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8/10/2019 Dissertation Vogler
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E cell
cathode
O2 H
2
H2O
O2-
. .
e- e
-
electrolyte
anode
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H2 + 1/2O2 H2O .
1/2O2 + 2e− O2− ,
H2 + O2− H2O + 2e− .
∆H
∆G = ∆H − T ∆S
ηFC = ∆G
∆H .
T 1
T 2
ηCarnot = T 1 − T 2
T 1.
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80 C
OH−
H2
80 C 150 C
H+
H2
≤
80 C H+
200 C
H+
H2
650 C
CO2−3
H2
900 C
600 C
O2− H2
H2
O2
E th
cell
E thcell = −
1
zF ∆G ,
z
F
E thcell = −
∆G0
zF −
RT
zF · ln
aH2O
aH2 a0.5O2
,
∆G0
R
T
ai
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H2
CO
H2
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Y2xZr1−2xO2−x
x
Y2O3
ZrO2
ZrO2
Gd2xCe1−2xO2−x−δ
x
Gd2O3 CeO2
δ
La1−xSrxMnO3
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E c e l l
[ V ]
i cell
00
E cell
OCV
a)
-0.5η [V]
0.5
l o g i c
e l l
[ A / c m ² ]
0
b)
cathodic branch
anodic branch
[A/cm²]
R pol
η = E th
cell
−E cell
η > 0
η < 0
i
E cell(i)
η(i) = E OCV
cell −E cell(i)
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E c e l l
[ V ]
i cell
00
a)
f [Hz]
10-1
100
101
102
103
104
R e ( Z ) [
Ω / c m ² ]
b)
R pol
[A/cm²]
E(t)
i(t)
I m ( Z ) [ Ω
/ c m ² ]
0
200
100R pol
Rpol
i(t)
Z
Rpol
Rpol
Rpol = dη
di .
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a)
100 μm
b)
YSZ
Ni
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HNi
O2−YSZ
Hgas2
Ogas2
OXOYSZ
Hx
i Ni
e−
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E
∆G = −zFE ,
∆G
F
z
E
H2 + 1/2O2 H2O .
Hgas2 + OX
OYSZ H2Ogas + V••OYSZ + 2 e− ,
1
2Ogas
2 + V••OYSZ + 2 e− O2−
YSZ .
V••
OYSZ
O2−YSZ
OX
OYSZ
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y
I,E cell I,E cell
η
counter
electrolyte
work ref
porous anode
porous cathode
electrolyte
LE
a) b)
∆φequil
∆φequil,an = ∆Gan
2F −
RT
2F · ln
a(H2) · a(OX
OYSZ)
a(H2O) · a(V••OYSZ)
,
∆φequil,ca = ∆Gca
2F −
RT
2F · ln
a(OX
OYSZ)
a(O2)1/2 · a(V••OYSZ)
.
E equil = ∆φequil,ca − ∆φequil,an .
∆φ
∆φan = φelde,an − φelyt,an and ∆φca = φelde,ca − φelyt,ca ,
φelde
φelyt
i
E (i) = φelde,ca − φelde,an(i) .
E (i)
i
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y
i
φelde,ca
∆φelde,ca = φelde,ca − φelyt,ca(y) and ∆φelde,an = φelde,an − φelyt,an(y) .
∆φca
∆φan φelyt
i
iV
F
iel
i = LE
y=0
iVF dy + iel .
iV
F
LE
i
η(i)
η(i) = φelde,work(i) − φelde,ref − iRelyt,
φelde,work(i)
φelde,ref
i
∆φelde,work = φelde,work−φelyt,work and ∆φelde,ref = φelde,ref −φelyt,ref .
i
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i∈Rf
ν
i A
i + z e−
j∈Rr
ν
j A
j
A
A
ν
ν
z
∆φ = φelde − φelyt
kr/f
kf = k0f exp−
E actf
RT exp− (1 − α) zF
RT · ∆φ ,
kr = k0r exp
−
E actr
RT
exp
α
zF
RT · ∆φ
.
E act
α
F,R,T
i
si
si = ν i kf j∈Rf ,
Aν
j
j − kr j∈Rr,
Aν
j
j ,
si
Ai
si
ji = zF si .
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∆φ = 0
si
∆G
∆G = ∆H − T ∆S ≡ 0 .
∆H
∆S
∆H =i∈Rf
ν i hi −i∈Rr
ν ihi ,
∆S =i∈Rf
ν i si −i∈Rr
ν isi .
k0
E act
E act
f − E act
r = ∆H ,
k0f
k0r
= exp
∆S
R
.
ρ
ctot = i ci
M = 1/ctot i ciM i
ci
X i = ci/ctot
Y i = M i/M X i M i
i
ρ = p M
RT ,
p
R
T
sV
i
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ci
Γk
θi = ci · σi
Γ k,
σi
i
sA
i
i
ηact
i = i0
exp
β a
F
RT ηact
− exp
−β c
F
RT ηact
,
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i0
β a
β c
β a
β c
i0an = i∗an exp
−
E actan
RT pan
H2
p∗H21/4
pan
H2O
101325 Pa3/4
1 +
panH2
p∗H2−1/2
,
β a = 1.5
β c = 0.5
i0ca = i∗ca exp
−
E actcath
RT
pca
O2
p∗O2
1/4 1 +
pcaO2
p∗O2
−1/2
,
β a = 0.5
β c = 0.5
i∗
p∗
lTPB
lA
TPB
lV
TPB
iF
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iF,ct = zF lTPBkf ,ct j∈Rct
Aν
j
j − kr,ct j∈Pct
Aν
j
j .
iF
iF =
all CTRs
iF,ct .
•
•
•
•
•
F
V
V
F (t) =
V
f (x, t) dV .
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F (t)
J f (x, t)
∂V
q f (x, t)
sf
dA
dV
J f n dA , q f dV , and sf dV .
n
dA
F
∂F
∂t = −
∂V
J f n dA +
V
q f dV +
V
sf dV .
∂F
∂t =
V
∂f
∂tdV
∂V V
∂f (x, t)
∂t = −div J f (x, t) + q f (x, t) + sf (x, t) .
