Fundamental Studies of SOFC Materials Eric D. Wachsman University of Florida - U.S. Department of Energy High Temperature Electrochemistry Center Department of Materials Science and Engineering University of Florida QuickTime™ and a GIF decompressor are needed to see this picture. UF-DOE HiTEC [email protected]http://hitec.mse.ufl.edu
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Fundamental Studiesof SOFC Materials...Mogensen et al., Solid State Ionics, 129 (2000) 63 4. K. Sasaki and J. Maier, Solid State Ionics, 134 (2000) 303 EXTENSION OF MODEL TO THERMO-MECHANICAL
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Fundamental Studies of SOFC Materials
Eric D. WachsmanUniversity of Florida - U.S. Department of Energy
High Temperature Electrochemistry CenterDepartment of Materials Science and Engineering
Determination of Electrochemical Performance and Thermo-Mechanical-Chemical Stability of SOFCs from Defect ModelingDOE SECA Contract No: DE-FC26-02NT41562DOE Project Manager: Travis Schultz•Advance the fundamental understanding of the continuum-level electrochemistry of oxide mixed ionic-electronic conductors.•Obtain fundamental constants required for implementing the continuum-level electrochemical model from experiment. •Extend the models to multilayer structures and incorporate microstructural effects.•Verify the models through experiment.•Develop a transient version of the continuum-level electrochemical model.•Obtain time constants for various transport processes from electrical impedance spectroscopy to examine the effects of transients on SOFC performance.•Develop and deliver software modules for incorporation of the continuum-level electrochemical model into SOFC failure analysis software used by NETL, PNNL, ORNL and the SECA industrial teams.
Electrocatalytically Active High Surface Area Cathodes for Low Temperature SOFCsDOE EE/FE Contract No: DE-FC26-03NT41959DOE Project Manager: Lane Wilson•Develop a fundamental understanding of heterogeneous electrocatalytic phenomena at the surface of ion conducting ceramics.•Fabricate high surface area SOFC cathodes with controlled microstructure and porosity.•Develop low ASR cathodes for low to intermediate temperature SOFCs.
UF - DOE High Temperature Electrochemistry CenterDOE Advanced Research, HiTEC Contract No: DE-AC05-76RL01830DOE Project Manager: Lane Wilson•Develop the fundamental understanding of ionic transport in, and electrocatalytic phenomena on the surface of, ion conducting materials, spanning the range from first-principles calculations and molecular dynamic simulations of ionic transport and gas-solid interactions to synthesis and characterization of novel ion conducting materials and electrocatalysts.
Defect Energetics and Mobility Based on:• Crystal structure• Cation radii• Cation polarizability• Cation oxidation state• Etc.
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Ebond = A
r m
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIES
− Br n
A, B, n and m are constants
Lattice constant, a, has linear relationship with cv
Therefore, r ~ a ~ cV
Thermal expansiona − a0
a0
= αΔT
Chemical expansiona − a0
a0
=θa0
cV
Thermo - chemical expansiona − a0
a0
= αΔT +θa0
