and description of species
transport phenomena coupled with electrochemical reactions proceeding inside SOFC.
The key findings and contributions from the study are summarized below.
• The analytical model for hydrogen oxidation at anode, species territory adsorption
model, was newly proposed. Based on the model, explicit expressions of the current
density with respect to oxygen activity and the anode overpotential with respect tocurrent density could be obtained. The latter could combine the overpotentials at lowand high-current-density regions to unique expression, which were conventionallyexpressed independently.
• Based on the model, the current density asymptotes the limiting value as the oxygen
coverage around the TPB approaches unity. The theoretical limitation of current density
given by the model is determined by the rate constants of surface reactions and thecoverage of adsorbed hydrogen on Ni.
• From referenced DFT-database and careful fitting process between the analytical andexperimental results, all thermodynamic and kinetic parameters for the species territory127

adsorption model were determined. This made it possible to estimate effective anode
thickness based on the model, which tends to increase with temperature in six kinds of
Ni/YSZ anodes used in this study and references.
• The proposed model can predict more precise dependence of anode overpotential on
steam partial pressure than that by Butler-Volmer equation with empirical exchange
current density when the same Ni-patterned anode experiment is selected as a basic
data.
• The power generation equipment with a nozzle for direct helium gas impinging jet tothe cell was newly constructed to quench an SOFC reaction for active sites imaging of
porous electrodes. By using the equipment, the temperature of YSZ electrolyte could
be decreased from 830 to 150 oC within 1.5 sec., which was in good agreement withanalytical results based on the average Nusselt number of impinging jet heat transfer.
• By using the developed quench apparatus and oxygen isotope labeling, active sites in
LSM/ScSZ porous cathode were first visualized in microstructure scale. The obtained18

O mapping showed that the reaction sites near the cathode/electrolyte interface are

more electrochemically active than those at other regions.
• Quantitative estimation of oxide ion flux incorporated from the cathode/electrolyte
interface to the electrolyte indicates that 22~31% of the overall electrochemical
reaction occurs at the interface, while the remaining 69~78% of those proceeds inside
the porous cathode.

6.2

Future perspective
Future perspective to extend this study are suggested and summarized as follows.

• The introduction of the species territory adsorption model into numerical simulation

128

instead of Butler-Volmer equation can give more accurate prediction of the polarization
behavior of Ni/YSZ anode. Based on numerically-solved local oxygen chemical
potential, the model can give local charge transfer current density.
• The information of effective anode thickness predicted by the model is useful to design
two-layered anode (Ni/YSZ as an active layer and porous metal as a current collecting
layer), which can reduce ohmic resistance of a tubular SOFC in the longitudinal
direction while enough anode reaction sites remain.
• The sensitivity analysis of the model indicates that anode overpotential can be
drastically reduced by changing the adsorption state of oxygen on oxide ion conductor
near the TPB, which can be new guideline to develop and design anode materials.
• The quench technique can be applied to visualize active sites of fuel electrode (e.g.
Ni/YSZ), where the species territory adsorption model was assumed in this study. The
adsorbed hydrogen, oxygen, or water around the Ni/YSZ/gas TPB in quenched anodecan be detected through surface analysis, e.g. X-ray photoelectron spectroscopy (XPS).
In addition, oxygen migration in the YSZ bulk near the TPB can be tracked by oxygenisotope labeling in the case of electrolysis reaction because oxygen incorporation sites
can be easily imaged in this method.
• The effect of cathode materials, operating temperature, gas compositions, and current
density on active sites distribution can be investigated by developed quench andoxygen isotope labeling method. In addition, the electrochemical impedance oroverpotential should be linked to the imaged active sites distribution.
• The changes of active sites distribution and cathode degradations such as chromium
poisoning, secondary phase formation, or segregation of strontium component can betracked simultaneously during long-term operation, which can give valuable129

information to further understand and improve SOFC stability.
• The correlation between oxide ion flux incorporated from a cathode/electrolyte interface
to an electrolyte and various parameters and factors, e.g., electrochemical impedance,
cathode composition or microstructure, and operating temperature, can be investigated.
• In order to suppress a cathode degradation by electrochemically-enhanced chromium
poisoning especially at the region near the cathode/electrolyte interface, the reaction
should proceed uniformly in the entire cathode. Active sites imaging can give useful
information to design a cathode material, composition, or structure to realize uniform
reaction distribution in the entire cathode.

130

Appendix A

Derivation of coverage formulas

In this Appendix, the detailed derivation of coverages in Areas 1 and 2, 𝜃𝑖(𝑘) [Eqs.
(2.21)–(2.28)], are given. From Eqs. (2.13)–(2.16), 𝜃H(1) , 𝜃H2 O(1) , 𝜃H2 O(2) , and 𝜃O(2)are expressed using 𝜃𝑉(1) or 𝜃𝑉(2) , as follows:H(1)  KH PH V (1)(A.1)

H O(1)  KH O PH OV (1)(A.2)

H O(2)  KH O PH OV (2)(A.3)

O(2)  KOaOV (2)

(A.4)

2

2

2

2

2

2

2

From Eqs. (2.18) and (2.19) and above expressions, 𝜃H(2) and 𝜃O(1) are expressedusing 𝜃𝑉(1) or 𝜃𝑉(2) , as follows: H(2)  K H(ex12)

 H(1)
  K H(ex12) K H PH V (2)V (1) V (2)(A.5)

 O(1)  K O(ex12)

 O(2)
  K O(ex12) K O aOV (1)V (2) V (1)

(A.6)

2

Substitution of Eqs. (A.1), (A.2), and (A.6) into Eq. (2.11) gives following equation:

1  K P  K
H H2

O(ex12)



KO aO  K H2O PH2O V (1)  1(A.7)

From Eq. (A.7), 𝜃𝑉(1) is derived as shown in Eq. (2.21). By substituting Eq. (2.21) into
Eqs. (A.1), (A.2), and (A.6), Eqs. (2.22)–(2.24) are derived.

131

In the same way, substitution of Eqs. (A.3)–(A.5) into Eq. (2.12) gives following
equation:1  KH(ex12)

K H PH2  KO aO  K H 2O PH2O V (2)  1(A.8)

From Eq. (A.8), 𝜃𝑉(2) is derived as shown in Eq. (2.25). By substituting Eq. (2.25) into
Eqs. (A.3)–(A.5), Eqs. (2.26)–(2.28) are derived.

132

Appendix B

Oxygen transport and reaction described by chemical
potential

B.1

Introduction
In Chapter 2, the relationship between anode potential and oxygen activity (Eq.