∂φelde
∂y = 0 .
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ielyt
ielyt = −σeff elyt
∂
∂yφelyt = −σelytf σ
∂
∂yφelyt ,
φelyt σeff elyt = σelytf σ
σelyt
f σ ≈ /τ
iF
∂ielyt
∂y
= iF .
∆φ = φelde−φelyt
∂
∂y
σelytf σ
∂
∂y∆φan
= −iF .
∂
∂y
σelyt
∂
∂yφelyt
= 0 .
σelyt = Aσ
T · exp
−
E σRT
,
Aσ
E σ
f σ
∂
∂yφelyt(dense) = f σ
∂
∂yφelyt(porous) ,
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φelyt(dense) = φelyt(porous) .
η = φelde,ref = φelde,work .
φelyt,center = 0 , φca = 0.
•
•
pO2
pO2
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iel = −ielyt
σeelyt( pca
O2, T )
σi
elyt
(T ) exp
ηcaF
RT · exp(EF /RT ) − 1
1 − exp (−ielytLelytF )/(
RT σi
elyt)
iel ielyt
σi
elyt σe
elyt
ηca
E
Lelyt
pca
O2
σeelyt( pcath
O2 , T ) =
pcathO2
p0
−1/4
· aelyt0
T · exp
belyt0
T
.
∂ (ρcPT )
∂t =
∂
∂y λq
∂T
∂y + sq ,
cP
T
ρ
λq
sq
sq = σielyt
∂φelyt
∂y
2
sqJoule
+
i∈S g,S s
sV i hi
sqchem
.
•
T ca = T an = T fluid .
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•
T anode = T gas .
janodeq = j gas
q + σSB · anq
T 4anode − T 4ref ,an
σ
SB
an
q
T ref ,an = T burner .
jcathodeq = α (T cathode − T ref ) + σca
SB · caq
T 4cathode − T 4ref
,
α = N uλgas
q
L .
T ref = 293 K
∂ρ
∂t = −div (ρv)
J f
+ S m
qf
.
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ρ
v
S m
ρi i
i
∂ρi
∂t = −div
ρiv + jdiff
i
J f
+ S i qf
.
jdiff i
jdiff i
S i
∂ (ρv)
∂t = −
∇ · ρvv
− grad p −
∇ · τ
−div J f
+ ρg
sf
.
J f ∇ · ρvv
ρvv
p
τ
ρg
h
∂ (ρh)
∂t = −
∇ · ρvh
−
∇ · jq
−
τ ∇ · v
+ ∂p
∂t + [v · grad p] + S q ,
jp
S q
p
T
ρ
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pM = ρRT .
M
1
M =i∈S g
Y iM i
.
S g
M i
i
Y i
jdiff 1 = −ρD12
∂Y 1∂x
and jdiff 2 = −ρD21
∂Y 2∂x
.
∂ci
∂x =
j∈S g
X iJ diff
j − X jJ diff i
Dij.
jdiff i = −ρ
Y iX i
Di∂X i∂x
Di
Di = 1 − Y i j∈S g,j=i X j /Dij
.
Dij
i
j
Dij = D ji
i
ci
X i Y i
jdiff i
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J diff
i
jdiff i = M i J diff
i und X i = Y iM
M i.
i∈S g
jdiff i = 0 .
jdiff , corri = j diff
i − Y i j∈S g
jdiff j .
jq
jq = −λ∂T
∂x +i∈S g
hi jdiff i
λi
λ = 1
2
i∈S g
X iλi +
i∈S g
X iλi
−1 ,
µi
µ = 1
2
i∈S g
X iµi +
i∈S g
X iµi
−1 .
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ρvy
V = vr/r
Y i
Λ = 1/r · (d p/dr)
∂ρ
∂t = −
∂ (ρvy)
∂y − 2ρV
∂ (ρV )
∂t = −
∂ (ρvyV )
∂y −
∂
∂y
µ
∂V
∂y
− ρV 2 − Λ
∂ (ρY i)
∂t = −∂ (ρvyY i)
∂y − ∂j diff
i
∂y + sV i M i
∂ (ρcPT )
∂t = −
∂ (ρvycPT )
∂y +
∂
∂y
λq
∂T
∂y
−i∈S g
cP,i jdiff i
∂T
∂y −
i∈S g
sV i hi .
ρ
inv
in
T in
vStef = 1
ρ
i
M i siA ,
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∂ (εci)
∂t = −
∂J diff i
∂y −
∂ J flowi
∂y + sV
i .
J diff i
i
J flowi
i
sVi
ε
sVi
sk
i AV
k
sVi = k∈S k
AVk sk
i .
Deff ij
Deff ij = Deff
ji = ε
2τ 2
DK
i Dij
DKi + Dij
+DK
j Dij
DK j + Dij
.
ε/τ 2
DK
i
rP
DKi =
2rP
3
8RT
πM i.
J flow
i
J flowi = −X icg B
µ
∂p
∂y ,
cg
µ
p
B
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B = ε3d2
P
72τ 2 (1 − ε)2 ,
dP
J diff i + J flow
i = sgas ,
p (electrode) = p (gas) .
J diff i = J flow
i = 0 .
−→J i
i
ai
−→J i = −Di ·
−→∇ · ai ,
Di
i
ai
ai = θi = σi/Γici
ai = ci/ctot
θtot =i∈S
θi = 1 .
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θ
−→J i = −θDi ·
−→∇θi .
−→∇ai = 0 .
ν at
D0
i
D0i = x2/2t = 1/s · ν at · l2 ,
x2
l2
1/t = ν at
E act
i
Di = D0 · e−Eact
R·T .
