Thermochemie und Mikrokinetik und Mikrokinetik Martin Kilo, Institut für Metallurgie, TU Clausthal...

ThermochemieThermochemie und Mikrokinetikund Mikrokinetik

Martin Kilo, Institut für Metallurgie, TU Clausthal 18. 03. 2004 1

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ETH Zürich Switzerland18/19.03.04

Experimental Investigation and Simulation of Oxygen Transport in SOFC Materials

Thermochemistry and microkinetics

1. Motivation and systems: ZrO2, LaGaO3, LaMnO3

2. Experimental: Tracer diffusion in electrolyte

3. Experimental: Tracer diffusion in LSM/YSZ pair

4. Modelling: Static lattice => migration mechanism

5. Modelling: Molecular dynamics => diffusionMartin Kilo, Christos Argirusis, Günter Borchardt, Rob A. Jackson*

TU Clausthal, Institut für Metallurgie, Robert-Koch-Str. 42D-38678 Clausthal-Zellerfeld, Germany

* Keele University, School of Physics and Chemistry, Keele, Staffs ST5 5GB / UK



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Motivation: Oxygen mixed and ionic conductors

Most common examples: doped ZrO2 or doped perovskites, e.g. (La0.8Sr0.2)(Ga0.8Mg0.2)O3-δ, LSGM, LaxSr1-xMnO3-δ, LSM

Doping with aliovalent cations leads to fast oxygen diffusion, but usually to slow cation diffusion

T = A(x) exp(-Ea(x) / RT)

n = 2: CaZr2'

n = 1: YZr1'

n x A: 0 < x < x' B: x > x'

n = 1

n = 2

x

AEa

σT

x

A

Ea

σT

x

AEa

σT

x' 0.08 – 0.12



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Open questions

Experimental

What is the practical connection between the experimental oxygen diffusion coefficient and conductivity?

Oxygen diffusion under applied electrical field

Influence of thermal ageing on oxygen diffusion

Simulation of oxygen diffusion

Static lattice: Mechanism of transport

Molecular dynamics: Transport coefficients

Finite element modelling: Simulation of real systems



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Gaseous tracer: 16O / 18O

gas tracer

Nat.: 0.2 % 18OTracer: >90% 18O

Surface limited: x(18O,x=0) < 90 %

18O 16O

Furnace: T, p, static

Sample

c(x,t)-c0=(cs-c0)·(erf(x/2(DOt)0.5)-exp(h·x+h2·DOt)·erf(x/2(DOt)0.5+h·(DOt)0.5))

-50 0 50 100 150 2000.00

0.02

0.04

0.06

0.08

0.10

analysed area

sin a = d/x

angle a

depth d

sample translation x

SIMS analyser

DO = 8.5·10-10 cm2s-1

k = DO·h = 1.3·10-8 cm·s-1

Begin of polishing

YSZ-18: 8.4h 600 °C

x(18

O)

Depth / mm [=sample translation · sin(4.5°)]



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Isotopic lateral and depth distribution: SIMS Analysis

VG SIMS-lab: Quadrupole detection; 7 kV Ar+

Detection of positively/negatively charged ionsCharge compensation with flood gun

Cameca 3f/5f: Magnetic sector field; >10 kV O+/-

Detection of positively charged ionsCharge compensation by conducting layer



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ZrO2-systems CSZ, ScSZ, YSZ: working conditions

CaO-ZrO2

(Duran, J.Mat.Sci. 22 1987 4348)

Sc2O3-ZrO2

(Ruh, J.Am.Ceram.Soc. 60 1977 399)

Y2O3-ZrO2

(Suzuki, SSI 81 1995 211)

All ZrO2-systems have a cubic part of the phase diagram with fast oxygen transport and slow cation transport

Cation diffusion

(red line: T = 1000 °C)

Oxygen diffusion

Working regions:

Mostly single crystals



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0.0008 0.0009 0.0010 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016

10-11

10-10

10-9

10-8

10-7

DH(YSZ-18) = 1.02±0.03 eV

D0 = 3.8(·/÷1.4) · 10-4 cm 2 s -1

DH(YSZ-10) = 1.01±0.13 eV

D0 = 3.7(·/÷5.8) · 10-3 cm 2 s -1

DO /

cm

2 s -

1

T -1 / K -1

1300 1200 1100 1000 900 800 700

10-11

10-10

10-9

10-8

10-7

T / K

Oxygen transport: Self diffusion

Oxygen Diffusion- Maximum in D(x) like σT, MD- ΔH not strongly dependent on Y2O3 content- Haven ratio no simple T-function- Fuel cell: Field, ageing

0,5 1,0 1,5 2,0 2,5-16

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

8

.