(2.47)) is used. This expression is originated from a concept of chemical potential, which
has been often introduced in solid state chemistry [1]. In the case of electrochemical
devices such as SOFCs, both ion/electron transports in solids and chemical reactions atelectrodes are described by using chemical potentials [2]. Several numerical studies haveexpressed overpotentials and ion/electron fluxes in SOFC electrodes using chemical
potentials [3,4]. In this Appendix, equations for particle transport in solid written bychemical potentials are explained, typical chemical potential distributions in an SOFC arepresented, and the derivation of Eq. (2.47) are shown.

B.2

Equation for particle transport in solid
As shown in Figure B-1, it is assumed that each particle (neutral atom, ion) in anordered crystal lattice in a solid receives a periodic potential energy with a barrier of
𝐸𝑎𝑐 ~10 − 100 kJ/mol. If a thermally-vibrated atom has an energy higher than 𝐸𝑎𝑐 , theatom can jump a potential barrier and move to a next lattice position. This probability 𝑝
is generally described by using Boltzmann factor as follows.

133𝑝: Probability that a thermally-vibrated
atom has an energy higher than 𝐸𝑎

Potential
energySolid(Crystal)

𝑝

𝑝

～1mm
𝐸𝑎𝑐 ~10 – 100
kJ/mol𝑟~5

𝑟~5

Figure B-1. Potential energy of each particle (neutral atom, ion) in an ordered crystal
lattice in a solid.

 E p  exp   act  RT 

(B.1)

The mean-square displacement of each particle per sec. 𝑅 2 av [m2/s] is described bylattice constant 𝑟 [m], vibrational frequency of atom 𝜈0 [/s], and 𝑝 as follows [2].
Rav 2  r 2 0 p(B.2)

The diffusion of particle in solid is assumed to occur equally in all 6 directions, which
gives self-diffusion coefficient D [m2/s].

DRav 2 r 2 0
 E exp   act 66
 RT 

(B.3)

The tracer diffusion coefficient D* discussed in Chapter 4 is generally smaller than D
especially for oxygen diffusion in oxide through vacancy-diffusion mechanism. This isbecause an oxygen can jump to a next lattice position only when the next site is a vacancy,
thus the diffusion is not isotropic. The relationship between D* and D is expressed byusing correlation factor f (0 < f < 1) as follows [2,5].

D  fD(B.4)

When particles in solid are under a potential gradient, such as chemical potential134

(including concentration) gradient, electric field, magnetic field, or temperature gradient,
the potential energy distribution changes as shown in Figure B-2. Here, only chemical
potential and electric field is considered as an external field, and sum of those is called anelectrochemical potential 𝜇̃𝑖 ( ). In this situation, diffused particle flux from left to right
direction 𝑗LR [mol/(m2•s)] is below:3 E  E 2 
 1  cr  0
jLR   
exp   act

RT
r 6


2

(B.5)

where c is a concentration of diffused particle [mol/m3] and ∆𝐸 is a potential difference
between two lattice positions generated by the potential gradient (Fig. B-2). Considering
the order of number of atoms in solid ~107 /cm, ∆𝐸~𝐸𝑎𝑐 /107 ≪ 𝐸𝑎𝑐 can be assumed.
Using this approximation, 𝑗LR is rewritten as follows.

jLR 

cr 0
 E   E 2 
exp   act   1 

6RT 
 RT  (B.6)

In the same manner, diffused particle flux from right to left direction 𝑗RL [mol/(m2•s)] is
obtained as follows.

Potential
energyWithout potential gradient∆𝐸/2

With potential gradient

𝐸𝑎𝑐
∆𝐸

𝑟

𝜇̃𝑖 ( )

Figure B-2. Potential energy of each particle (neutral atom, ion) in an ordered crystal
lattice in a solid with and without potential gradient. 𝜇̃𝑖 ( ) is an electrochemical
potential.

135cr 0 E   E 2 
exp   act   1 

6RT 
 RT  

jRL 

(B.7)

Finally, net flux of diffused particle from left to right 𝑗 [mol/(m2•s)] is below.

j  jLR  jLR cr 0cD i E 
exp   act   E  

6RT
RT x
 RT 

(B.8)

Here, Eq. (B.3) and following relationship are used.

  
E    i  r x 

(B.9)

Eq. (B.8) is a general form of a basic equation for particle transport in solid.

B.3

Fick’s first law and equation for ion conduction
Electrochemical potential of species 𝑖, 𝜇̃𝑖 , consists of chemical potential 𝜇𝑖 andelectric field 𝑍𝑖 𝐹𝜙 below:

i ( x)  i ( x)  Zi F ( x)
 i  RT ln ai ( x)  Zi F ( x)(B.10)

 i  RT ln  i ( x)ci ( x)  Zi F ( x)where 𝑍𝑖 is a valence, 𝐹 a Faraday constant [C/mol], 𝜙 an electro-static potential[J/C], 𝜇𝑖° a chemical potential at standard condition [J/mol], 𝑎𝑖 an activity (= 𝛾𝑖 𝑐𝑖 ), 𝛾𝑖an activity coefficient (0 ≤ 𝛾𝑖 ≤ 1), and 𝑐𝑖 a concentration [mol/m3]. Substitution of Eq.
(B.10) into Eq. (B.8) gives:cD  ln  i ln ci 
ji   i i  RT
 RT
 Zi F
RT 
x
x
x 

(B.11)

The first, second, and third term on the right side in the above expression is a contributionof activity coefficient gradient, concentration gradient, and electrical potential gradient,
respectively.
In the case of neutral atom (𝑍𝑖 = 0) or ∇𝜙 = 0, Eq. (B.11) is reduced to following
expression.

136  ln  i  ci  ln  i  ln ci 
ji  ci Di   Di 1 


x 
 x
  ln ci  x
Here, (1

(B.12)

𝜕 ln 𝛾𝑖 ⁄𝜕 ln 𝑐𝑖 ) is called a thermodynamic factor. If species 𝑖 behaves as an

ideal solution in a solid, 𝛾𝑖 becomes unity and Eq. (B.12) corresponds Fick’s first law.
ji   Di

ci
x(B.13)In the case of ion (𝑍𝑖 ≠ 0) and ∇𝜇𝑖 = 0, Eq. (B.11) becomes below.
ji  

Zi Fci Di 
RTx(B.14)

Using the definition of current density 𝑖𝑖 = 𝑍𝑖 𝐹𝑗𝑖 [A/m2] and Ohm’s law, 𝑖𝑖 =𝜎𝑖 (− 𝜕𝜙⁄𝜕 ), following Nernst-Einstein equation is derived.

i 

Z i2 F 2 ci Di
RT(B.15)

Here 𝜎𝑖 is an ionic conductivity [S/m]. Finally, basic equation for ion conduction can beobtained as follows.
ii  

i

i
Z i F x

(B.16)As shown here, both Fick’s first law and basic equation for ion conduction are derived
from the same equation (B.11).

