1 Strain Effects on Defects and Diffusion in Perovskites Dane Morgan , Tam Mayeshiba , Milind Gadre, Anh Ngo University of Wisconsin, Madison Yueh-Lin Lee , Yang-Shao Horn Massachusetts Institute of Technology Stuart Adler University of Washington, Seattle October 6, 2014 MMM Berkeley, California
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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
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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
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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
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Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
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Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
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Importance of Fast Oxygen Diffusion
Oxygen diffusion is critical in many “active oxygen” materials applications
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
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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
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To understand strain we focus on Hm and Hvf vs. strain
Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
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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
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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
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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
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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
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Two Kinds of Hops
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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)
• Significant range of values• No trend for in-plane vs. out-of-place slopes
Comparison to Other Systems
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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
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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
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• 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
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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
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
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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
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• 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