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

1. 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

2. 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 ).

3. NSF National Center for
Supercomputing Applications
DOE BES
Materials Chemistry
DE-SC0001284
Financial Support Computing Support
3
National Science
Foundation
SI2 Program
grant 1148011

4. 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 Shen
Undergraduate student
* Andrew Sanville
4

5. Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
5

6. Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
6

7. 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)
• …

8. Solid Oxide Fuel Cell (SOFC)
8
Electrolyte (YSZ)
Anode
Cathode
CHx
H2O
CO2
O2
e–
CHx + (2+x/2)O2- →
CO2 + (x/2)H2O + (4+x)e–
O2 + 4e– → 2O2-
O2-
e–

9. Solid Oxide Fuel Cells (SOFCs)
http://www.powergeneration.siemens.com/products-solutions-
services/products-packages/fuel-cells/sofc-gt-hybrid/
9
Advantages
Clean, low-emission, quiet, reliable,
fuel adaptable, and highly efficient
Applications
Auxiliary 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/2009/02/1
9/aist-introduces-sugar-cube-sized-
fuel-cell/

10. Oxygen Diffusion and SOFC Electrolytes
Brett, et al, Chem. Soc. Rev. ‘08
Production
challenges

11. 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

12. Oxygen Diffusion in SOFC Cathodes
12
ASR = AT cvgDktr( )
1 2
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!

13. 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

14. Diffusion in Perovksites
Perovskites have vacancy mediated diffusion of oxygen
14
D = A´exp -Hm kT( )cv
» A'
´exp -Hm kT( )
´ cv
0
+cv
1
exp -Hvf kT( )é
ë
ù
û
To understand strain we focus on Hm and Hvf vs. strain

15. Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
15

16. 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

17. What Are Effects of Epitaxial Strain on HM?
YSZ Example
17A. Chroneos, EES ’11
A. 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
DHm = -
2
3
Y
1-v
é
ëê
ù
ûúVmexx

18. Effect of Strain on Oxygen Migration from
Experiment
18
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% tension
D*=1.9×10‐14 cm2/s
400°C
1.9% compression
D*=8.0×10‐16 cm2/s

19. 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
DHm = -
2
3
Y
1-v
é
ëê
ù
ûúVmexx
N. Schichtel, et al. PCCP ‘09
DHm » 5exx Þ DHm
%strain
» 50 meV
%strain
0.7
0.8
0.9
1
1.1
1.2
-2 -1 0 1 2
Hm(eV)
Strain (%)

20. Optimize
Out of plane
Parameter
Apply in-plane epitaxial strain (0-±2)%
Full relaxed bulk
Perovskite
Applying Strain: Plane Strain Geometry
to Simulate Films
20

21. Two Kinds of Hops
21
In-Plane Hop Out-of-Plane Hop

22. 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(relaxation)
a (apply biaxial strain)
IP
OOP
2x2x2 perovskite
supercell, 40 atoms
Calculations automated with the Materials Simulation
Toolkit (MAST)
pypi.python.org/pypi/MAST
DOI: 10.5281/zenodo.11917

23. La(M)O3 Systems
La(M)O3 compounds, M= 3d transition metals, Sc, Ga
23

24. 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
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-2 -1 0 1 2
Migraonbarrier(eV)
Biaxial strain (%)
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Ga

25. LaMO3 Migration Barriers vs. Strain
25
-160
-120
-80
-40
0
Slope(meV/%strain)
In-Plane
Out-of-plane
Sc Ti V Cr Mn Fe Co Ni Ga
• Significant range of values
• No trend for in-plane vs. out-of-place slopes

26. Comparison to Other Systems
26
Similar slopes compared to other fluorite and perovskite systems
IP = Plane, OOP = Out-of-plane

27. Comparison to (La0.8Sr0.2)CoO3 Experiments
27
-0.4
-0.2
0.0
0.2
0.4
-4 0 4
Changeinmigraonbarrier(eV)
Normalizedto0eVat0strain
Percent biaxial tensile strain
OOP LaCoO₃, This paper
-0.4
-0.2
0.0
0.2
0.4
-4 0 4
Changeinmigraonbarrier(eV)
Normalizedto0eVat0strain
Percent biaxial tensile strain
OOP LaCoO₃, This paper
OOP LSC/LAO LSC/STO, Kubicek 2013, Expt.
Calculation match trends in D from experiments
Assumes all changes in D
are from changes in Hm

28. 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 -2 0 2 4
Log[D(strained)/D(bulk)]
Strain (%)
Weakest
Average
Strongest
500°C
D = A´exp -Hm kT( )cv

29. 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

30. 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 16
0.65
0.7
0.75
0.8
0.85
0.9
Central B-site cation
No-strainbarrierfromfirstendpoint(eV)
B=Mn
ip
oop
8 10 12 14 16
-90
-80
-70
-60
-50
-40
-30
-20
Central B-site cation
Slopeinmigrationbarrier,meV/%strain
B=Mn
ip
oop