B.4

Chemical potential distribution in SOFC
In this section, typical chemical and electrochemical potential distributions in an

SOFC are explained. Here, a single cell consisting of YSZ electrolyte, Pt porous cathode,and Ni porous anode is assumed as shown in Figure B-3. In this figure, the number 1–8
represents the position of electrode top surfaces or electrode/electrolyte interface. In thiscell, electrochemical reaction sites are limited to Pt/YSZ/gas TPB (position 2, 6) for137

Non-biased
Ni porous
anode

BiasedLocal equilibrium𝜇̃O2 = 𝜇O 2𝜇̃e
Pt porous
cathode

YSZ

O2

𝜇̃O2

𝜇̃O2
𝜇O in gas phase

𝜇O in gas phase

𝜇O,cTPB𝑃O2 low

𝑃O2 hi h𝜇O

𝜇O,aTPB𝜇O in gas phase

𝑃O2 low𝜇O

𝑃O2 hi h𝐼𝑅𝑒 𝑒Terminal
voltage𝜇O in gas phase
𝜂𝑎

𝜇̃e

OCV

𝐼𝑅𝑎

𝜇̃e

𝜇𝑖 , 𝜇̃𝑖
4 3

2 1

𝐼𝑅𝑐

𝜂𝑐
8 7

6 5

Measurement

Measurement

Figure B-3. Typical chemical and electrochemical potential distributions (𝜇𝑖 , 𝜇̃𝑖 ) withrespect to thickness directionof an SOFC consisting of YSZ electrolyte, Pt porous
cathode, and Ni porous anode. Both non-biased and biased conditions are shown. The
number 1–8 represents the position of electrode top surface or electrode/electrolyte
interface.

cathode and Ni/YSZ/gas TPB (position 3, 7) for anode. The cathode side is exposed tohigh oxygen partial pressure 𝑃O2 hi h (~0.21–1 atm) while the anode side to low oxygen
partial pressure 𝑃O2 low (~10-20 atm in humidified hydrogen). Fig. B-3 shows the
distributions of chemical potential of oxygen 𝜇O and electrochemical potentials of oxide
ion 𝜇̃O2

and electron 𝜇̃ewith respect to the thickness direction

and biased conditions.

138

at both non-biased

In addition to oxide ion, electron also exists as a minor career in YSZ. From Eq.
(B.16), the equations for oxide ion and electron conduction in YSZ are described asfollows:
iO2- 
ie- 

O

2-

2F



O2-

 e e-F

where 𝜎O2



(B.17)

x-(B.18)

xand 𝜎eshows an ionic and electronic conductivity of YSZ, respectively.

In the non-biased condition, 𝜇O (equivalent to oxygen partial pressure) in YSZcontinuously decreases from the cathode to anode side as shown in Fig. B-3. In a steadystate ( 𝑖O2

and 𝑖ebecause 𝜎O2

is independent of), ∇𝜇̃O2

is constant based on Eq. (B.17)

is independent of 𝜇O . On the other hand, ∇𝜇̃e is not constant because

𝜎e in YSZ depends on 𝜇O [6]. In addition, local equilibrium between O2 , O, and
(O2

O

2

) is assumed in any position of YSZ [3], giving following relationship.

O  O  2e2-(B.19)-

In non-biased condition, there is no oxide ionic flow and ∇𝜇̃O2 is zero. As a result, 𝜇̃econtinuously increases from the cathode to anode side and its profile has an upside-down
curve of 𝜇O , as shown in Fig. B-3. The 𝜇̃eof Pt and Ni, which are actually detected inelectrochemical measurement, can be assumed to be the same as those of YSZ atelectrode/electrolyte interface at non-biased condition (position 2 and 3). The differenceof 𝜇̃ebetween anode and cathode (𝜇̃e (4) − 𝜇̃e (1)) detected here is an OCV.

The origin of OCV can be also qualitatively interpreted based on thephenomenological description. An oxygen vacancy formation in YSZ is described asfollows:
1
OO  VO  2e-  O2
2

(B.20)

139

×
where OO
and 𝑉O∙∙ represent O2− and oxygen vacancy in the YSZ bulk, respectively. The

equilibrium constant 𝐾e of reaction (B.20) is below.
K e = VO  ce- 2  PO2 1 2(B.21)In YSZ, vacancy concentration [𝑉O∙∙ ] is determined by the additive amount of yttrium andis independent of 𝑃O2 . Therefore, electron concentration in YSZ 𝑐e is proportional to
𝑃O2 1⁄4 . At anode side (𝑃O2 low ), more electrons are stored compared to cathode side
(𝑃O2 hi h), resulting in the higher 𝜇̃e .
In the biased condition, 𝜇̃O2

linearly decreases from cathode to anode sideaccompanied by an O2- flow, and the decrement of 𝜇̃O2

corresponds IR loss ofelectrolyte (𝐼𝑅𝑒 𝑒 ). At the cathode/electrolyte interface, 𝜇O drastically decreases from𝜇O (5), which corresponds to 𝑃O2 hi h, to 𝜇O,cTPB , and the difference 𝜇O (5) − 𝜇O,cTPB
is equivalent to cathode overpotential 𝜂𝑐 . Here 𝜇O (𝑘) (k = 1–8) denotes 𝜇O in position
k. In the same manner, the difference 𝜇O,aTPB − 𝜇O (8) corresponds to anodeoverpotential 𝜂𝑎 . In addition, 𝜇̃eof Pt and Ni linearly decreases from position 5 to 6(Pt) and 7 to 8 (Ni), which come from IR losses in cathode layer (𝐼𝑅𝑐 ) and anode layer(𝐼𝑅𝑎 ), respectively. As a result, terminal voltage corresponding to 𝜇̃e (8) − 𝜇̃e (5) issmaller than OCV, as shown in Fig. B-3. The calculation method of precise 𝜇O profile
inside YSZ electrolyte is given by Choudhury and Patterson [7]B.5

Overpotentials described by oxygen activity
The oxygen activity of YSZ near the anode TPB, 𝑎O , introduced in Chapters 2 and3 corresponds to 𝜇O,aTPB in Fig. B-3. From Fig. B-3,

