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Strain Effects on Defects and Diffusion in Perovskites
Dane Morgan, Tam Mayeshiba, Milind Gadre, Anh NgoUniversity of Wisconsin, Madison
Yueh-Lin Lee, Yang-Shao HornMassachusetts Institute of Technology
Stuart AdlerUniversity of Washington, Seattle
October 6, 2014MMM
Berkeley, California
Publication
2
The final versions of all our perovksite strain data shown in this talk is now published in
T. Mayeshiba and D. Morgan, Strain Effects on Oxygen Migration in Perovskites, Phys. Chem. Chem. Phys. 17, p. 2715-2721 (2015 ).
NSF National Center for Supercomputing Applications
DOE BESMaterials ChemistryDE-SC0001284
Financial Support Computing Support
3
National Science FoundationSI2 Programgrant 1148011
http://matmodel.engr.wisc.edu/
Research Group
COMPUTATIONAL MATERIALS GROUP
Faculty* Izabela Szlufarska * Dane Morgan Assistant Scientist* Ramanathan Krishnamurthy
Postdocs* Guangfu Luo * Henry Wu* Hyo On Nam * Jie Deng* Katharina Vortler * Min Yu* Ming-Jie Zheng * Parijat Sengupta
Graduate Students* Amy Kaczmarowski * Ao Li* Cheng Liu * Chaiyapat Tangpatjaroen* Hao Jiang * Huibin Ke* Hyunseok Ko * Hyunwoo Kim* James Gilbert * Jie Feng
* Kai Huang * Kumaresh V. Murugan* Lei Zhao * Leland Bernard* Mehrdad Arjmand * Milind Gadre
* Ryan Jacobs * Shenzen Xu
* Tam Mayeshiba * Wei Xie
* Xing Wang * Zhewen Song
* Zhizhang ShenUndergraduate student
* Andrew Sanville
4
Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
5
Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
6
Importance of Fast Oxygen Diffusion
Oxygen diffusion is critical in many “active oxygen” materials applications
• solid oxide fuel cells (esp. low T)
• Gas separation membranes
• Sensors (response time)
• Chemical looping combustion
• Memristors (response time)
• …
Solid Oxide Fuel Cell (SOFC)
8
Electrolyte (YSZ)
An
od
eC
atho
de
CHx
H2OCO2
O2
e–
CHx + (2+x/2)O2- → CO2 + (x/2)H2O + (4+x)e–
O2 + 4e– → 2O2-
O2-
e–
Solid Oxide Fuel Cells (SOFCs)
http://www.powergeneration.siemens.com/products-solutions-services/products-packages/fuel-cells/sofc-gt-hybrid/
9
AdvantagesClean, low-emission, quiet, reliable, fuel adaptable, and highly efficient
ApplicationsAuxiliary truck power, Integrated coal
gasification fuel cell (99% CO2 capture, >50% efficiency), Distributed power supply, …
Problem: High operating temperature (~800°C) limits uses, reduces lifetime, increases costs
http://www.innovations-report.com/html/reports/energy_engineering/report-42356.html
http://cleantechnica.com/2009/02/19/aist-introduces-sugar-cube-sized-fuel-cell/
Oxygen Diffusion and SOFC Electrolytes
Brett, et al, Chem. Soc. Rev. ‘08
Production challenges
SOFC Cathode losses
11
M. Mogensen and P. V. Hendriksen, in High-Temperature Solid Oxide Fuel Cells: Fundamentals, Design and Applications, edited by S. C. Singhal and K. Kendall (Elsevier Science Ltd, New York, 2003),
Cathode losses are major limitation at lower temperatures
Oxygen Diffusion in SOFC Cathodes
12
S.B. Adler, et al., JES, ‘96 (ALS model)S.B. Adler, et al. J. of Catalysis ’07
R.A. De Souza and J.A. Kilner, SSI ‘99
• SOFC cathode losses depend critically on D
• Surface catalysis correlated with D, strengthening this dependence
• Overall SOFC performance strongly influenced by D - 10x changes matter!
Focus on Perovskites
• [ABO3] perovksites widely used for
fast oxygen conduction applications
• Primary materials for SOFC cathodes
– (La,Sr)MnO3 (LSM)
– (La,Sr)(Co,Fe)O3 (LSCF)
• Also used for SOFC electrolytes
– (La,Sr)(Ga,Mg)O3 (LSGM)
• Very flexible structural family with many opportunities for materials design (dope 90% of periodic table1) 13
A B O
1M.A. Pena and L.G. Fierro Chem. Rev. ‘01
Diffusion in Perovksites
Perovskites have vacancy mediated diffusion of oxygen
14
To understand strain we focus on Hm and Hvf vs. strain
Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
15
What Are Effects of Strain on Hm?