cV
cV =34
Kr
12PO2
− 14 +
A2
⎛ ⎝ ⎜
⎞ ⎠ ⎟
32
⎡
⎣
⎢ ⎢
⎤
⎦
⎥ ⎥
23
0
5000
10000
15000
20000
25000
0 24 48 72 96 120 144
Heat up in air
Dry Argon
5% wet H2/N
2
50% wet H2/N
2
Wet H2
Dry H2
Cool down in H2
Decreasing pO2
Ther
mo-
Che
mic
al E
xpan
sion
Δl/l
o x 1
0-6
Time (hrs)
Thermo-Chemical Expansion of GDC
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIES
0 100
3 103
6 103
9 103
12 103
0 5 10 15 20 25-log( pO
2 ) /atm
Che
mic
al E
xpan
sion
Δl/l
o x 1
0-6
0 100
3 103
6 103
9 103
12 103
0 5 10 15 20 25Che
mic
al E
xpan
sion
Δl/l
o x 1
0-6
-log( pO2 ) /atm
Kr = 1072 m-9atm-0.5 [1]
A = 0 m-3
θ = 3.2 x 10-3 nm3 [2,3]
Undoped Ceria GDC
Δll0
= αΔTthermal{ +θ 3
4KR
12 PO2
−14 + 1
2A( )
32
⎛
⎝ ⎜
⎞
⎠ ⎟
23
chemical1 2 4 4 4 3 4 4 4
Kr = 1072 m-9atm-0.5 [1]
A = 2.5 x 1027 m-3
θ = 3.2 x 10-3 nm3 [2,3]
1. T. Kobayashi et al., Solid State Ionics, 126 (1999) 3492. D.J. Kim, J. Am. Ceram. Soc., 72 (1989) 14153. M. Mogensen et al., Solid State Ionics, 129 (2000) 63 4. K. Sasaki and J. Maier, Solid State Ionics, 134 (2000) 303
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIES
0 100
3 103
6 103
9 103
12 103
0 10 20 30 40 50-log( pO
2 ) /atm
Che
mic
al E
xpan
sion
Δl/l
o x 1
0-6
Kr = 1060 m-9atm-0.5 [4]
A = 4.4 x 1027 m-3
θ = 3.2 x 10-3 nm3 [2]
YSZ
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
Ybond = 1r0
d 2Edr2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟ r=r0
Ebond = A
r m − Br n
A, B, n and m are constants
Lattice constant, a, has linear relationship with cv
Therefore, r ~ a ~ cV
1. D-J. Kim, J. Amer. Ceram. Soc. 72 (1989) 1415.2. M. Mogensen, N. Sammes, G. Tompsett, Solid State Ionics 129 (2000) 63
YY∗
≈ aa0
⎛
⎝ ⎜
⎞
⎠ ⎟ − δ+3( )
aa0
= θcV +1
Y ≈ Y∗ θcV +1( )− δ+3( )
δ is equivalent to:• n (if A is constant)• m (if B is constant)as oxygen vacancies are introduced
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIES
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIESExperimental Validation
PO 2= 0.22 atm
PO2=9.5x10-5 atm
PO2=1.8x10-17 atmPO
2=4.5x10-22 atmPO
2 =5.1x10 -25atm
A
B
C
D
E
F
PO 2= 0.22 atm
PO2=9.5x10-5 atm
PO2=1.8x10-17 atmPO
2=4.5x10-22 atmPO
2 =5.1x10 -25atm
A
B
C
D
E
F
PO 2= 0.22 atm
PO2=9.5x10-5 atm
PO2=1.8x10-17 atmPO
2=4.5x10-22 atmPO
2 =5.1x10 -25atm
A
B
C
D
E
F
P O2
Vacancies preserved by fast cooling
5oC/
min
Fast cool
800oC, 5 hr
Tem
p. o C
Time, hr
H2, H2/H2O,N2, Air
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIESExperimental Validation - Nanoindents and Microstructure
SEM image of surface after thermal etch. Average grain size ~12 µm.
20 μ m
1 µ m
Nanoindents
Size: ~0.6 µm
Depth: ~125 nm
•Effect of crystallographic orientation on elastic modulus and hardness evaluated statistically by applying many indents on grains of known orientation.
•In-plane anisotropy can be measured by changing the indent orientation.
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIESExperimental Validation - Nanoindents and Microstructure
SEM image of surface after thermal etch. Average grain size ~12 µm.
• 100 indents were applied on the sample, which covered 100 µm X 100 µm ( ~25 different grains)
Modulus: 218.35±11.12 GPa
Hardness: 9.00±0.73 Gpa
• The small variations imply that ceria is elastically isotropic.