O,aTPB  O (8)  2Fa

(B.22)

140

Here gas phase 𝑃O2 is assumed be constant at non-biased and biased condition in bothanode and cathode sides, that is, 𝜇O (1) = 𝜇O (5) and 𝜇O (4) = 𝜇O (8). As a result,

O,aTPB  O (4)  2 Fa(B.23) O (1)  2 F  OCV  2 Fa
𝜇O is rewritten by 𝑎O as follows:O  RT ln aO,aTPB  O  RT ln aO (1)  2 F a  OCV (B.24)

where 𝑎O,aTPB and 𝑎O (1) represents an oxygen activity of YSZ at anode TPB and ofgas phase in positon 1, respectively. From Eq. (B.24), following relationship is obtained.

 a  OCV 

RT  aO,aTPB 
ln 
2 F  aO (1) (B.25)

Replacing 𝑂𝐶𝑉 with 𝑉𝑅 𝑅 and 𝑎O (1) with 𝑎O(CR) gives Eq. (2.47) in Chapter 2.
In the same manner, 𝜂𝑐 can be also described by 𝑎O,cTPB , an oxygen activity of
YSZ at cathode TPB. From Fig. B-3,

O (1)  O,cTPB  2Fc

(B.26)

𝜇O is rewritten by 𝑎O as follows:O  RT ln aO (1)  O  RT ln aO,cTPB  2Fc

(B.27)

This gives following expression.

c RT  aO (1) ln 2 F  aO,cTPB (B.28)As shown in Eqs. (B.25) and (B.28), both anode and cathode overpotentials are related tooxygen activities near the reaction sites [8,9].

141

References[1] H. Yokokawa, Materia Japan 35 (9) (1996) 1025–1030. (in Japanese)[2] 水田進，脇原將孝（編），固体電気化学，実験法入門，講談社サイエンティフ
ィク (2001). (in Japanese)[3] N. Shikazono, D. Kanno, K. Matsuzaki, H. Teshima, S. Sumino, N. Kasagi, J.
Electrochem. Soc. 157 (5) (2010) B665–B672.
[4] K. Matsuzaki, N. Shikazono, N. Kasagi, J. Power Sources 196 (2011) 3073–3082.
[5] H. Mehrer, Diffusion in Solids, Springer, Maruzen (2012). (in Japanese)[6] 田 川博 章，固体酸化物燃料電池と地球環境，アグ ネ承風社 (1998). (inJapanese)[7] N.S. Choudhury, J.W. Patterson, J. Electrochem. Soc. 118 (9) (1971) 1398–1403.
[8] M. Ihara, T. Kusano, C. Yokoyama, J. Electrochem. Soc. 148, 3 (2001) A209–A219.
[9] H. Fukunaga, M. Koyama, N. Takahashi, C. Wen, K. Yamada, Solid State Ionics 132(2000) 279–285.

142

Appendix C

IV curves and fitting results of impedance spectra

The I-V curves of power generation experiment at 1073 K using YSZ electrolytesupported single cell with Ni/YSZ anode and LSM/ScSZ cathode are summarized in
Figure C-1, which were mentioned in Chapter 3, section 3.2. In addition, impedance
spectra, fitting curves, and obtained Rohm, R1, and R2 are shown in Figure C-2 for(𝑃H2 , 𝑃H2 O ) = (0.97,0.03) atm, in Figure C-3 for (𝑃H2 , 𝑃H2 O ) = (0.07,0.03) atm, in
Figure C-4 for (𝑃H2 , 𝑃H2 O ) = (0.02,0.03) atm, and in Figure C-5 for (𝑃H2 , 𝑃H2 O ) =(0.015,0.01) atm.

𝑃H2 , 𝑃H2O

Terminal voltage [V]

1.4

atm

0.97,0.03
0.07,0.03
0.02,0.03
0.015,0.01

1.2

1
0.8
0.6

0.4
0.2
0
0

0.1

0.2

0.3

0.4

Current density [A/cm2]
Figure C-1. I-V curves of YSZ electrolyte-supported single cell with Ni/YSZ anodeand LSM/ScSZ cathode at 1073 K under different four fuel compositions on anodeside. At cathode side, pure oxygen is supplied.
143

(b) 𝑖 = 0.082 A/cm2

0.3

0.3

0.2

0.2

0.1

0
0.4
-0.1

0.8

1.2

1.6

-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2](a) 𝑖 = 0 A/cm2

Rohm: 0.656
R1: 0.449
R2: 0.147 [Ω•cm2]

-0.2

0.1
0
0.4
-0.1

0.8

-0.3

Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2](d) 𝑖 = 0.24 A/cm2

0.2

0.2

0.1

0.1

-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2](c) 𝑖 = 0.16 A/cm2

0

-0.1

0.6

1.6

Rohm: 0.652
R1: 0.335
R2: 0.0894 [Ω•cm2]

-0.2

-0.3

0.4

1.2

0.8

1

1.2

Rohm: 0.646
R1: 0.164
R2: 0.124 [Ω•cm2]

0
0.4

-0.1

-0.2

-0.2

0.6

0.8

1

1.2

Rohm: 0.650
R1: 0.181
R2: 0.0481 [Ω•cm2]
Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2]

Figure C-2. Impedance spectra and fitting curves of Ni/YSZ anode at a direct currentof (a) 0 A/cm2, (b) 0.082 A/cm2, (c) 0.16 A/cm2, and (d) 0.24 A/cm2 under(𝑃H2 , 𝑃H2 O ) = (0.97,0.03) atm. The obtained fitted values Rohm, R1, and R2 are also
shown. The equivalent circuit for the fitting process is shown in Figure 3-4(b) in
Chapter 3.