Hx
i Ni
H•
i YSZ
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H2,gas + OXOYSZ H2Ogas + V••
OYSZ + 2e−Ni
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YSZ Ni
YSZ Ni
YSZ Ni
H2O
OH-
OH
-
--
H2
H
YSZ Ni
Ni
a)
b)
c)
d)
e)
--OO
x
H1 H2
--
-- OO
x
-
OH
O
O5
O4
O2O1
O3
H2O
OH-
---
--
H2
OHOO
x
H2O
H2
Hi
*
Hi
xx
H-int
--OO
x
--
-
--
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H2
H2O
O2−
YSZ
H2
H2O
OH−
YSZ
OH−
YSZ
H2
H2O
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a)
b)
c)
½ d Ni
½ d YSZ
d)
Surface spillover reaction Bulk-bulk interchange
TPB
Edge
d Ni
Repeat unit d YSZ
1D surface transport 1D surface transport +2D bulk transport
Ni YSZ
d YSZ d
Ni
½ d YSZ
TPB½ d
Ni
y =0
z =0 z =0
Surface diffusion
Ni stripe
YSZ crystal
•
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•
•
•
•
•
µm
Rpol
Rpol = dη
di .
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si
J/(K·mol)
hi
kJ/mol
hi si hi si
H2Ogas OH−YSZ
H2,gas O2−YSZ
O2,gas H2OYSZ
YSZ
HNi
ONi
V••O YSZ
OHNi Hxi Ni
H2ONi H•i YSZ
Ni OXO YSZ
H2,gas
H2O,gas O2,gas
Ni
HNi
ONi OHNi
H2ONi Ni
O2−
YSZ OH−
YSZ H2OYSZ YSZ
OX
OYSZ V••
OYSZ H•
iYSZ Hx
i Ni
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k0
f ,m
β m E act
f ,m
OX
OYSZ
O2−
YSZ
H2O
YSZ
k0 = ν at
Γ k
ν at
1013
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H2O
TiO2
H
2O
OXOYSZ
Hxi Ni
H•i YSZ
YSZ
YSZ
ZrO2
TiO2
H2O
YSZ
YSZ
1.4 ·10−7 cm2/s
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Γ Y S Z
=
1 . 3
·
1 0 − 9
m o l / c m 2
Γ N i =
6 . 1
·
1 0 − 9
m o l / c m 2
S i
k 0 i
k 0 i
E a c t
i
[ k J /
m o l ]
β i
Y S Z
H 2 O
g a s
+
Y S Z
H 2 O
Y s Z
6 . 6
·
1 0 1 1
c m
3 /
( m o l · s )
S
H 2 O
Y S Z +
O 2 −
Y S Z
2 ·
O H − Y
S Z
7 . 7
·
1 0 2 1
c m 2 /
( m o l · s )
H • i Y
S Z +
O H − Y
S Z
V Y S Z +
H 2 O
Y S Z
7 . 7
·
1 0 2 1
c m
2 /
( m o l · s )
O 2 − Y S
Z +
V • •
O Y S Z
O XO
Y S Z +
Y S Z
7 . 7
·
1 0 2 1
c m
2 /
( m o l · s )
H 2 O
g a s
+
N i
H 2 O
N i
1 . 4
·
1 0 1 0
c m
3 /
( m o l · s )
S
H 2 , g
a s +
2 ·
N i
2 ·
H N i
9 . 8
·
1 0 1 7
c m 5 /
( m o l · s )
S
H N i
+
O N i
O H
N i +
N i
5 . 0
·
1 0 2 2
c m
2 /
( m o l · s )
H 2 O
N i +
O N i
2 ·
O H
N i
5 . 4
·
1 0 2 3
c m
2 /
( m o l · s )
O H
N i +
H N i
H 2 O
N i +
N i
3 . 0
·
1 0 2 0
c m
2 /
( m o l · s )
H N i
+
V N i
H x i
N i +
N i
1 . 6
·
1 0 2 1
c m
2 /
( m o l · s )
H N i
+
O H − Y
S Z
H 2 O
Y S Z +
e N
i +
N i
α =
0 . 5
H N i
+
O 2 −
Y S Z
O H − Y
S Z +
e N
i +
N i
α =
0 . 5
O 2 − Y S
Z
O − Y
S Z +
e N
i
α =
0 . 5
O − Y S
Z +
N i
O N i +
e N
i +
Y S Z
α =
0 . 5
O 2 − Y S
Z +
N i
O − N
i +
e N
i +
Y S Z
α =
0 . 5
O − N i
O N i +
e N
i
α =
0 . 5
O 2 − Y S
Z +
N i
O N i +
2 ·
e N
i +
Y S Z
α =
0 . 5
O H − Y
S Z +
N i
O H
N i +
e N
i +
Y S Z
α =
0 . 5
V Y S
Z +
H x i
N i
V N i +
H • i
Y S Z +
e N
i
α =
0 . 5
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D0
i
ν at = 1013Hz
lNi = 3.6·10−10m
lYSZ = 5.1 · 10−10m
E act
i
ZrO2
D0i
ˆcm2/s
˜ E acti [kJ/mol]
Di
ˆcm2/s
˜
HNi 3.7 · 10−3 9.2 · 10−4
2.8 · 10−3 2.7 · 10−4
6 · 10−3 1.0 · 10−3
6 · 10−3 1.2 · 10−3
4.6 · 10−3 7.8 · 10−4
ONi 7 · 10−3 8 · 10−5
3 · 10−5
6 · 10−3 6.6 · 10−6
6 · 10−3 3.0 · 10−9
6.3 · 10−3 3.2 · 10−6
OHNi 6 · 10−3 6.5 · 10−6
6 · 10−3 2.9 · 10−3
6.0 · 10−3
1.4 · 10−4
H2ONi 6 · 10−3 6 · 10−6
6 · 10−3 ∼ 0 6 · 10−3
6 · 10−3 1.8 · 10−4
Hxi Ni 7.6 · 10−2
4.7 · 10−4
O2−YSZ 5.5 · 10−7
8.1 · 10−12 ZrO2
CeO2
3 · 10−9 7.3 · 10−11 TiO2
5.5 · 10−7 8.1 · 10−12
H2OYSZ 1.3 · 10−2 1.5 · 10−5
OH−YSZ 1.3 · 10−2
1.5 · 10−5
H•i YSZ 5.6 · 10−3
1.4 · 10−7
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∂∂t
θi = σiΓ k
sAi − ∂∂z
J surf i
sAi =
Xm
νi,m
0B@kf ,m
Yj∈Rf ,m
cν
jj − kr,m
Yj∈Rr,m
cν
jj
1CA
kf ,m = k0f ,m · T βm · exp
−Eactf ,mRT
!
kr,m = kf ,m · exp
„∆Gm
RT
«
∆Gm =X
i∈Rf ,m
ν
i,m (hi − T · si) −X
i∈Rr,m
ν
i,m (hi − T · si)
J surf i = −Dsurf i · θ ·
∂θi∂z
Dsurf i = D0
i · e−EactiRT .