20 μ m
1 µ m
Nanoindents
Size: ~0.6 µm
Depth: ~125 nm
experiment
Y,Effect of Oxygen Vacancy Population on Elastic Modulus of
Ceria(measured in air)
Y,
experiment
model
Y( PO2) ≈ Y∗ θcV (PO2
) +1( )− δ+3( )
Effect of Oxygen Vacancy Population on Elastic Modulus of
Ceria(measured in air)
Y,
experimentmodel
Effect of Oxygen Vacancy Population on Elastic Modulus of
Ceria(measured in air)
Y( PO2) ≈ Y∗ θcV (PO2
) +1( )− δ+3( )
Y,
experiment
Effect of Oxygen Vacancy Population on Elastic Modulus of
Gadolinia-Doped Ceria (GDC)
(measured in air)
Y,
experiment model
Y( PO2) ≈ Y∗ θcV (PO2
) +1( )− δ+3( )
Effect of Oxygen Vacancy Population on Elastic Modulus of
Gadolinia-Doped Ceria (GDC)
(measured in air)
Y,
experiment model
Effect of Oxygen Vacancy Population on Elastic Modulus of
Gadolinia-Doped Ceria (GDC)
Y( PO2) ≈ Y∗ θcV (PO2
) +1( )− δ+3( )
(measured in air)
Y,
experiment
Effect of Oxygen Vacancy Population on Elastic Modulus of
Yttria-Stabilized Zirconia (YSZ)
(measured in air)
Y,
experimentmodel
Y( PO2) ≈ Y∗ θcV (PO2
) +1( )− δ+3( )
(measured in air)
Effect of Oxygen Vacancy Population on Elastic Modulus of
Yttria-Stabilized Zirconia (YSZ)
Higher temperature and higher current will shift decrease in modulus to higher PO2
Y,Effect of Oxygen Vacancy Population on Elastic Modulus of
Ceria, GDC,YSZ
Y( PO2) ≈ Y∗ θcV (PO2
) +1( )− δ+3( )
Extend to Include Microstructural Effects:
Y(p) = Yp=0(1−p)r where p is porosity and r ≈ 2 for porous ceramics [1]
Y(PO2, p) = Y*(θcV(PO2)+1)-(δ+3)(1−p)r
1. A. S. Wagh, R. B. Poepel, J. P. Singh, J. Mat. Sci., 26 (1991) 3862.
EXTENSION OF MODEL TO THERMO-MECHANICAL PROPERTIESY,
Y(PO2) ≈ Y ∗ θ 3
4 KR
12 PO2
− 14 + 1
2 A( )32( )
23
chemical1 2 4 4 4 3 4 4 4
+1⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
− δ +3( )
0 100
3 103
6 103
9 103
12 103
0 5 10 15 20 25-log( pO
2 ) /atm
Che
mic
al E
xpan
sion
Δl/l
o x 1
0-6
Δll0
= αΔTthermal{ + θ 3
4 KR
12 PO2
− 14 + 1
2 A( )32( )
23
chemical1 2 4 4 4 3 4 4 4
SAME!
1. D-J. Kim, J. Amer. Ceram. Soc. 72 (1989) 1415.2. M. Mogensen, N. Sammes, G. Tompsett, Solid State Ionics 129 (2000) 63
KR = Equilibrium constant for VO•• formation
A = Dopant concentration
θ = Empirical constant = 3.2 x 10-3 nm3 [1,2]
FUNDAMENTAL QUANTITATIVE DEFECT CONSTANTS
UF-DOE HiTEC
Thermodynamics of Oxides•Computational and experimental thermodynamicsof SOFC materials.
Calculated Zr-O phase diagram
Equilibrium constant for VO•• formation
OOX = VO
•• + 2e’ + 1/2O2
KR = [VO•• ] n2 PO2
0.5/[OOX]
KR
FUNDAMENTAL QUANTITATIVE DEFECT CONSTANTS
UF-DOE HiTEC
Computational Materials Thrust•Large-scale molecular dynamics simulations to elucidate the effects ionic radius and polarizability of on ionic conductivity, the structure of vacancy clusters, and the mechanisms of oxygen transport.•First principles, electronic structure simulations. Calculation of defect formation energy in oxides from first principles and thermodynamics. Study of oxygen reactions at surfaces and interfaces.
Ni-GDC GDC LSCF
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Ebond = A
r m − Br n
A, B, n and m are constants
θ = ?
FUNDAMENTAL QUANTITATIVE DEFECT CONSTANTS
Ni-GDC GDC LSCF
Ab-initio calculation of ZrO2 grain boundary and comparison with Z-contrast TEM image
Defect formation energiesas a function of PO2
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
VO••
VO•
VOx
Computational Materials Thrust•Large-scale molecular dynamics simulations to elucidate the effects ionic radius and polarizability of on ionic conductivity, the structure of vacancy clusters, and the mechanisms of oxygen transport.•First principles, electronic structure simulations. Calculation of defect formation energy in oxides from first principles and thermodynamics. Study of oxygen reactions at surfaces and interfaces.
UF-DOE HiTEC
θ = ?
log
[ i ]
(m
-3)
log PO2 (atm.)