144

(b) 𝑖 = 0.082 A/cm2(a) 𝑖 = 0 A/cm2
0.3

0.2

0.1
0.1

0
0.4
-0.1

0.8

1.2

1.6

Rohm: 0.684
R1: 0.279
R2: 0.219 [Ω•cm2]-0.2-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2]

0.2

0
0.4

0.6

0.8

1

1.2

Rohm: 0.681
R1: 0.187
R2: 0.147 [Ω•cm2]

-0.1

-0.2

-0.3

Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2](d) 𝑖 = 0.24 A/cm2(c) 𝑖 = 0.16 A/cm2

0.15

0.2

-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2]

0.1
0.1

0
0.4
-0.1

0.6

0.8

1

1.2

Rohm: 0.668
R1: 0.150
R2: 0.0946 [Ω•cm2]

0.05
0
0.5
-0.05
-0.1

-0.15

-0.2

Re(Z) [Ω•cm2]

0.7

0.9

1.1

Rohm: 0.672
R1: 0.110
R2: 0.0696 [Ω•cm2]
Re(Z) [Ω•cm2]

Figure C-3. Impedance spectra and fitting curves of Ni/YSZ anode at a direct currentof (a) 0 A/cm2, (b) 0.082 A/cm2, (c) 0.16 A/cm2, and (d) 0.24 A/cm2 under(𝑃H2 , 𝑃H2 O ) = (0.07,0.03) atm. The obtained fitted values Rohm, R1, and R2 are also
shown. The equivalent circuit for the fitting process is shown in Figure 3-4(b) in
Chapter 3.

145

(b) 𝑖 = 0.082 A/cm2(a) 𝑖 = 0 A/cm2
0.3

0.2

-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2]

0.2
0.1
0
0.4
-0.1

0.8

1.2

1.6

Rohm: 0.710
R1: 0.225
R2: 0.364 [Ω•cm2]

-0.2

0.1

0
0.4

0.8

1.2

1.6

Rohm: 0.703
R1: 0.163
R2: 0.289 [Ω•cm2]

-0.1

-0.2

-0.3

Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2](d) 𝑖 = 0.24 A/cm2(c) 𝑖 = 0.16 A/cm2

0.3

0.2

-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2]

0.2
0.1

0
0.4
-0.1

0.8

1.2

1.6

Rohm: 0.686
R1: 0.139
R2: 0.348 [Ω•cm2]

0.1
0
0.4
-0.1

-0.2
-0.3

-0.2

0.8

1.2

1.6

2

Rohm: 0.698
R1: 0.104
R2: 1.58 [Ω•cm2]
Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2]

Figure C-4. Impedance spectra and fitting curves of Ni/YSZ anode at a direct currentof (a) 0 A/cm2, (b) 0.082 A/cm2, (c) 0.16 A/cm2, and (d) 0.24 A/cm2 under(𝑃H2 , 𝑃H2 O ) = (0.02,0.03) atm. The obtained fitted values Rohm, R1, and R2 are also
shown. The equivalent circuit for the fitting process is shown in Figure 3-4(b) in
Chapter 3.

146

(b) 𝑖 = 0.082 A/cm2

0.4

0.4

0.2

0.2

-Im(Z) [Ω•cm2]-Im(Z) [Ω•cm2](a) 𝑖 = 0 A/cm2

0
0

0.5

1

1.5

2

2.5

Rohm: 0.615
R1: 0.450
R2: 0.961 [Ω•cm2]

-0.2

0
0
-0.2

0.5

1

1.5

2

2.5

Rohm: 0.755
R1: 0.499
R2: 0.937 [Ω•cm2]

-0.4

-0.4

Re(Z) [Ω•cm2]

Re(Z) [Ω•cm2](c) 𝑖 = 0.16 A/cm2-Im(Z) [Ω•cm2]

1

0.5

0

0
-0.5

1

2

3

4

5

6

Rohm: 0.930
R1: 0.682
R2: 4.01 [Ω•cm2]-1

Re(Z) [Ω•cm2]

Figure C-5. Impedance spectra and fitting curves of Ni/YSZ anode at a direct currentof (a) 0 A/cm2, (b) 0.082 A/cm2, and (c) 0.16 A/cm2 under (𝑃H2 , 𝑃H2 O ) =(0.015,0.01) atm. The obtained fitted values Rohm, R1, and R2 are also shown. The
equivalent circuit for the fitting process is shown in Figure 3-4(b) in Chapter 3.

147

Appendix D

Thermal design of quench system

D.1

Detailed structure of quench nozzle
In this Appendix, the detailed thermal design of the developed quench system in

Chapter 4 is presented. Figure D-1 shows the detailed structure of the helium nozzle
covered by the water cooling jacket and heat insulator. Inside the stainless tube with an
inner diameter of 𝐷1 = 6 mm and outer diameter of 𝐷2 = 8 mm, other two stainlesstubes for supply of cooling water (outer diameter 𝐷 ,O = 3.5 mm, wall thickness = 0.5mm) and for helium nozzle (outer diameter 𝐷He,O = 2 mm, wall thickness = 0.5 mm)
are inserted. The tube is covered by the heat insulator made of a ceramic fiber (3M TM,
NEXTELTM) with an outer diameter of 𝐷3 = 10 mm. This cooling unit is set inside amullite tube with an inner diameter of 𝐷4 = 16 mm and outer diameter of 𝐷5 = 21mm. The mullite tube is fixed with a SOFC single cell using a glass seal.

D.2

Assumed temperature distribution
Figure D-2 shows a schematic of an assumed temperature distribution of in a radial

direction of the cooling tube. Here, 𝑄 is a heat flux from a tubular electric furnace (Asahi
Rika Seisakusho Co., Ltd., ARF-50KC, Power output: 700 W). For simplicity in heatcalculation, the helium nozzle tube is not considered and the coaxial structure of two tubes
with the outer diameter of 𝐷 ,O and 𝐷2 are assumed in Fig. D-2, which are actually

148

𝐷3

𝐷2

𝐷1

𝐷w,o

SOFC cell

𝐷He,oCooling water

Fuel
or He

𝐷5

Stainless steel tube

Heat insulator

𝐷4

Mullite tube

Figure D-1. Detailed structure of the helium nozzle covered by the water cooling jacket
and heat insulator. The cooling unit is set inside a mullite tube, which is fixed with a
SOFC single cell using a glass seal.

eccentric as shown in Fig. D-1. The flow rate of cooling water and hydrogen gas are
assumed to be 0.9 L/min and 0.2 L/min, respectively. Each position in the radial direction
is numbered by 0 to 5 in Fig. D-2, and the temperature and radius of each position are
denoted by 𝑇𝑖 and 𝑟𝑖 ( 𝑖 = 0~5 ), respectively. 𝑇34 is a temperature of a middle
position between wall 3 and 4. In the experiment, an inside of the nozzle should be kept
at around room temperature while the SOFC cell is operated at 1073 K. Therefore, therequirement of the thermal design is 𝑇1 < 100℃ and 𝑇34 ≈ 800℃.