A number of recent studies on films have suggested that strain can dramatically alter defect chemistry, migration energies, and catalytic kinetics
16
What Are Effects of Epitaxial Strain on HM? YSZ Example
17A. Chroneos, EES ’11A. Kushima and B. Yildiz, J Mat. Chem. ‘10
• Equation matches data for 50% strain release• Ab initio shows complex phenomenon at higher strains• How does strain impact migration in bulk perovskites?
N. Schichtel, et al. PCCP ‘09
18
Effect of Strain on Oxygen Migration from Experiment
M. Kubicek, et al., ACS Nano ‘13
Tensile strain increases both surface-exchange coefficient and the bulk-diffusion coefficient in (La0.8Sr0.2)CoO3.
1.0% tensionD*=1.9×10 14‐ cm2/s
400°C
1.9% compressionD*=8.0×10 16‐ cm2/s
What do We Expect for Strain Effects on Hm in Perovskites?
Assume simple strain model works
•Y ~ 1 eV/Å3
•v ~ 1/3
•Vm ~ 5 Å3
•Em ~ 1 eV
19
N. Schichtel, et al. PCCP ‘09
-2 -1 0 1 20.7
0.8
0.9
1
1.1
1.2
Strain (%)H
m (e
V)
OptimizeOut of plane Parameter
Apply in-plane epitaxial strain (0-±2)%
Full relaxed bulk Perovskite
Applying Strain: Plane Strain Geometry to Simulate Films
20
Two Kinds of Hops
21
In-Plane Hop Out-of-Plane Hop
Ab initio Modeling
• Plane Wave Projector Augmented-Wave (PAW) Density Functional Theory (DFT) methods
• GGA (PW-91) (explored GGA+U but instabilities are challenging)
• Spin polarized FM calculations
• VASP code
• Migrations barriers from CNEB
• Vacancies electrons are compensated
22Y.-L. Lee, J. Kleis, J. Rossmeisl, and D. Morgan, PRB (2009) Y.-L. Lee and D. Morgan, ECST (2009)
c (r
elax
ation
)
a (apply biaxial strain)
IP
OOP
2x2x2 perovskite supercell, 40 atoms
Calculations automated with the Materials Simulation Toolkit (MAST)
pypi.python.org/pypi/MASTDOI: 10.5281/zenodo.11917
La(M)O3 Systems
La(M)O3 compounds, M= 3d transition metals, Sc, Ga
23
LaMO3 Migration Barriers vs. Strain (In-Plane Hops)
compression tension
• Hm(strain) is ~linear
– Significant instabilities (metastable distortions, e.g., V)
• All slopes negative (tension reduces barriers)
• Significant range
LaMO3 Migration Barriers vs. Strain
25
Sc Ti V Cr Mn Fe Co Ni Ga
• Significant range of values• No trend for in-plane vs. out-of-place slopes
Comparison to Other Systems
26
Similar slopes compared to other fluorite and perovskite systems
IP = Plane, OOP = Out-of-plane
Comparison to (La0.8Sr0.2)CoO3 Experiments
27Calculation match trends in D from experiments
Assumes all changes in D are from changes in Hm
Impact of Hm(strain) on Diffusivity
28
Impact can be orders of magnitude on diffusivity/conductivity
-4 -3 -2 -1 0 1 2 3 4
-4
-3
-2
-1
0
1
2
3
4
Weakest
Average
Strongest
Strain (%)
Lo
g[
D(s
trai
ned
) /
D(b
ulk
) ]
500°C
A Complication in Quantitative Modeling of D from Em(strain) Slopes
This 2x2 cell has 96 hops (12 symmetry distinct in LaMnO3). • Which govern diffusion changes at high temperature, if any?• Which Hm vs. strain slopes govern changes in diffusion, if any?29
A Complication in Quantitative Modeling of D from Em(strain) Slopes
30
• Migration values and their slopes with strains vary significantly!• More work is needed to obtain impact on D
8 10 12 14 160.65
0.7
0.75
0.8
0.85
0.9
Central B-site cation
No-
stra
in b
arrie
r fro
m fi
rst e
ndpo
int (
eV)
B=Mn
ipoop
8 10 12 14 16-90
-80
-70
-60
-50
-40
-30
-20
Central B-site cation
Slo
pe in
mig
ratio
n ba
rrie
r, m
eV/%
str
ain B=Mn
ipoop
What is Origin of the Slopes of Em with Strain?
