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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

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/

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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

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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)

pypi.python.org/pypi/MASTDOI: 10.5281/zenodo.11917

La(M)O3 Systems

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

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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

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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

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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

terms, anistropy, anharmonicity, electronic effects, numerical issues. 32

Outline

Fast Oxygen Diffusion

Migration Under Strain

Vacancies Under Strain

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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

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

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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

vf (e

V)

Vacancy Formation Volumes

Significant range of formation volumes could lead to wide range of Hvf vs. strain slopes.

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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

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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

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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

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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

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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

Thank You

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