149

Mullite tube

Temperature

Radius5
4

𝑇34

𝑄

Heat insulator

H2

𝐷w,o (3.5 mm)

𝑇0

𝑟5 = 10.5 mm
𝑟4 = 8 mm

Water

3
2
1

𝑟3 = 5 mm
𝑟2 = 4 mm
𝑟1 = 3 mm

00 mm

Stainless steel
tube= 150 mm (length of heated region)
Figure D-2. Assumed temperature distribution of in a radial direction of the coolingtube. 𝑄 is a heat flux from a tubular electric furnace.

D.3

Heat transfer calculation
In order to calculate temperature of each position (𝑇0 ~𝑇5 ), heat resistance of eachposition needs to be calculated. Nusselt number near the wall 1 cooled by water (𝑁𝑢1 ) is
given as follows, which is for turbulence heat transfer in concentric annulus [1].

D 
Nu1
 1  0.14  W,O 
Nu ( Dh ) D1 

0.6(D.1)

Here, 𝐷ℎ = 𝐷1 − 𝐷 ,O is a hydraulic diameter and 𝑁𝑢(𝐷h ) is a Nusselt number of a
tube flow with a diameter of 𝐷h , which is calculated by Gnielinski’s expression [2].

Nu ( Dh ) ( f 2)  Re( Dh )  1000 Pr



(D.2)



1  12.7 f 2 Pr 2 3  1

150

where 𝑃𝑟 is a Prandtl number of water and 𝑅𝑒(𝐷ℎ ) is a Reynolds number based on the
representative length 𝐷ℎ . Friction factor in the pipe

is calculated by Blasius equation

as follows [2]:
f 

0.079
Re0.25(D.3)

As a result, 𝑁𝑢1 = 17.9 and heat transfer coefficient in the wall 1, ℎ1 = 4.39 × 103
W/(m2•K) are obtained. The heat resistance near the wall 1, 𝑅1 is expressed as follows:

R1 
where

1

1
2 L r1h1
(D.4)

is a length of heated region (= 150 mm).

Nusselt number near the wall 3 (𝑁𝑢3 ) or 4 (𝑁𝑢4 ) (𝑁𝑢3 = 𝑁𝑢4 ) is given by Stephan
as follows, which is for laminar heat transfer in concentric annulus [1].
0.8
Dh 4 

0.11
0.5
1
3
0.19
RePr












D
D
Pr
L




3
3

Nu3  3.66  1.2   1  0.14  
0.467   Prw 
D
D


4
 D4 




h4


1  0.117  RePr


L 




(D.5)
Here, 𝐷ℎ4 = 𝐷4 − 𝐷3 is a hydraulic diameter, 𝑅𝑒 is a Reynolds number based on the
representative length 𝐷ℎ4 , 𝑃𝑟 is a Prandtl number of hydrogen at 800 ℃, and 𝑃𝑟𝑤 is a
Prandtl number of hydrogen at wall temperature (𝑃𝑟 = 𝑃𝑟𝑤 is assumed). As a result,
𝑁𝑢3 = 𝑁𝑢4 = 4.61 and heat transfer coefficient in the wall 3 or 4, ℎ3 = ℎ4 = 3.97 ×
102 W/(m2•K) are obtained. The heat resistances near the wall 3 and 4, 𝑅3 and 𝑅4 areexpressed as follows.
R3 

1



1
2 L r3 h3

(D.6)

R4 

1



1
2 L r4 h4

(D.7)

151

The heat resistances by heat conduction from wall 1 to 2, 2 to 3, and 4 to 5 aredenoted by 𝑅12 , 𝑅23 , and 𝑅45 , respectively. These are expressed as follows.

R12 

r 
1
ln  2 
2 Lks  r1 

(D.8)

R23 

r 
1
ln  3 
2 Lki  r2 

(D.9)

R45 

r 
1
ln  5 
2 Lkm  r4 

(D.10)

Here 𝑘 , 𝑘i , and 𝑘m is a thermal conductivity of a stainless steel (𝑘 = 16.7 W/(m•K)),
heat insulator made of a ceramic fiber (𝑘i = 0.1 W/(m•K)), and mullite (𝑘m = 3.4
W/(m•K)), respectively.
As shown in Figure D-3, linear temperature profile is assumed for cooling waterflowing in the stainless tube to roughly estimate water temperature 𝑇0 . The energybalance of the water is described as follows: Cp u x

 D12 T4x  Cp u x

 D12 T0  Tin
4L q D1(D.11)

where 𝜌 and 𝐶 is a density and specific heat of water at room temperature, 𝑢𝑥 is aflow velocity, 𝑞 is a heat flux from the tubular electric furnace (𝑞 = 𝑄 ⁄( 𝐷1 )), and𝑇in is an inlet temperature of cooling water (𝑇in = 25℃). Here, total heat flux 𝑄 should
be lower than 350 W (half of maximum output of the electric furnace, 700 W). In thiscalculation, 𝑄 = 260 W is assumed and 𝑇0 is determined as follows.

T0 

4qL
 Tin  29.2 o C
Cpux D1

(D.12)

Finally, 𝑇1 ~𝑇5 are determined as follows.
T1  T0  QR1  50.1o C(D.13)

152

𝑄

Water, 0.9 L/min

𝑇0𝑟

𝐷1 = 6 mm
𝑇in = 25 ℃

Temperature profile

Stainlesssteel tube

𝑄
= 150 mm (length of heated region)

Figure D-3. Assumed linear temperature profile of cooling water. 𝑄 is a heat flux
from a tubular electric furnace.

T2  T1  QR12  54.9 o C(D.14)

T3  T2  QR23  670 o C(D.15)

T34  T3  QR3  809 o C(D.16)

T4  T3  QR4  896 o C(D.17)

T5  T4  QR45  918 o C(D.18)

These results fulfill the requirement of the thermal design: 𝑇1 < 100℃ and 𝑇34 ≈800℃.
Figure D-4 shows a drawing of the helium nozzle combined with water-coolingjacket used in this study. In this figure, flow directions of helium and water are also shown.
The total pressure drop of helium (10 L/min) and water (0.9 L/min) lines are estimated tobe 62.7 kPa and 28.9 kPa, respectively.

153

Helium out

Stainless pipe is brazed.
Side view of component 2
1

O-ring2
3

O-ringA-A’ cross section
4

WeldedWater out

WeldedO-ring A

A’

5
Water in6
Brazed[mm]

7Water outNo.

Component

1

Nut

2, 3

Joint

4, 5

Flange6

Water jacket

7

Coupling

Helium in

Figure D-4. A drawing of the helium nozzle combined with water-cooling jacket. Flow
directions of helium and water are shown.

