2016 SOFC Workshop - Yueh-Lin Lee - Ab initio Modeling …...
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Research & Innovation Center Science & Engineering To Power Our Future Science & Engineering To Power Our Future Ab initio Modeling of Cation Diffusion in La 1-x Sr x MnO 3 ± δ for Solid Oxide Cell Electrodes Applications Yueh-Lin Lee a , Yuhua Duan a , Dane Morgan a,b , Dan Sorescu a , and Harry Abernathy a,c a National Energy Technology Laboratory, U.S. Department of Energy; b University of Wisconsin-Madison, Madison, WI; c AECOM, Morgantown, WV ‐13.5 ‐13 ‐12.5 ‐12 ‐11.5 ‐11 ‐10.5 ‐10 ‐9.5 ‐5 ‐4 ‐3 ‐2 ‐1 0 1 Log(D/cm 2 sec ‐1 ) Log(PO 2 /bar) Slop 1 Slop 0.5 T=1473 K Concentration of defect complexes involved in cation diffusion in LSM is calculated based on the DFT interaction energies e.g., for V A ’’’ ‐V B ’’’ defect complex in LSM,: V A ’’’ + V B ’’’ V A ’’’ ‐V B ’’’ ΔG association ≈ ΔE association ( +0.4 eV from DFT) → [V A ’’’ ‐V B ’’’ ] = [V A ’’’ ]·[V B ’’’ ]·exp(‐ ΔE association k b T ), where [V A ’’’ ]=[V B ’’’ ] from LSM point defect mode Motivation Equilibrium Defect Chemistry Acknowledgement This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education. Diffusion Model (Random Walk Diffusion) T k ) E ( k S a Z complex def D b migration b migration Self Mn exp exp 6 ] [ 0 2 0 Carrier concentration of defects (clusters) vs. P(O 2 ) and T: • Point defect equilibrium model • Defect interactions for defect clusters Fitting parameters: ν 0 and ∆S migration Migration barriers of the cation diffusion pathways obtained from DFT NEB calculations Summary Puchala, Lee, and Morgan, JES 2012 LaMnO 3±δ T=873K, 973K, 1073K, 1173K, 1273K, 1473K La 0.8 Sr 0.2 MnO 3±δ T=873K, 973K, 1073K, 1173K, 1273K Lee and Morgan PCCP 2012 Lee and Morgan PCCP 2012 7 4 5 3 2 0 1 2 3 4 5 6 7 8 9 10 0 0.5 1 1.5 2 2.5 0 2 4 6 8 10 12 14 eV Reaction Coord. 0 6 8 9 10 Pathway 1 (V A ‐V B ) Palcut, PCCP 2008 Miyoshi ,PCCP 2009 Harvey, EES 2012 0 1 2 3 4 5 6 7 8 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 2 4 6 8 eV Reaction Coord. Pathway. 4 (V o ‐V B ) This work 6 5 4 3 2 1 0 0 1 2 3 4 5 6 7 8 9 0 2 4 6 8 eV Reaction Coord. Pathway 3 (2 nd NN V B ) De Souza J Mater Chem 1999 (Classical MD) Pathway 2 (Curved V B ) De Souza J Mater Chem 1999 (Classical MD) B‐site Cation Diffusion Pathways A‐site Cation Diffusion Pathways Cation diffusion can directly or indirectly influence degradation of LSM/YSZ • Diffusion of cations from the interfaces to surfaces under current load. • May increase the number of TPB and improve the performance in a short time • Leads to increase of the interface resistance in the long‐term operation due to morphological and compositional evolution near the LSM/YSZ interfaces Set ΔS migration = 4.5k b and attempt frequency ν 0 = 10 13 Hz Develop quantitative theoretical models based on ab initio energetics to assess cation diffusivity in bulk LSM vs T and P(O 2 ) Miyoshi SSI 2002 The interface degradation was identified as: 1. loss of LSM coverage 2. loss of three‐phase‐ boundary (TPB) length. Backhaus SSI 2008 • Cation interdiffison of LSM/YSZ interfaces. • Property assessment of diffuse interfaces LMO morphological instability upon annealing Annealing at 1273 K for 300 h PO 2 =10 ‐4 atm PO 2 = 1 atm PO 2 =10 ‐2 atm Cation Self‐diffusion Coefficients vs. T and P (O 2 ) This work 2 4 5 7 9 ‐1 0 1 2 3 4 5 0 2 4 6 8 eV Reaction Coord. 