D0i = 1
2 · νat · l
2 .
kf ,ct = k0f ,ct exp
−
Eactf ,ct
RT
!exp
„αzF
RT · ∆φ
«
kr,ct = kf ,ct exp
„∆Gm
RT
«exp
„− (1 − α)
zF
RT · ∆φ
«
∆φwork = φelde,work − φelyt,work
∆φref = φelde,ref − φelyt,ref
∂∂y
“σelyt
∂∂y φelyt
”= 0
Relyt = T AΣ
· exp“EσRT
”
η = φelde,work − φelde,ref
iAF,ct = zFlATPB
0B@kf
Yj∈Rf ,ct
θν
jj − kr
Yj∈Rr,ct
θν
jj
1CA
mTafel = α · z
iAF =X
allCTRs
iAF,ct
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Rexp
pol
f s
lA
TPB
lATPB = 3.7 m/cm2
Rexppol [Ω/cm2] f s lA
TPB [m/cm2]
p(H2) = 2.5 · 104 − 7.5 · 104
p(H2O) = 4 · 101 − 2 · 103
T = 673 − 973
η = 0 − 200
H2
H2O
N2
H2
H2O
Rpol
mTafel
Rexp
pol
f s = lsTPB/lref
TPB = Rexp,ref pol /Rexp,s
pol
m/cm2
Si, Al
Na
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pH2 2.5 · 104
pH2O 5 · 101
ptot
lATPB
m/cm2
dNi µm
dYSZ µm
η
T
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k0
E act
pH2
pH2O T
H2
H2
H2O
pH2O
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k 0 H 1 =
2 . 5 · 1 0 3 m
o l / ( c m · s )
E a c t
H 1
=
1 7 5 k J / m o l
D 0 H 2 O
Y S Z
=
6 . 3 · 1 0 + 3 c m 2 / s
D 0 O H
− Y S Z
=
3 . 3 · 1 0 + 3 c m 2 / s
O H − Y S Z
H 2 O
k 0 H 2 =
1 . 2 · 1 0 − 2
m o l / ( c m · s )
E a c t
H 2
=
1 1 3 k J / m o l
D 0 H 2 O
Y S Z
=
7 . 3 · 1 0 − 2 c m 2 / s
D 0 O H
− Y S Z
=
6 . 3 · 1 0 − 3 c m 2 / s
O H − Y S Z
H 2 O
∼
1
k 0 H 1 =
6 . 0 · 1 0 2 m
o l / ( c m · s )
E a c t
H 1
=
1 8 5 k J / m o l
k 0 H 2 =
8 . 0 m o l / ( c
m · s )
E a c t
H 2
=
1 6 7 k J / m o l
D 0 H 2 O
Y S Z
=
1 . 3 · 1 0 − 3 c m 2 / s
D 0 O H
− Y S Z
=
5 . 3 · 1 0 − 3 c m 2 / s
O H − Y S Z
H 2 O
H 2 O
k 0 H 1 =
2 . 0 · 1 0 2 m
o l / ( c m · s )
E a c t
H 1
=
1 7 4 k J / m o l
k 0 H 2 =
4 . 2 m o l / ( c
m · s )
E a c t
H 2
=
1 1 3 k J / m o l
D 0 H 2 O
Y S Z
=
3 . 3 · 1 0 + 3 c m 2 / s
D
0 O H − Y S Z
=
3 . 3 c m 2 / s
H 2 O
O H − Y S Z
H 2 O
H 2 O
k 0 O 1 =
2 . 4 · 1 0 − 2
m o l / ( c m · s )
E a c t
O 1
=
7 1 k J / m o l
k 0 O 2 =
2 . 5 · 1 0 − 5
m o l / ( c m · s )
E a c t
O 2
=
7 1 k J / m o l
D 0 O H N i =
1 . 0 · 1 0 − 1 c m 2 / s
D 0 O
N i =
8 . 0 · 1 0 − 1 c m 2 / s
O H N i
O N i
∼
2
k 0 O 3 =
7 . 3 · 1 0 − 5
m o l / ( c m · s )
E a c t
O 3
=
7 3 k J / m o l
k 0 = O 4 =
1 . 1 · 1 0 −
4 m o l / ( c m · s )
E a c t
O 4
=
7 3 k J / m o l
D 0 O
N i =
5 . 0 · 1 0 − 2 c m 2 / s
O N i
k 0 O H
=
4 . 5 · 1 0 − 4 m o l / ( c m · s )
E a c t
O H
=
7 3 k J / m o l
D 0 O H N i =
6 . 0 c m 2 / s
D 0 O H − Y S Z
=
5 . 3
c m 2 / s
O H N i
O H − Y S Z
k 0 O 5 =
4 . 0 · 1 0 − 4
m o l / ( c m · s )
E a c t
O 5
=
7 4 k J / m o l
D 0 O
N i =
1 . 0 · 1 0 + 1 c m 2 / s
O N i
H 2 O
k 0 H
− I n t =
4 . 5 · 1 0 − 4 m o l / ( c m · s )
E a c t
O H
=
7 3 k J / m o l
D 0 H • i Y S Z
=
0 . 6 c m 2 / s
H • i Y S Z
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100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g i [ A / c m
2 ]
p H2 [Pa] p H2O [Pa] T [K] η [V]
O5
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g
i [ A / c m
2 ]
OH
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950-5-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R
p o l [ Ω c
m 2 ]
l o
g i [ A / c m
2 ]
O3+O4
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g i [ A / c m
2 ]
H1+H2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g i [ A / c m
