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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
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 BES
Materials Chemistry
DE-SC0001284
Financial Support Computing Support
3
National Science
Foundation
SI2 Program
grant 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 Shen
Undergraduate 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)
Anode
Cathode
CHx
H2O
CO2
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
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/
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
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!
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
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
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 ’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
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
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 (%)
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
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(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
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
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
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
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
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
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
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 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
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
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
Outline
Fast Oxygen Diffusion
Migration Under Strain
Vacancies Under Strain
33
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
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 (%)
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
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)
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)
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
-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
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
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
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
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
Thank You
45

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Morgan mmm 2014 10-06 v4.1 dist

  • 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