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 0 2 4 5 7 9 4 Mn diffusion pathways Mn O V A V B La/Sr V O Developed an ab initio‐based cation diffusion model to quantitatively predict cation self‐diffusion coefficients of La 1‐x Sr x MnO 3±δ vs. a wide range of T and P(O 2 ) • Good agreement with experimental LaMnO 3±δ D Mn * T and P(O 2 ) dependences • Results support the Mn B ‐V A ‐V B model as the dominant Mn diffusion pathway at high P(O 2 ) • Predict to have a crossover of D Mn * (V A ‐V B ) vs. D Mn * (V B ‐V O ]) at intermediate/low PO 2 • LaMnO 3 D Mn * [V A ‐V B ] is 2~3 orders magnitude greater than La 0.75 Sr 0.25 MnO 3 due to higher cation vacancy conc. • Predicted apparent activation energies ( ΔE a ’s) at P(O 2 ) = 0.2 bar D Mn * : 1.5 eV in LaMnO 3±δ; ; between the reported exp. values 0.6 eV (Radio‐isotope diffusion) D La * : 2.5 eV in LaMnO 3±δ vs. exp. Pr Impurity diffusion in 1.3±0.1 eV (Palcut PCCP 2008) ΔE a of D Mn * vs. Sr doping: 1.5 eV in LaMnO 3±δ vs. 2.2 eV in La 0.75 Sr 0.25 MnO 3 ‐30 ‐25 ‐20 ‐15 ‐10 ‐5 0 ‐20 ‐15 ‐10 ‐5 0 Log (D mn self /cm 2 sec ‐1 ) Log (PO 2 ) D[V_A‐V_B] D[V_B‐V_O] D[V_A‐V_B] D[V_B‐V_O] LaMnO 3 La 0.75 Sr 0.25 MnO 3 T=1073 K Future Work • Extend to model cation interdiffusion of LSM/YSZ interface • The formalism can be applied to other SOFC perovskite systems (e.g. LSCF, LSC, BSCF) • Direct 1 st NN A‐site vacancy migration • Lower migration barriers of Sr than that of La in La 0.75 Sr 0.25 MnO 3 despite a larger ionic radius • Sr‐V A repulsion increases the effective Sr migration energy to be about 3.2 eV, close to the effective La migration energy, at low P(O 2 ) LaMnO 3±δ Exp. data (●) and the B/W figure from Miyoshi PCCP 2009 D Mn * (LMO), ΔE a =1.5eV D Mn * (LSM ) ΔE a =2.2eV D La * (LMO) ΔE a =2.5eV 16 17 16. Pr 17. Mn P(O 2 )=0.2 bar • T dependence at P(O 2 )=0.2 atm • P(O 2 ) dependences of D Mn * This work Miyoshi PCCP 2009 • Model predictions capture the experimental P(O 2 ) dependences (transition of slopes) P(O 2 ) dependences governed by nonideality of cation vacancies • Decrease of D Mn * with decrease of P(O 2 ), due to lower cation vacancy concentration • Predict to change from D Mn * (V A ‐V B ) at higher P(O 2 ) to D Mn * (V o ‐V B ) at lower P(O 2 ), due to change of dominant point defect population Exp. ΔE a D Mn * (LMO) Miyoshi PCCP 2009 0.6 eV D Mn * (LMO) Palcut, JPCC, 2007 2.9±0.4 eV D Pr * (LMO) Palcut, SSI, 2008 1.3±0.1 eV Model (This work) ΔE a D Mn * (LMO) 1.5 eV D La * (LMO) 2.5 eV D Mn * (LSM) 2.2 eV 80‐atom 2√2a×2√2a×2a supercell (a: perovskite lattice constant) • Calculated DFT migration barrier for La in LaMnO 3±δ : 2.8 eV • Impurity diffusion (Y, Zr, Pr, Co, etc. ) in LSM This work Fixed constants
Transcript of 2016 SOFC Workshop - Yueh-Lin Lee - Ab initio Modeling …...