2 ]
H1
100
101
102
103
101
102
103
104 101
102
103
104
750 850 950-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g i [ A / c m
2 ]
H2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g i [ A / c m
2 ]
O1+O2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950-5
-4
-3
-2
-1
-0.5 0 0.5
η=0 mV η=50 mV η=100 mV η=200 mV
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100
101
102
103
103
104
105
p H2 [Pa]
R
p o l
[ Ω c
m 2 ]
l o g i [ A / c m
2 ]
H1+H2
100
101
102
103
101
102
103
104
p H2O [Pa]
101
102
103
750 850 950
T [K]
-5
-4
-3
-2
-1
-0.5 0 0.5
η [V]
η=0 mV η=50 mV η=100 mV η=200 mV
H2OYSZ
η = ±200
10−8
10−7 m
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-10
-8
-6
-4
-2
0
-6 -7 -8 -9 -9 -8 -7 -6
l o g c
o v e r a g e
H1+H2 η = +200mV
HNi
ONi
H2ONi
OHNi
OH-YSZ
H2OYSZ
O2-
YSZ
-6 -7 -8 -9 -9 -8 -7 -6
H1+H2 η = -200mV
HNi
ONi
H2ONi
OHNi
OH-YSZ
H2OYSZ
O2-
YSZ
-10
-8
-6
-4
-2
0
-6 -7 -8 -9 -9 -8 -7 -6
l o g c
o v e r a g e
log dist. from TPB [m]
O1+O2 η = +200mV
HNi
ONi
H2ONi
OHNi
OH-YSZ
H2OYSZ
O2-
YSZ
O-YSZ
-6 -7 -8 -9 -9 -8 -7 -6
log dist. from TPB [m]
O1+O2 η = -200mV
HNi
ONi
H2ONi
OHNi
OH-YSZ
H2OYSZ
O2-
YSZ
O-YSZ
i
η = ±200
η = 0
P i
P 0i
P +i = 1.1 ·P 0i ∂i = (i+−i0)/i0
∂P i = (P +i −P 0i )/P 0i = 0.1
f rel = ∂i/∂P i
P i
f rel
f rel >
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-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1-1 -0.5 0 0.5 1
H2 + 2Ni = 2HNi
H2O + Ni = H2ONi
HNi + ONi = Ni + OHNi
H2O + ONi = 2OHNi
OHNi + HNi = Ni + H2ONi
H2O + YSZ = H2OYSZ
H2OYSZ + O2-YSZ = 2OH-
YSZ
HNi + OH-YSZ = H2OYSZ + Ni + e'Ni
HNi
OHNi
H2ONi
ONi
O2-YSZ
OH-YSZ
H2OYSZ
HNi
H2ONi
ONi
OH-YSZ
H2OYSZ
OHNi
O2-YSZ
O2-YSZ + VO,YSZ = OO,YSZ + YSZ
x
HNi + O2-YSZ = OH-
YSZ + Ni + e'Ni
k i
Di
μ i
η = -200 mV η = 0 mV η = +200 mV
CTR
Sensitivity of cuent !f e"
# Sensitivity of R ct
Sensitivity of cuent !f e"
#
1.$
10.%
-2.%
-&%
(
&.2
-5.1
-(.2
&.
-).&
-1.(
i
η = +200
η = −200
Rpol
η = 0
ki
Di
µi = hi − T · si
OH−
YSZ
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OH−
YSZ
OH−
YSZ
OH−
YSZ
OH−
YSZ
OH−
YSZ
µi
∆G
µi
OH−
YSZ
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a) b) c)
1 12 3 1+33
dist from TPB
c o v e r a g e
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100
101
102
103
103
104
105
R p o l
[ Ω c
m 2
]
l o g i [ A / c m
2 ]
p H2 [Pa] p H2O [Pa] T [K] η [V]
H1+H2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950
-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l
[ Ω c
m 2 ]
l o g i [ A / c m
2 ]
O1+O2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950
-5
-4
-3
-2
-1
-0.5 0 0.5
η=0 mV η=50 mV η=100 mV η=200 mV
dYSZ = 60 nm dNi = 10 µm
dYSZ =
10 µm dNi = 70 nm
100
101
102
103
103
104
105
R p o l
[ Ω c
m 2 ]
l o g i [ A / c m
2 ]
p H2 [Pa] p H2O [Pa] T [K] η [V]
H1+H2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950
-5
-4
-3
-2
-1
-0.5 0 0.5
100
101
102
103
103
104
105
R p o l [ Ω c
m 2 ]
l o g i
[ A / c m
2 ]
O1+O2
100
101
102
103
101
102
103
104
101
102
103
104
750 850 950
-5
-4
-3
-2
-1
-0.5 0 0.5
η=0 mV η=50 mV η=100 mV η=200 mV
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TPB
Edge
y
z =0
Surface diffusion
Hxi, Ni
H•i, YSZ
z =½ d YSZ
½ hYSZ
d Ni
Repeat unit d YSZ
Ni stripe
YSZ crysta
a!
"!