High-PO2 (model)
FUNDAMENTAL PROPERTIES
Brouwer Region Ice = 2cVO
Brouwer Region IIacD = 2cVO
Brouwer Region IIbcD = ch
Brouwer Region III3cVA
+ 3cVB = ch
′ ′ ′ V A
′ e
VO••
′ M A
h •
Intermediate-PO2 (model)
Low-PO2 (model)
′ ′ ′ V B
20 15 10 5 0 515
10
5
0
Same approach being applied to perovskites• Defect equilibria already developed
DEFECT EQUILIBRIADEFECT STRUCTURE
LaFeO3: Rhombohedrally distorted perovskite
• Structural optimization in progress
UF-DOE HiTEC
Calculated Lattice Constants
a= 3.7822 Å c= 3.6493 Å
Cutoff Energy : 500 eVExchange-Correlation approximation: LDAK-POINT spacing: 2X2X2
J.-W. Kim, A. Virkar, K.-Z. Fung, K. Mehta and S. Singhal, J. Electrochem. Soc., 146 (1999) 69-78S. Chan, K. Khor, Z. Xia, J. Power Sources, 93 (2001) 130
CATHODE
EXTEND MODEL TO INCLUDE MICROSTRUCTURAL EFFECTS
21
2O
2
0 1P
ccc
kTqK
V
eVJ −
=⎟⎠⎞
⎜⎝⎛ η
=exp
DEFECT CONCENTRATION
( ) ⎥⎦⎤
⎢⎣⎡
⎟⎠⎞
⎜⎝⎛ ηα−−−⎟
⎠⎞
⎜⎝⎛ αη= 10 kT
qkTqJJ expexp
ACTIVATION OVERPOTENTIAL
⎟⎟⎠
⎞⎜⎜⎝
⎛Φ−Φ
η−−−
⎟⎟⎠
⎞⎜⎜⎝
⎛Φ−Φ
η−−−
⋅
⎟⎟⎠
⎞⎜⎜⎝
⎛Φ−Φ
η−−
⎟⎟⎠
⎞⎜⎜⎝
⎛Φ−Φ
η−+=−Φ−Φ
extthVe
VAeV
extthVe
VAeV
V
B
extthVe
extthVeV
V
V
V
Bthext
uu
zcuc
uu
zcuc
qzTk
uu
uuz
cc
qzTk
L
L
1
1
1
1
00
lnln
POTENTIAL
•Electrochemical model (with pore diffusion incorporated) matches “Virkar”* model, but with less fitting parameters, (3 vs. 10)
•Fitting parameters: τa/Da (effective tortuosity anode), τc/Dc (effective tortuosity cathode) and io (exchange current density).
wTPB ≡ f(geometry, contact area, material property)
UF-DOE HiTEC
UF-DOE HiTEC
QuickTime™ and a decompressor
are needed to see this picture.
LSM (Nextech) on YSZ
Consecutive 50nm slices
QUANTIFYING MICROSTRUCTURE
Tortuosity
τ = zpath/zthickness
ACKNOWLEDGEMENTCollaborating Faculty:Dr. Kevin Jones - FIB/SEM CharacterizationDr.’s Susan Sinnott & Simon Philpott - Computational MaterialsDr. Fereshteh Ebrahimi - Mechanical PropertiesDr. Juan Nino - Novel Oxide Materials DevelopmentDr. Wolfgang Sigmund - Novel Synthesis & MicrostructuresDr. Hans Seifert - Materials ThermodynamicsDr. Xin Guo - Nano Ionics and Interfaces
Results by post-docs:Dr. Keith Duncan, Dr. Jiho Yoo & Dr. Heesung YoonResults by graduated students:Dr. Abhishek Jaiswall, Dr. Jun-Young Park, Dr. Jamie Rhodes, Dr. Sun-Ju Song, Dr. Keith Duncan, Terry Clites, Su-Ho Jung, Sai Boyapati, Naixiong JiangResults by current graduate students:Jeremiah Smith, Matthew Camaratta, Sean Bishop, Yanli Wang, Briggs White, Joshua Taylor, Vincenzo Esposito, Chiara Abate, Jin Soo Ahn, Aidhy Dilpuneet, Brian Blackburn, Chin-Tang Hu, Shobit Omar, Eric Armstrong, Martin VanAssche, Cynthia Chao, Eric Macam, Tak-keun Oh, Doh Won Jung, Dan Gostovic, Aijiie Chen, JianlinLi, Chris Woan, Guojing Zhang UF-DOE HiTEC