2.9 mol%

23.8 mol%

17.8 mol%15.7 mol%

12.4 mol%

ZrO2 - Y

2O

3

ln (T

/ K

/cm

)

1000 T -1

/ K -1

1000800 600 400 200

10.3 mol%

7.8 mol%

T / °C

HR := DO/DσT = fO/fσT



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Methods:ml : mechanical lossDC : dielectrical conductivityDO* : self diffusion dl : dielectric loss

Oxygen diffusion: Activation enthalpies and ageing

0 2 4 6 8 10 12 14 16 18 20 22 24 260.8

1.0

1.2

1.4

1.6

DHml

DHDC

DHD

O

*

DHdl

DH /

eV

x(Y2O

3) / mol%

Ageing:Preannealing decreasesOxygen diffusion coefficientfor x(Y2O3) ≠ 8mol%

6 8 10 12 14 16 18 20 22 24 2610-9

10-8

10-7

x(V..

O)

DO

* [cm

2 /s]

x(Y2O

3) [Mol-%]

0,04 0,05 0,06 0,07 0,08 0,09

10-9

10-8

10-7

Tdiff=973K, Tpre:1150 °C1400 °C1700 °C



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Static oxygen diffusion: Summary

Different experimental methods reveal different information

Self diffusion Activation enthalpy of oxygen diffusion lowest

Oxygen diffusion is dependant on thermal history

Oxygen diffusion under working condition of SOFC ?

Conductivity Conductivity nonlinear => association. What are the contributions of association and migration?

Mechanical loss What is the difference between local and diffusive jumps?



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Oxygen incorporation into SOFC electrolyte

20 µm20 µm

ZrO2

LSM

3PB2PB

Surface diffusion

Oad,LSM

O2

O2-

e-

300nm

Three possible mechanisms: - 3 phase boundary (3PB) - electrode surface - through electrode + 2PB



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Model system for SOFC electrode/electrolyte

100 μm

LSM surface, dense, unstructured

200 μm

LSM stripe(s)

YSZ substrate

LSM stripes 20 µm wideLSM layer ~ 300 nm thick

PLD of LSM on YSZ at 800 °C



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Experimental setup

Pt ink referenceelectrode

Pt contact

Pt ink counter electrode

LSM structured cathode

YSZ



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Oxygen exchange in cathode / YSZ

FEM calculation of oxygen distribution after diffusion from a line source

LSM

YSZ

Assumptions:Line source at the 2PBDYSZ >> DLSM

k1 at 2PB (LSM/YSZ) = k2 at 2PB (18O/LSM) = k3 at 2PB (18O/YSZ) = 0

FEMlab



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Experimental results: LSM/YSZ-10

18OZrLa

0 20 40 60 80 100

100

200300400500

scan length [mm]

100

200300400500

ca. 250 nm

ca. 150 nm

100

1000

18O Zr La

10

100

1000

ca. 310 nmno La !LSM/YSZinterface

[cps

]

-300 mV / 7 minLine scans

10

100

1000

ca. 350 nm

ca. 50 nm

3PB activity

0 10 20 30 40 50 60 70 80

0.11

10100

1000

[cps

]

scan length [mm]

1

10

100

1000

1

10

100

1000

0.11

10100

1000

18O Zr La

0 mV / 10 minLine scans

0 minLSM surface

3 minca. 45 nm

13 minca. 200 nm

18 minca. 270 nm

20 minca. 300 nm

22 minca. 325 mnZrO2 surface

1

10

100

1000

1

10

100

1000

0 mV / 10 min -300 mV / 10 min-100 mV / 10 min

0 20 40 60 80 100

100

200300

scan length (mm)

100

200300400

10

100

18O Zr La

10

100

1000

10

100

1000

28.5 minca. 430 nm

23.5 minca. 350 nm

10 minca. 150 nm

[cps

]

-100 mV / 10 minLine scans

0 minLSM surface

18.5 minca. 280 nmLSM/YSZinterface



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Depth profile analysis

100 μm

LSM surface, dense, unstructured

on the LSM stripe on the YSZ (LSM free area)

Crater 200x200 µm

Oxygen content under dense LSM, LSM stripe, free YSZ



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18O content: Variation of overpotential

surface concentration

bulk



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Oxygen diffusion under field: Summary

The bulk path seems to be very sensitive regarding the

applied cathodic overpotential.

Even at low cathodic overpotentials, the bulk path is

blocking.

The 3PB is more active at low cathodic overpotentials.

The higher the cathodic overpotential, the more

inactive becomes the 3PB.

The solid/solid interface-resistance is clearly visible with

SIMS and depends on the applied overpotential.



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ZrO2: Modelling oxygen migration

Cubic Fluorite Unit Cell

O – A (¼,¼,¼)O – B (¾,¼,¼)

Zr – a (0,0,0)Zr – b (½,½,0)

77

66

88

33 44

11

55

22

xx

yy

zz

bb

aa0,0,0

A B

Migration energies, hopping energies, migration pathways… Association energies



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Migration pathway from static lattice calculations

0.2 0.3 0.4 0.5 0.6 0.7 0.80.20

0.22

0.24

0.26

0.28

0.30Migration energy / eV

y / r

el.

units

x / rel. units

-0.3

-0.2

-0.1

-0.1

-0.1

-8.7E-5

0.0

0.1

0.2

- Single jump between two vacancies in undoped ZrO2:

ΔE(O2-) < 0.2 eV

- Equilibrium position of O2- ion: (0.333,0.25,0.25)

Code:GULP(J. Gale, London)



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Association energy from supercell calculations