Research amp Innovation Center
Science amp Engineering To Power Our FutureScience amp Engineering To Power Our Future
Ab in i t io Model ing of Cat ion Di f fus ion in La 1-xSr xMnO 3plusmnδ for Sol id Oxide Cel l E lect rodes Appl icat ionsYueh-Lin Leea Yuhua Duana Dane Morganab Dan Sorescua and Harry Abernathyac
a National Energy Technology Laboratory US Department of Energy b University of Wisconsin-Madison Madison WI c AECOM Morgantown WV
‐135‐13
‐125‐12
‐115‐11
‐105‐10‐95
‐5 ‐4 ‐3 ‐2 ‐1 0 1
Log(Dcm
2 sec
‐1)
Log(PO2bar)
Slop 1
Slop 05
T=1473 K
Concentration of defect complexes involved in
cation diffusion in LSM is calculated based on the
DFT interaction energies
eg for VArsquorsquorsquo‐VBrsquorsquorsquo defect complex in LSM
VArsquorsquorsquo + VBrsquorsquorsquo VArsquorsquorsquo‐VB
rsquorsquorsquo
ΔGassociation asymp ΔEassociation( +04 eV from DFT)
rarr [VArsquorsquorsquo‐VBrsquorsquorsquo ] = [VArsquorsquorsquo][VB
rsquorsquorsquo]exp(‐ΔEassociationkbT) where
[VArsquorsquorsquo]=[VBrsquorsquorsquo] from LSM point defect mode
Motivation
Equilibrium Defect Chemistry
Acknowledgement
This research was supported in part by an appointment to the National Energy Technology Laboratory Research Participation Program sponsored by the US Department of Energy and administered by the Oak Ridge Institute for Science and Education
Diffusion Model (Random Walk Diffusion)
Tk)E(
kS
aZcomplexdefDb
migration
b
migrationSelfMn
expexp
6][ 0
20
Carrier concentration of defects (clusters) vs P(O2) and Tbull Point defect equilibrium model bull Defect interactions for defect clusters
Fitting parametersν0 and ∆Smigration
Migration barriers of the cation diffusion pathways obtained from DFT NEB calculations
Summary
Puchala Lee and Morgan JES 2012
LaMnO3plusmnδT=873K 973K 1073K 1173K 1273K 1473K
La08Sr02MnO3plusmnδT=873K 973K 1073K 1173K 1273K
Lee and Morgan PCCP 2012
Lee and Morgan PCCP 2012
7
4
53
2
01 2
34
56
7
8
9
100
05
1
15
2
25
0 2 4 6 8 10 12 14
eV
Reaction Coord
0
6
8
9
10
Pathway 1 (VA‐VB)
Palcut PCCP 2008Miyoshi PCCP 2009Harvey EES 2012
01
2
34
5
67
80051
152
253
354
45
0 2 4 6 8
eV
Reaction Coord
Pathway 4 (Vo‐VB)
This work
6
5
432
1
00123456789
0 2 4 6 8
eV
Reaction Coord
Pathway 3 (2nd NN VB)
De Souza J Mater Chem 1999 (Classical MD)
Pathway 2 (Curved VB)
De Souza J Mater Chem 1999 (Classical MD)
B‐site Cation Diffusion Pathways
A‐site Cation Diffusion Pathways
Cation diffusion can directly or indirectly influence degradation of LSMYSZbull Diffusion of cations from the interfaces to surfaces under current load bull May increase the number of TPB and improve the performance in a short time bull Leads to increase of the interface resistance in the long‐term operation due to
morphological and compositional evolution near the LSMYSZ interfaces
Set ΔSmigration = 45kb and attempt frequency ν0 = 1013 Hz
Develop quantitative theoretical models based on ab initio energetics to assess cation
diffusivity in bulk LSM vs T and P(O2)
Miyoshi SSI 2002