154

References[1] Verein Deutscher Ingenieure (Ed.), VDI Heat Atlas, 4th Edition, Springer (1984),
Japan Management Association. (in Japanese)[2] The Japan Society of Mechanical Engineers, JSME Data Book: Heat Transfer 5th
Edition, pp. 45, Maruzen (2009). (in Japanese)155

Appendix E

Oxygen tracer diffusion coefficient and surface
exchange coefficient of LSM

Oxygen tracer diffusion coefficient D* and surface exchange coefficient k* of LSM
particles were determined by fitting Eq. (4.8) to line profiles of 18O concentration 𝑐18O
in Chapter 4, section 4.3. All measured points, examples of fitted graph, and obtained D*
and k* values are shown in Appendix E. All measured points in section A (OCV) and C(biased, directly under the contact area of the current collector) are shown in Figure E1(a) and (b), respectively. Examples of fitting results are shown in Figure E-2, and all D*
and k* values obtained here are summarized in Table E-1 for section A and in Table E-2
for section C. In Table E-1 and E-2, distance d of each point (LSM/gas interface at eachmeasured line profile) from electrolyte/cathode interface is also shown.

156

(a) Section A
7

8

14

4

3

7

8

14

15

4

3

15

12

12

9

9

10

10

6

1

6

1

5

2

5

2

13

13
11

11

(b) Section C
12

12

5

5

6

10

6

10

3

3

14

14

4

15

15

1

1

7

2

8

4

8

13

7

2
13

9

9

11

11

Figure E-1. All measured points of 𝑐18O line profiles to determine oxygen tracer
diffusion coefficient D* and surface exchange coefficient k* for (a) section A (OCV)
and (b) section C (biased, directly under the contact area of the current collector).

157

(a) Point #13 in section A(b) Point #11 in section C
0.15

Exp.
Fitting

0.1

𝑐18O [-]

𝑐18O [-]

0.15

0.1

0.05

0.05

0

0
0

0.2

0.4

0.6

Position

[µm]

0.8

Exp.
Fitting

0

0.2

0.4

Position

0.6

0.8

[µm]

Figure E-2. Fitting results of diffusion equation [Eq. (4.8)] to 18O concentration profile
𝑐18O at (a) Point #13 in Section A (OCV, Fig. E-1(a)) and (b) Point #11 in Section C(biased, Fig. E-1(b)). Positive direction in position x corresponds to each arrow
direction in Fig. E-1.

158

Table E-1. All fitted D* and k* of LSM at point #1-15 in section A (OCV, Fig. E-1(a)).
Distance of each point from electrolyte/cathode interface (d) is also shown.

Point #

D* [cm2/s]

k* [cm/s]

d [µm]

1

6.70 × 10-14

5.50 × 10-10

0.424

2

5.00 × 10-14

4.40 × 10-10

0.693

3

2.00 × 10-13

1.30 × 10-9

4.977

4

7.00 × 10-14

7.00 × 10-10

5.762

5

9.00 × 10-14

4.80 × 10-10

9.676

6

7.00 × 10-14

4.33 × 10-10

10.003979.50 × 10-14

9.30 × 10-10

6.63

8

1.50 × 10-13

1.10 × 10-9

5.822

9

1.50 × 10-13

1.10 × 10-9

4.7

10

1.80 × 10-13

1.30 × 10-9

4.199

11

5.50 × 10-14

8.70 × 10-10

6.858

12

8.80 × 10-14

1.85 × 10-9

10.73913

1.30 × 10-13

1.65 × 10-9

3.458

14

1.85 × 10-13

2.40 × 10-9

1.452

15

2.30 × 10-13

2.40 × 10-9

8.412

159

Table E-2. All fitted D* and k* of LSM at point #1-15 in section C (biased, Fig. E1(b)). Distance of each point from electrolyte/cathode interface (d) is also shown.

Point #

D* [cm2/s]

k* [cm/s]

d [µm]

1

5.50 × 10-13

6.20 × 10-9

4.367

2

3.50 × 10-13

4.80 × 10-9

5.089

3

2.70 × 10-13

3.00 × 10-9

9.131

4

3.70 × 10-13

3.20 × 10-9

9.045

5

3.00 × 10-13

1.50 × 10-8

12.9096

2.40 × 10-13

1.25 × 10-8

12.8217

1.00 × 10-13

1.35 × 10-9

12.6338

2.70 × 10-13

6.50 × 10-9

3.786

9

2.60 × 10-13

2.60 × 10-9

4.289

10

2.20 × 10-13

8.00 × 10-9

5.016

11

3.00 × 10-13

5.05 × 10-9

5.361

12

4.40 × 10-13

4.00 × 10-9

10.79513

3.80 × 10-13

2.90 × 10-9

10.18414

2.50 × 10-13

7.20 × 10-9

6.299

15

5.60 × 10-13

6.30 × 10-9

7.42

160

Acknowledgements

First of all, my greatest appreciation goes to my supervisor, Professor Katsunori
Hanamura, a respectable scientist and engineer in mechanical and thermal engineering.
His continuous encouragements, valuable ideas, essential comments, and abundant
knowledge has greatly helped my research go well. Many of ideas in this thesis were bornfrom the fruitful discussions with him, and his critical insights often illuminated the newresearch directions. It’s my great pleasure to continue the research activities with him for
6 years from undergraduate to Ph.D. course.
I would like to express my gratitude to members of my committee, Professor Isao
Satoh, Professor Shuichiro Hirai, Professor Ichiro Yamanaka, and Associate Professor
Kazuyoshi Fushinobu for spending precious time to evaluate the thesis and giving
valuable comments, which were truly helpful to improve the quality of the thesis.
My deep thanks also go to the faculty members and staff of Hanamura laboratory. I
want to thank Assistant Professor Hirotatsu Watanabe for his critical comments andfruitful discussions. His active attitude toward researches is a good example for me as ayoung researcher. I also thank Assistant Professor Masamichi Nakagawa for his valuablecomments in seminars. I want to show my special thanks to Ms. Hiroe Shikata, a secretaryof the laboratory, for her works in office procedure, which was indispensable for our
research and daily activities.
I would like to show my appreciation to the faculty members and staffs of HiraiSasabe laboratory. I thank Professor Shuichiro Hirai for his valuable comments in the
joint seminars and daily life. His attitude and vision in research always reminds me the161importance of research background, value, and role in society. I thank Project Associate
Professor Suguru Uemura for his kind and continuous help in research and daily activities.
I thank Associate Professor Takashi Sasabe, Project Professor Toshihiko Yoshida, and all
the other current and former staffs. My special thanks goes to Project Associate Professor
Yuki Kameya for his great help and many valuable advices about my future career.
The days at Georgia Institute of Technology as a visiting researcher was also an
irreplaceable experience for me. I specially thank Professor Meilin Liu, my supervisor in
Atlanta. His abundant ideas and knowledge of material science and practical attitude in
research made my stay so productive. I would like to express my thanks to Dr. DongchangChen, Dr. Samson Yuxiu Lai, and all the other members in Liu group.
The connection with many researchers in SOFC field is of great value andimportance. I thank Professor Manabu Ihara in Tokyo Tech for giving precise knowledge
in solid state electrochemistry and discussing with me many times. I also thank themembers of Ihara laboratory for the support in fuel cell preparation. I thank Associate
Professor Tomofumi Tada in Tokyo Tech for telling me fundamentals of first principle
calculation. I thank Professor Michihisa Koyama in Kyushu University, Associate
Professor Hiroshi Iwai in Kyoto University, and Professor Naoki Shikazono in The
University of Tokyo, for discussing with me many times.
I got many technical supports in experiments. I thank staffs in Ookayama Materials
Analysis Division, especially Mr. Jun Koki for the support in sample preparation forsecondary ion mass spectroscopy (SIMS). I thank staffs in the factory of Tokyo Tech. My
special thanks goes to Dr. Miyuki Takeuchi in The University of Tokyo for the great
support in SIMS measurement.
I received generous supports in financial and research environment. I thank162