0 10 20 30 40 50 60

-0.4

-0.2

0.0

0.2

0.4

0.6association energy in ZrO

2-Y

2O

3

as

so

cia

tio

n e

ne

rgy

/ e

V

x(Y2O

3)

Eassoc.(x) = {Elatt(x)-Elatt(x=0)-x•(E(VO2•)+2*E(YZr')}/x

Supercells of 4×4×4 unit cells, varying Y/Zr content

Association energy:

difference between supercell lattice energy and perfect lattice energies



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Summary static lattice calculations

Results Low migration energy, high association energy Oxygen vacancies affects local oxygen surroundings

Limitation of static lattice calculations

Calculation of one single jump Assumption of a perfect or at least well-defined surrounding Temperature effects difficult to describe

Molecular dynamics

Information as function of temperature and time More realistic description of highly disordered systems Trajectory allows conclusions on jump mechanisms But: Slow diffusion difficult



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Oxygen diffusion: Molecular dynamics on YSZ

0.0004 0.0006 0.0008 0.0010 0.0012 0.0014 0.0016 0.0018

0.1

1

YSZ-24

ideal value: 1

Jump type:: Y-Y: Y-Zr: Zr-Zr

no

rma

lise

d n

um

be

r o

f ju

mp

s

T -1 / K -1

Jumps between one or two Y ions are less likely than between two Zr ions

Restricted diffusion path for high dopant level

Cubic unit cell



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MD: Oxygen diffusion coefficient in YSZ

Maximum in D similar to experimental point, but higher values of D

Like experimental observed, ΔH independent of x(Y2O3) .

At high x(Y2O3), D independent of x(Y2O3)

0.0008 0.0009 0.0010 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016

10-11

10-10

10-9

10-8

10-7

DH(YSZ-18) = 1.02±0.03 eV

D0 = 3.8(·/÷1.4) · 10-4 cm 2 s -1

DH(YSZ-10) = 1.01±0.13 eV

D0 = 3.7(·/÷5.8) · 10-3 cm 2 s -1

DO /

cm

2 s -

1

T -1 / K -1

1300 1200 1100 1000 900 800 700

10-11

10-10

10-9

10-8

10-7

T / K

0.05 0.10 0.15 0.20 0.25

10 -8

10 -7

D(O

) /

cm

2 s

-1

x(Y2O

3)

MD

exp



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MD: Oxygen diffusion coefficient in LSGM-8282

0.00030 0.00035 0.00040 0.00045 0.00050 0.00055 0.00060 0.00065 0.0007010-12

10-11

10-10

DH = 1.05 eV

D /

cm 2

s -1

T -1 / K -1

Activation enthalpy close to the experimental valuesDiffusion goes along (110) direction



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MD: Oxygen diffusion coefficient in ULSM

Two activation enthalpies due to local hopping

4 6 8 10 12 14 16 18 20 22 24 26

10 -11

10 -10

10 -9

10 -8

10 -7

10 -6

DH(LT) = 0.18 eV; D0=2· 10 -8cm2s -1

DH(HT) = 0.66 eV; D0=3· 10 -5cm2s -1

D /

cm

2 s -

1

T -1 / 10 4 K -1

Sketch of migration pathway along (100); T = 1200K, 1250 psgreen : oxygenpink, grey : La, Srred : Mn



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Summary of computer simulation results

Static lattice calculations Migration energies too low

Supercell method good estimation of association energies

What are the limitations ?

Molecular Dynamics calculations Diffusion coefficients similar to the experiment

Activation enthalpies of O almost identical

Percolation network ?



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Conclusions I: Experimental results

Static oxygen diffusion experiments Activation enthalpy of oxygen diffusion lowest

Oxygen diffusion is dependant on thermal history

Oxygen diffusion under SOFC conditions Even at low cathodic overpotentials, the bulk path is blocking

The 3PB is less active at high cathodic overpotential

How are the diffusivities affected ?



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Conclusions II: Modelling results

Static lattice calculations O/ZrO2

Estimate of association energies using supercells

Molecular dynamics on YSZ

Diffusion coefficients and activation energies are close to the experimental values

Existence of percolation pathways?

Molecular dynamics on LSGM, ULSM

Oxygen migration only along (110)

Localised jumps according to the cation surrounding of A- and B-sublattices



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Future perspectives

Dynamic oxygen diffusion

• YSZ/ULSM : Variation of time, polarisation, p(O2)• Variation of the cathode material• Oxygen exchange coefficient at the solid/solid interface?• Anode/Electrolyte : Hydrogen

Computer simulations

• Atomistic modelling of oxygen transport across interfaces solid/solid and gas/solid

• Modelling of oxygen transport under electrical field• Other materials: LSCF, Apatites• Advanced methods: QM, finite elements …



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Acknowledgements

M. Weller, MPI Stuttgart: Experimental results

Prof. P. Schmidt, TU Darmstadt: Use of computer centre

Deutsche Forschungsgemeinschaft (DFG): Financial support

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Thermochemie und Mikrokinetik und Mikrokinetik Martin Kilo, Institut für Metallurgie, TU Clausthal...

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