31. 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:
DHm = -
2
3
Y
1-v
é
ëê
ù
ûúVmexx
FormulaFull DFT
DHm = -
2
3
Y
1-v
é
ëê
ù
ûúVmexx
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
-2 -1 0 1 2
Migraonbarrier(eV)
Biaxial strain (%)
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Ga

32. 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
Co
Fe
Ga
Mn
Ni
Cr
Sc
Ti
V
Co
Fe
GaMn
Ni
Cr
Sc
Ti
V
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
-180 -160 -140 -120 -100 -80 -60 -40 -20 0
Slopefromelascstrainmodel(meV/%strain)
Slope fit to DFT barriers (meV/%strain)
in-plane
out-of-plane

33. Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
33

34. Diffusion in Perovksites
Perovskites have vacancy mediated diffusion of oxygen
34
D = A´exp -Hm kT( )cv
» A'
´exp -Hm kT( )
´ cv
0
+cv
1
exp -Hvf kT( )é
ë
ù
û
To understand strain we focus on Hm and Hvf vs. strain

35. 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
DHvf = -
2
3
Y
1-v
é
ëê
ù
ûúVvfexx
N. Schichtel, et al. PCCP ‘09
DHvf » 5exx Þ
DHvf
%strain
» 50 meV
%strain
0.7
0.8
0.9
1
1.1
1.2
-2 -1 0 1 2
Hvf(eV)
Strain (%)

36. Vacancy Formation Volumes
Significant range of formation volumes could lead to wide range
of Hvf vs. strain slopes.
36
0
2
4
6
8
10
Sc Ti V Cr Mn Fe Co Ni Ga
VacancyformationvolumeÅ3
B-site cation

37. Trends in Em and Evf vs. Strain
• Comparable values for slopes of Em and Evf vs. strain
• Some correlation which will enhance effects 37
Sc
Ti
V
Cr
Mn
Fe
Co
Ni
Ga
-120
-100
-80
-60
-40
-20
0
-120 -100 -80 -60 -40 -20 0
SlopeinHm(DFT)(eV/%strain)
Slope in Hvf (strain formula) (eV/% strain)

38. 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 ‘13
Achauer, et al., PRB ‘13
Kubicek, et al. ACS Nano’13
Jalili, et al. JPCL ’11-200
-150
-100
-50
0
50
100
SlopeinHm(eV/%strain)

39. Vacancy Effects
• Vacancy effects depend
on balance of dopant
vs. formation enthalpy
induced changes.
• If formation energy
dominates we can very
approximately write
39
D = A´exp -Hm kT( )cv
» A'
´exp -Hm kT( )´ cv
0
+cv
1
exp -Hvf kT( )é
ë
ù
û
» A'
´exp -Hm kT( )´ cv
1
exp -Hvf kT( )é
ë
ù
û
T. Kawada, et al. JES ‘02

40. -8
-6
-4
-2
0
2
4
6
8
-4 -3 -2 -1 0 1 2 3 4
Log[D(strained)/D(bulk)]
Strain (%)
Weakest
Average
Strongest
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
D » A'
´exp -Hm kT( )´ cv
1
exp -Hvf kT( )é
ë
ù
û

41. 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
-300
-200
-100
0
100
-2 -1 0 1 2 3 4
HM(eV)
Strain (%)
DFT
Simple Strain model

42. Epitaxial Strain Response for Oxygen
Vacancies: (La0.875Sr0.125)CoO3-d
42Oxygen vacancies soften material, reducing Young’s modulus
-0.5
0
0.5
1
1.5
2
2.5
-4 -2 0 2 4 6
E0-unstrainedE0(eV)
Strain (%)
δ=0.0625
δ=0.125
Y = 186 GPa
Y = 164 GPa

43. 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
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
-3 -2 -1 0 1 2 3 4 5
EvacrelavetounstrainedEvac(eV)
Strain (%)
Simple strain model
with softening

44. Summary
Epitaxial 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
-8
-6
-4
-2
0
2
4
6
8
-4 -3 -2 -1 0 1 2 3 4
Log[D(strained)/D(bulk)]
Strain (%)
Weakest
Average
Strongest
Co
Fe
Ga
Mn
Ni
Cr
Sc
Ti
V
Co
Fe
GaMn
Ni
Cr
Sc
Ti
V
-180
-160
-140
-120
-100
-80
-60
-40
-20
0
-180 -160 -140 -120 -100 -80 -60 -40 -20 0
Slopefromelascstrainmodel(meV/%strain)
Slope fit to DFT barriers (meV/%strain)
in-plane
out-of-plane
• 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

45. Thank You
45