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z = 0
z = 1/sdYSZ
y = 1/2 (hYSZ + hNi)
k0
H−Int
D0H•
i YSZ
ai
±300
ai = ci/cmax
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100
101
102
103
103
104
105
p H2 [Pa]
R p o l
[ Ω c
m 2 ]
l o g i [ A / c m
2 ]
H-int
100
101
102
103
101
102
103
104
p H2O [Pa]
101
102
103
104
750 850 950
T [K]
-5
-4
-3
-2
-1
-0.5 0 0.5
η [V]
η=0 mV η=50 mV η=100 mV η=200 mV
0 5 10 15 20
10-2
10-1
100
101
102
0 5 10
10-3
10-2
10-1
100
0 5 10
10-3
10-2
10-1
100 −4
1.56 10−4
1.58 10
−4
1.59 10
b)
d)
−4
a)
c)
activity at 300 mV activity at −300 mV
0 5 10 15 20
10-2
10-1
100
101
102
µ
[
m
]
y
µ
[
m
]
y
µz [ m ] µz [ m ]
1.58 10
YSZ
Ni
10
10 10
10
10
−6
−4 −6
−7
−5
±
y = 10 µm
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10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
10-2
10-1
100
101
C o v e r a g e N i s u r f a c e
Dist from TPB [µm]
H(NI)
OH(NI)
H2O(NI)
O(NI)
10-3
10-2
10-1
100
10110
-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
C o v e r a
g e Y S Z
s u r f a c e
Dist from TPB [µm]
O2-
(YSZ)
H2O(YSZ)
OH-(YSZ)
y ≈ 1/2hYSZ
OH−YSZ
•
1 µm
•
•
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10-4
10-3
10-2
10-1
100
101
0 5 10
Dist. from TPB [µm]
edge
H2 ads. on Ni
10-4
10-3
10-2
10-1
100
101
0 5 10
Dist. from TPB [µm]
H2O desorp. from YSZ
10-4
10-3
10-2
10-1
100
101
0 5 10
Dist. from TPB [µm]
CT reaction
a)
F l u x
[ m o l / m ² / s ]
c)b)
η = 300 mV
8 µm
z = 2 µm
•
•
H•
i YSZ
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hYSZ
cm2
pmol/s
µA
H2
H2O
H2
β
β = 1/2
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β = 1/2
β = 3/2
H2OYSZ
OH−
YSZ + O2−YSZ
H2OYSZ
β = 3/2 H2OYSZ
> 1/2 · (RT )/F
H2OYSZ
H2OYSZ
H2O
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SiO2
SiO2
•
•
•
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•
H2 H2O
•
<
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•
C1
C2
•
•
•
•
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glowing Ptwire
thermocouple
fuel cell
a) Experimental setup b) Modelling domain
y
flat-flameburner
45 mm
13 mm
mCH4 mair
φ
φ = r/rstoich
r = ˙mfuel/ ˙mOx rstoich
C3H4
N2 : O2 = 79 : 21
ptot,std = 1 bar
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Ce0.8 Sm0.2 O2−δ
175 µm
13 mm
1300 C
500 − 770 K
Sm0.5 St0.5 CoO3
5 wt% Rh2O3
57 wt%
8 mol%
38 wt%
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1200 C
lcon = 60 cm
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∂ρ∂t = −
∂ (ρvy)∂y − 2ρV
∂ (ρV )∂t = −
∂ (ρvyV )∂y − ∂
∂y
“µ∂V
∂y
”− ρV 2 −Λ
∂ (ρY i)∂t
= −∂ (ρvyY i)
∂y −
∂jdiff i∂y
+ sV i M i
∂ (ρcPT )∂t =
−∂ (ρvycPT )
∂y + ∂ ∂y
“λq
∂T ∂y
”−P
i∈Sg
cP,i jdiff i
∂T ∂y −
Pi∈Sg
sV i hi
∂ Λ∂y = 0
sV i =Pm
ν i,m
kf ,mQ
j∈Rf ,m
cν
jj − kr,mQ
j∈Rr,mcν
jj!
∂ (ci)∂t = −
∂J diff i∂y −
∂J flowi∂y + sV i
J diff i = −ciDi
∂Xi∂x
J flowi = −X icg
Bµ
∂p∂y
Di = (1 − X i)
Pj∈Sg,j=i
Xj/Deff ij
!−1
Deff ij = Deff
ji = τ
12
„ 1
1/DKi +
1/Dij+ 1
1/DKj +
1/Dij
«
B =
2d2P
72·τ (1−)2
sV i =P
AV k si
A
k∈SN
∂ (ρcPT )∂t = ∂
∂y “λq ∂T ∂y ”+ sq
sq = σielyt
“∂φelyt
∂y
”2+
Pi∈Sg,Ss
sV i hi
α = N u · λair
q
Lchar
jelecq = α (T elec − T gas) + σSBq
`T 4elec − T 4ref
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θi = ciΓk
sAi =
Xm
ν i,m
0@kf ,m
Yj∈Rf ,m
cν
j
j − kr,m
Yj∈Rr,m
cν
j
j
1A
kf ,m = k0f ,m · T βm · exp
„−
Eactf ,m
RT
«
kr,m = kf ,m · exp
„∆Gm
RT
«
∆Gm =X
i∈Rf ,m
ν
i,m (hi − T · si) −X
i∈Rr,m
ν
i,m (hi − T · si)
kf ,ct = k0f ,ct exp
−
E actf ,ct
RT
!exp
„α
zF
RT · ∆φan
«
kr,ct = kf ,ct exp
„∆Gm
RT
«exp
„− (1 − α)
zF
RT · ∆φan
«
iV tot =P
j∈CTRsiV j
iVCTR = zF lV
TPB
0@kf
Yj∈Rf ,ct
θνjj − kr
Yj∈Rr,ct
θνjj
1A
i0ca = i∗ca exp
„−
EactcathRT
«„pcaO2p∗O2
«1/4„1 +
pcaO2p∗O2
«−1/2
ica = i0ca ·
hexp
“β a
zF RT ηca
”− exp
“−β c
zF RT ηca
”i
E (i) = φelde,cath − φelde,an(i)
∆φan = φelde,an − φelyt,an
∆φcath = φelde,ca − φelyt,ca
η = ∆φ − ∆φequil
∂ ∂y φelde = 0
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∂ ∂y
“σelyt
∂ ∂y φelyt
”= 0
∂ ∂y
“σelytf σ ∂
∂y ∆φan”
= −iVtot
i =R
iVtot dy + iel
ielyt = −σeff elyt
∂ ∂y φelyt = −σelytf σ
∂ ∂y φelyt
iel = −ielytσeelyt(pcaO2
,T )
σielyt
(T ) exp
“ηcaF RT
”·
exp(EF /RT )−1
1−exp“
(−ielytLelytF )/“RTσi
elyt
””
σeelyt( pcath
O2 , T ) =
pcath
O2
p0
!−1/4
·a
elyt0
T · exp
b
elyt0
T
!