Academy for Co-creative Education of Environmental and Energy Science (ACEEES), a
leading graduate school in Tokyo Tech, and its staffs for financial support and giving
many valuable opportunities including the stay in Georgia Tech. I thank the Japan Society
for the Promotion of Science (JSPS) for financial support.
Most memories in the graduate school are brought back with many lab-mates. I
would like to express my deep gratitude to all the current and former members of Tanso
Center (Hanamura and Hirai-Sasabe laboratories), with whom I greatly enjoyed theresearch and daily activities. Special thanks go to two former Ph.D. students in Hanamura
laboratory, Dr. Ryoko Chijiiwa (Sanui) and Dr. Naphatsorn Vongsoasup. We shared thelong time as lab-mates and encouraged and stimulated each other, which are important
memories for me. I also specially thank Mr. Masaru Kanie and Ms. Merika
Chanthanumataporn in Hanamura laboratory for spending a long time on the SOFC
research together. It’s my great fortune and pleasure to share the time with all themembers in Tanso Center.
The last words of appreciation go to my family. I would like to express the deepest
gratitude from the bottom of my heart to my parents and sister for their continuous, kind,
and warm encouragements and supports throughout my long Ph.D. life.

Tsuyoshi Nagasawa
Ookayama, Tokyo
March 2018163

Publications

Journals (reviewed)
Related to the thesis
1. Tsuyoshi Nagasawa, Katsunori Hanamura, “Power generation characteristics of a
SOFC with a Ni/YSZ anode incorporating a SrZr0.95Y0.05O3-α proton conductor”,
Journal of Thermal Science and Technology 10 (1) (2015) 15-00112. (Chapter 3)
2. Tsuyoshi Nagasawa, Katsunori Hanamura, “Theoretical analysis of hydrogen oxidation
reaction in solid oxide fuel cell anode based on species territory adsorption model”,
Journal of Power Sources 290 (2015) 168–182. (Chapter 2)
3. Tsuyoshi Nagasawa, Katsunori Hanamura, “Prediction of overpotential and effective
thickness of Ni/YSZ anode for solid oxide fuel cell by improved species territory
adsorption model”, Journal of Power Sources 353 (2017) 115–122. (Chapter 3)
4. Tsuyoshi Nagasawa, Katsunori Hanamura, “Microstructure-scaled active sites imaging
of a solid oxide fuel cell composite cathode”, Journal of Power Sources 367 (2017)57–62. (Chapter 4)

Others
5. Masaru Kanie, Warit Ua-Amnueychai, Merika Chanthanumataporn, Keiji Asada,
Tsuyoshi Nagasawa, Katsunori Hanamura, “Surface reaction controlling hydrogen
permeation through lanthanum-doped ceria membrane with asymmetric structure”,
Mechanical Engineering Letters 1 (2015) 15-00359.
6. Tsuyoshi Nagasawa, Dongchang Chen, Samson Yuxiu Lai, Meilin Liu, Katsunori

164

Hanamura, “In situ Raman spectroscopic analysis of the coking resistance mechanism
on SrZr0.95Y0.05O3-x surface for solid oxide fuel cell anodes”, Journal of Power Sources
324 (2016) 282–287.

International Conference Proceedings (reviewed)
Related to the thesis
1. Tsuyoshi Nagasawa, Katsunori Hanamura, “Reaction Characteristics around Triple
Phase Boundary in Anode including Proton Conductor for Solid Oxide Fuel Cell”, ECS
Transactions 64 (2) (2014) 117–134.
2. Tsuyoshi Nagasawa, Katsunori Hanamura, “Overpotential and Interfacial Conductivityof Ni/YSZ Anode Based on Species Territory Adsorption Model in SOFCs”, ECS
Transactions 68 (1) (2015) 1315–1322.
3. Tsuyoshi Nagasawa, Katsunori Hanamura, “Particle-scaled Visualization of Active
Sites in LSM/ScSZ Composite Cathode of SOFC through Oxygen Isotope Labeling”,
ECS Transactions 78 (1) (2017) 855–859.
4. Tsuyoshi Nagasawa, Katsunori Hanamura, “Quenching of chemical species transport
in SOFC by He impinging jet for visualization of oxide ion path in composite
electrodes”, Extended Abstracts of the Ninth JSME-KSME Thermal and Fluid
Engineering Conference (2017) TFEC9-1072.

Others
5. Merika Chanthanumataporn, Tsuyoshi Nagasawa, Masaru Kanie, Katsunori Hanamura,“A Proton-Conducting Solid Oxide Fuel Cell with an Yttrium and Tin Co-Doped
Barium Zirconate Electrolyte”, The 27th International Symposium on Transport

165

Phenomena, ISTP27 Proceedings (2016) pp.27.
6. Hirotatsu Watanabe, Masaru Kanie, Merika Chanthanumataporn, Tsuyoshi Nagasawa,
Katsunori Hanamura, “Experimental and Detailed Kinetic Modeling Study of Carbon
Deposition on Ni/YSZ Anode in SOFC”, ECS Transactions 78 (1) (2017) 1107–1114.

166