• Simplest model is strain dominated– Assume dilational defect strain model– Assume cubic symmetry
31
Test model: Calculate Y/(1-n) and Vm from ab initio and compare:
FormulaFull DFT
DFT vs. Strain Model for Em vs. Strain
• “Simple” strain formula accounts for majority of strain effects.• Remaining discrepancies can be due to: local distortion (tilting), shear
terms, anistropy, anharmonicity, electronic effects, numerical issues. 32
Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
33
Diffusion in Perovksites
Perovskites have vacancy mediated diffusion of oxygen
34
To understand strain we focus on Hm and Hvf vs. strain
What do We Expect for Strain Effects on Evf in Perovskites?
Assume simple strain model works
•Y ~ 1 eV/Å3
•v ~ 1/3
•Vvf ~ 5 Å3
•Evf ~ 1 eV
35
N. Schichtel, et al. PCCP ‘09
-2 -1 0 1 20.7
0.8
0.9
1
1.1
1.2
Strain (%)H
vf (e
V)
Vacancy Formation Volumes
Significant range of formation volumes could lead to wide range of Hvf vs. strain slopes.
36
Sc Ti V Cr Mn Fe Co Ni Ga0
2
4
6
8
10
B-site cation
Vaca
ncy
form
ation
vol
ume
Å3
Trends in Em and Evf vs. Strain
• Comparable values for slopes of Em and Evf vs. strain• Some correlation which will enhance effects 37
-120 -100 -80 -60 -40 -20 0
-120
-100
-80
-60
-40
-20
0
-35.51
-63.72
-103.66
-85.09
-64.37
-89.13
-59.81-70.45
-44.44
Slope in Hvf (strain formula) (eV/% strain)
Slop
e in
Hm
(DFT
) (eV
/% s
trai
n)
Hvf(strain) Perovskite “slopes” from Literature
• Our values are generally consistent with literature slopes for perovskites.• However range and uncertainty seem quite large – more work is needed
38
Yang, et al. JAP ‘13Achauer, et al., PRB ‘13 Kubicek, et al. ACS Nano’13Jalili, et al. JPCL ’11
Yang
Achauer
Kubicek
JaliliYang
Our model
-200
-150
-100
-50
0
50
100Sl
ope
in H
m (e
V/%
str
ain)
Vacancy Effects
• Vacancy effects depend on balance of dopant vs. formation enthalpy induced changes.
• If formation energy dominates we can very approximately write
39T. Kawada, et al. JES ‘02
-4 -3 -2 -1 0 1 2 3 4
-8
-6
-4
-2
0
2
4
6
8
10
WeakestAverageStrongest
Strain (%)
Log[
D(s
trai
ned)
/ D
(bul
k) ]
Potential Impact of Em and Evf on Diffusivity
40
Impact of relatively small 1-2% strain can be orders of magnitude on diffusivity/conductivity!
500°C
Does Simple Strain Model Predict Hvf(strain) Slopes? Case of (La0.875Sr0.125)CoO3
• Seems like poor agreement DFT vs. Simple Strain model• But we must be careful about what elastic constants we use
41
Donner et al., Chem. Mater. ‘11
-2 -1 0 1 2 3 4
-300
-200
-100
0
100
DFTSimple Strain model
Strain (%)
HM
(eV)
Epitaxial Strain Response for Oxygen Vacancies: (La0.875Sr0.125)CoO3-d
42Oxygen vacancies soften material, reducing Young’s modulus
Y = 186 GPa
Y = 164 GPa
Oxygen Vacancy Formation Energy vs. Epitaxial Strain: DFT and Simple Strain Model
Ab initio energies show significant stabilization of LSC oxygen vacancies with epitaxial strain (tensile and compressive) due to vacancy induced softening
43
Donner et al., Chem. Mater. ‘11
Simple strain model with softening
SummaryEpitaxial Strain Effects in Perovskites
• Hm(strain) is ~linear for small strains (±2%)
• Slope values investigated range about -20 to -140 meV/%strain.
• Values agree qualitatively with simple Vm strain
model, but not quantitatively – other physics matters!
• Hvf(strain) predicted by simple strain model to
have similar scale slopes as Hm but more
validation is needed
44
• Strain effects can “easily” lead to ~100x improvements (~2% strain) which changes a material’s utility in SOFCs
• Critical next modeling step is to quantitatively assess combined vacancy formation and migration energy changes on D
Thank You
45