σelyt = AσT · exp
“−Eσ
RT
”
Ra = ρcon · lcon
Acon
ρcon = ρ0con · (1 + αcon · (T − T 0))
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T cath
φ
d
P max
T cath
φ
vinlet
d
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φ vinlet [cm/s] d [cm]
φ vinlet [cm/s] d [cm]
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200
400
600
800
1000
1200
1400
1600
1800
2000
0 0.25 0.5
SOFC
1 2 3 4 5 6 7 8 9 10
flame front
gas phase
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 20 40 60 80 100 120 140 160 180 0
10
20
30
40
U c e l l
[ V ]
I cell [mA/cm2]
P cell [mW/cm2]
U cell [V]
10-14
10-12
10-10
10-8
10-6
10-4
10-2
100
0.4 0.5
anode
1 2 3 4 5 6 7 8 9 10
flame front
gas phase
10-14
10-12
10-10
10-8
10-6
10-4
10-2
100
0.4 0.5
anode
1 2 3 4 5 6 7 8 9 10
gas phase
0
20
40
60
80
100
0 2 4 6 8 10 0
0.2
0.4
0.6
0.8
1
v rad [1/s]
v ax [m/s]
10-14
10-12
10-10
10-8
10-6
10-4
10-2
100
0.4 0.5
anode
1 2 3 4 5 6 7 8 9 10
flame front
gas phase
v
G a s v e l o c i t i e s
X
M o l e f r a c t i o n
X
M o l e f r a c t i o n
X
M o l e f r a c t i o n
b)a)
c)
f)e)
Dist. from cathode surface [mm] Dist. from cathode surface [mm]
Dist. from cathode surface [mm]
E
Exp
C A T e m p e r a t u r e [ K ]
d)
ExpSim Sim Exp
Dist. from cathode surface [mm]
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10−10
10−5
H2O
H2
CO CO2
φ = 1.2
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10-14
10-12
10-10
10-8
10-6
10-4
10-2
100
0 0.1 0.2
anode
1 2 3 4 5 6 7 8 9 10
flame front
gas phase
CH4 O2 CH H OH
10-2
10-1
0 0.1 0.2
anode
1 2 3 4 5 6 7 8 9 10
flame front
gas phase
H2 H2O CO CO2
Distance from cathode surface mm
M o l e f r a c t i o
n
CO2
H2
CO2
CO2
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29.7
29.8
29.9
30
30.1
30.2
30.3
30.4
0 50 100 150 200
C o v e r a
g e [ % ]
H(Ni)
39.6
39.8
40
40.2 40.4
40.6
40.8
41
41.2
41.4
0 50 100 150 200
CO(Ni)
3.34 3.36 3.38
3.4 3.42 3.44 3.46 3.48
3.5 3.52 3.54
0 50 100 150 200
H2O(Ni)
2.21
2.22
2.23
2.24
2.25
2.26
2.27
2.28
0 50 100 150 200
Distance from dense electrolyte [µm]
C o v e r a g e [ ‰ ]
OCV 150 mA
CO2(Ni)
CO2
CO2
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 50 100 150 200
U c e l l [ V
]
Current [mA/cm2]
ExpFull modelIV model
0
5
10
15
20
25
30
35
40
0 50 100 150 200
P [ m W / c m
2 ]
Current [mA/cm2]
ExpFull modelIV model
C3H7
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Full model Thermal model
500
1000
1500
2000
2500
0 0.250.5
SOFC
1 2 3 4 5 6 7 8 9 10
flame front
gas phase
T e m p e r a t u r e [ K ]
Distance from cathode [mm]
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∆T = T an − T cath
∆T
P max
φ
vinlet
φ = 1.1
vinlet = 0.1m/s
φ = 1.1 vinlet = 0.2m/s
φ = 1.2
vinlet = 0.1m/s
P max
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0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.1 v =0.1
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.1 v =0.2
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.1 v =0.3
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.2 v =0.1
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.2 v =0.2
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.2 v =0.3
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.3 v =0.1
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.3 v =0.2
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.3 v =0.3
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.4 v =0.1
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3
φ =1.4 v =0.2
I mA I mA I mA
Exp
Sim
C e l l v o l t a g e [ V ]
C e l l v o l t a g e [ V ]
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0.6
0.7
0.8
0.9
1
1.1
1.2
1 2 3 4 5 6 7 8 9 10 11
O C V
[ V ]
Flame condition
φ =1.1 φ =1.2 φ =1.3 φ =1.4
model experiment
0
20
40
60
80
100
1 2 3 4 5 6 7 8 9 10 11
P m a x
[ m W / c m
2 ]
Flame condition
φ =1.1 φ =1.2 φ =1.3 φ =1.4
model experiment
v v
a
P max
φ
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600
700
800
900
1000
1100
1 2 3 4 5 6 7 8 9 10 11
T
[ K ]
Flame condition
φ =1.1 φ =1.2 φ =1.3 φ =1.4
model experiment
OCVNernst
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0
20
40
60
80
100
120
140
160
600 800 1000 1200 1400
P m a x
[ m W
/ c m
2 ]
Temperature [K]
Sim. flat-flameExp. porousExp. flat-flame
0.2
0.4
0.6
0.8
1
1.2
600 800 1000 1200 1400
O C V [ V ]
Temperature [K]
Exp. porousExp. flat-flameSim. flat-flameOCVNernst
a) b)
P max
T peak
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0
10
20
30
40
50
600 800 1000 1200 1400
P o w e r l o s s [ m W / c m
2 ]
Temperature [K]
Cath.Elyt. ionicElyt. electronicAnodeRa
0
20
40
60
80
100
600 800 1000 1200 1400
R e l a t i v e p o w e r l o s s [ % ]
Temperature [K]
a) b)
•
Ra
•
•
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•
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0
50
100
150
200
250
0.5 1 1.5 2 2.5 3 3.5 4
P m a x
[ m W / c m
2 ]
Wire radius [mm]
standard
60
70
80
90
100
110
0 50 100 150 200 250 300 350
P m a x
[ m W / c m
2 ]
Electrolyte thickness [µm]
standard
60
70
80
90
100
110
0 50 100 150 200 250 300 350 400
P m a x
[ m W / c m
2 ]
Anode thickness [µm]
standard
60
70
80
90
100
110
0 50 100 150 200 250 300 350 400
P m a x
[ m W / c m
2 ]
Cathode thickness [µm]
standard
a) b)
c)
T = T peak
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H2
CO
P max
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mW/cm2
mW/cm2
dan µm β
an E actcath
kJmol
τ an i∗ca 5.9 · 1017 A
m3
dcath µm p(O2)
cath lV,an
TPB 1 · 1012 m/m3
τ cath
k0H1 135 mol
s
E actH1 185 kJmol
Acell cm2 E actel
kJmol
aelyt0 7.3 · 1011 K
(Ω·m·Pa1/4)
pO2cath 4.9 · 108
belyt0 2.7 · 10−4
E σ Lchar
Aσ 5.2 · 107 1/K Nu
delyt µm λairq
W/(mK)
lcon λelytq
W/(mK)
Acon mm2 λan
q
W/(mK)
αcon 3.8 · 10−3 1/K λcatq
W/(mK)
ρ0con 110
(Ω·mm2)m ca
q
anq
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H2
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H•
iYSZ
H2Ogas + V••OYSZ 2 H•
i YSZ + OXOYSZ ,
H•
iYSZ
exp−∆G
RT =
a (H•iYSZ)2 · a OX
OYSZa H2Ogas · a (V••
OYSZ) .