The interface degradation was identified as1 loss of LSM coverage 2 loss of three‐phase‐boundary (TPB) length
Backhaus SSI 2008
bull Cation interdiffison of LSMYSZ interfaces
bull Property assessment of diffuse interfaces
LMO morphological instability upon annealing
Annealing at 1273 K for 300 hPO2=10‐4 atm
PO2= 1 atmPO2=10‐2 atm
Cation Self‐diffusion Coefficients vs T and P (O2)
This work
2
4 5
79
‐1
0
1
2
3
4
5
0 2 4 6 8
eV
Reaction Coord
0
1
2
34 5
6
7
8
0
1
23
4
5
6
0
2
45 7
9
4 Mn diffusion pathways
Mn
O
VA
VB
LaSr
VO
Developed an ab initio‐based cation diffusion model to quantitatively predict cation self‐diffusion coefficients of La1‐xSrxMnO3plusmnδ vs a wide range of T and P(O2)bull Good agreement with experimental LaMnO3plusmnδ DMn
T and P(O2) dependencesbull Results support the MnB‐VA‐VB model as the dominant Mn diffusion pathway at high P(O2)bull Predict to have a crossover of DMn
(VA‐VB) vs DMn(VB‐VO]) at intermediatelow PO2
bull LaMnO3 DMn [VA‐VB] is 2~3 orders magnitude greater than La075Sr025MnO3 due to higher cation vacancy conc
bull Predicted apparent activation energies ( ΔEarsquos) at P(O2) = 02 bar DMn 15 eV in LaMnO3plusmnδ between the reported exp values 06 eV (Radio‐isotope diffusion) DLa
25 eV in LaMnO3plusmnδ vs exp Pr Impurity diffusion in 13plusmn01 eV (Palcut PCCP 2008) ΔEa of DMn vs Sr doping 15 eV in LaMnO3plusmnδ vs 22 eV in La075Sr025MnO3
‐30
‐25
‐20
‐15
‐10
‐5
0
‐20 ‐15 ‐10 ‐5 0
Log (D
mnse
lf cm
2 sec
‐1)
Log (PO2)
D[V_A‐V_B]D[V_B‐V_O]D[V_A‐V_B]D[V_B‐V_O]
LaMnO3
La075Sr025MnO3
T=1073 K
Future Workbull Extend to model cation interdiffusion of LSMYSZ interfacebull The formalism can be applied to other SOFC perovskite systems (eg LSCF LSC BSCF) bull Direct 1st NN A‐site vacancy migration
bull Lower migration barriers of Sr than that of La in La075Sr025MnO3 despite a larger ionic radius
bull Sr‐VA repulsion increases the effective Srmigration energy to be about 32 eV close to the effective La migration energy
at low P(O2)
LaMnO3plusmnδ
Exp data () and the BW figure from Miyoshi PCCP 2009
DMn (LMO) ΔEa=15eV
DMn (LSM )
ΔEa=22eV
DLa (LMO)
ΔEa=25eV
16
17
16 Pr17 Mn
P(O2)=02 bar
bull T dependence at P(O2)=02 atm
bull P(O2) dependences of DMn
This work
Miyoshi PCCP 2009
bull Model predictions capture the experimental P(O2) dependences (transition of slopes)
P(O2) dependences governed by nonideality of cation vacancies
bull Decrease of DMn with decrease of P(O2) due to
lower cation vacancy concentrationbull Predict to change from DMn
(VA‐VB) at higher P(O2) to DMn
(Vo‐VB) at lower P(O2) due to change of dominant point defect population
Exp ΔEaDMn
(LMO)Miyoshi PCCP 2009
06 eV
DMn(LMO)
Palcut JPCC 2007
29plusmn04 eV
DPr(LMO)
Palcut SSI 200813plusmn01 eV
Model(This work)
ΔEa
DMn(LMO) 15 eV
DLa(LMO) 25 eV
DMn(LSM) 22 eV
80‐atom 2radic2atimes2radic2atimes2a supercell(a perovskite lattice constant)
bull Calculated DFT migration barrier for La in LaMnO3plusmnδ 28 eV
bull Impurity diffusion (Y Zr Pr Co etc ) in LSM
This work
Fixed constants