H•
iYSZ
a (H•iYSZ) =
exp
−
∆G
RT
· a (V••
OYSZ)
a (OXOYSZ)
· a
H2Ogas
.
∆G
∆G = 2 · ∆G (H•iYSZ) + ∆G OX
OYSZ− ∆G (H2O) − ∆G (V••OYSZ) .
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∆G
∆G (H•iYSZ) = −
RT
2
· lna (H•
i YSZ)2 · a
OX
OYSZ
a H2Ogas · a (V••
OYSZ)
+1
2 ·
∆G
H2Ogas
+ ∆G (V••
OYSZ) − ∆G
OXOYSZ
.
a (H•
iYSZ)
∆S (H•
iYSZ)
∆H (H•iYSZ)
∆G = ∆H − T · ∆S .
∆S (H•iYSZ) = 64.5 J
mol
∆H (H•iYSZ) = 16.4
kJ
mol .
∆H
OX
OYSZ
≡ 0
ZrO2
YO3
CaF2
csat
H•i YSZ
H•iYSZ
csatH•
i YSZ=
1
4 · ρYSZ ,
ρYSZ = 0.05 mol/cm3
ρH•i YSZ
= 1.25 · 104 mol
m3 .
Hx
i Ni
vNi = 6.59 cm3/mol
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Hx
i Ni
csatHx
i Ni= 3.8 · 104 mol
m3 .
Hxi Ni
H2,gas 2 Hxi Ni ,
−∆G = RT · lna (Hx
i Ni)2
a (H2,gas)
.
Hx
i Ni H2,gas
∆S Hxi Ni
= 43 J
mol ; ∆HHx
i Ni= 36
kJ
mol .
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10-6
10-5
10-4
10-3
10-2
10-1
0.8 1 1.2 1.4 1.6 1.8 2
σ
[ K / c m ]
1000/ T [1/K]
Fit: σ T =a * exp(-E act /R/T )
a =5.17e+05 [K*S/cm]
E act=80.2 [kJ/mol]
FitExp Jung et al.
Exp Shinko
C3
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k0 β E act
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k0 β E act
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k0 β E act
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k0 β E act
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k0 β E act
H2
H2O CO2
CH4 O2
k0 β E act
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T wall
A T fluid
∂
∂tQwall = A · α · (T wall − T fluid) ,
α
α = N u · λ
L ,
N u
L
λ
Nu = 1
∂
∂tQwall = −λ ·
A
L · (T wall − T fluid)
λ ≈ 5.848 · 10−2 W
m·K
L ≈ 1.2 · 10−2m
T
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AVk
m2/m3
Acell cm2
Aσ K/Ω m
ai i
aelyt0
K/(Ω·m·Pa1/4)
B m2
belyt0
1/K
ci mol/m2
i
ci mol/m3
i
cg mol/m3
cq J/K·kg
d
d
dP
Di m2/s
i
Di m2/s
i
Dij m2/s
i
j
Deff ij
m2/s
DKi
m2/s
i
delyt
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E actf ,r
J/mol
E
E σ J/mol
F C/mol
f
f σ
∆G J/mol
g m/s2
hi J/mol
i
∆H J/mol
hNi
i0 A/m3
i∗ A/m3
icell A/m2
iel A/m2
iAF
A/m2
i
V
F
A
/m3
itot A/m2
J diff i
mol/m2s i
J flowi
mol/m2s i
jdiff i
kg/m2s i
jq J/m2s
k0ct
mol/m s
k0 mol/mns
lVTPB
m/m3
lATPB
m/m2
lcon
M kg/mol
M i kg/mol i
P cell W/m2
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p
pi i
p0O2
R J/Kmol
R Ω
Rpol Ω cm2
S g
∆S J/Kmol
sAi
mol/m2s
sVi
mol/m3s
T
t
U th V
V m3
v m/s
vStef m/s
X i i
Xi i
Y i iy
z
z
α
α W/m2K
αcon 1/K
β
Γ mol/m2
ε
q
η
θi i
λq W/K m
i
µi kg/s m
i
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µ kg/s m
ν i i
ν at
ρi kg/m3
i
ρcon (Ωmm2)/m
σi i
σelyt 1/Ω m
σeff elyt
1/Ω m
τ
τ w
φ V
∆φ V
Λ kg/m3s2
V••OYSZ
Hxi Ni
H•iYSZ
OXOYSZ
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2 2
H2
H2
H2
H2O
Ni
YSZ
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2
2 3
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H2/H2O/Ni/YSZ
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H2
H2 − H2O
Y2O3 ZrO2
2 2
OYSZ
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Y2O3
ZrO2
18O2
16O
SiO2
Al2O3
ZrO2
CeO2
CeO2
Al2O3
TiO2
8/10/2019 Dissertation Vogler
http://slidepdf.com/reader/full/dissertation-vogler 136/137
8/10/2019 Dissertation Vogler
http://slidepdf.com/reader/full/dissertation-vogler 137/137
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