materials challenges in solid oxide fuel cells1 materials challenges in solid oxide fuel cells anil...

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Materials Challenges in Solid Oxide Fuel Cells

Anil V. VirkarDepartment of Materials Science & Engineering122 S. Central Campus Drive, University of Utah

Salt Lake City, UT 84112Phone: (801) 581-5396

[email protected]

A Lecture on Solid Oxide Fuel CellsPresented at UCSB Summer School

Santa Barbara, CAAugust 7, 2006

2

Objectives of the Lecture

1) To serve as an introduction to SOFC; scienceand technology.

2) To identify key materials and microstructure- related parameters which determine performance of SOFC.

3) To identify and discuss thermo-mechanical issues concerning anode-supported cells.

4) To provide information on the fabrication ofanode-supported SOFC and testing of button cells.

5) To provide a source of relevant literature.

3

Notes and Disclaimers

• The material given here is not complete, either in content, coverage of topics, and should be considered as reference material. There are numerous research articles, review articles, books, and symposia proceedings on this subject.

• Important source of literature is the series of proceedings volumes of ECS SOFC symposia, including the SOFC-IX being held at this meeting.

• The instructor’s own knowledge of the field is by no means complete (it is a constant process of learning) and also the instructor cannot guarantee that it is without misconceptions.

4

Lecture Format

1) To provide a number of viewgraphs with severalpictorials and illustrations.

2) To provide parametric equations that can assist in designing cells by allowing for parameter measurements- the objective is not to conduct detailed modeling.

3) To provide illustrative calculations.4) To provide a list of selected references for one

interested in further details. 5) The approach will be to give more material in these slides

than can be covered in a two hour lecture.

5

Course Organization: Topics

Topic 1: A Brief Discussion of Solid Oxide Fuel Cell (SOFC) including relevant thermodynamics.Topic 2: SOFC Materials: Electrolyte, Cathode, Anode; Cell Architecture on the Basis of SupportTopic 3: Sources of various voltage losses, and their dependence on cell parameters and test conditions.Topic 4: Cell Design for Enhanced PerformanceTopic 5: Cell Design – Thermo-mechanical ConsiderationsTopic 6: Cell FabricationTopic 7: Cell Testing

6

Topic 1: A Brief Description of Solid Oxide Fuel Cells (SOFC)

O2

Porous Cathode

H2O

H2or

H2 + COelectrons

Porous Anode

H2OorH2O + CO2

nFGE ∆−=

NernstPotential

Load

H+

and/orO-2

Dense

Electrolyte

Three Components:a) Cathodeb) Electrolytec) Anode

Most of the SOFCuse oxygen ion (O-2)conducting solidelectrolyte. Limitedwork has been doneon SOFC based onproton (H+) conductors.

7

A Planar Cell and Test Fixture

8" cell8" cell(400 cm²)4" cell

(100 cm²)

Cartridge heater + insulator

SEM Micrograph

Anode

Cathode

Electrolyte (~10 microns)

8

SOFC 1 kW Stack

Stack dimensions: 5.5” × 5.5” × 4.625”Volumetric power density = ~500 Watt/LiterInternal manifolds; Cross-flow

Technology Objective: Higher specific power, greater efficiency, longer life, and lower cost

9

Functions of the Three Components

• Cathode: Transport of oxygen from the gaseous oxidant (O2 + N2) through the porous cathode to the cathode/electrolyte interface – diffusion/convection. Transport of electrons.

• Cathode: Conversion of O2 into 2O-2 ions and transfer into the electrolyte – electrochemical reaction of reduction.

• Electrolyte: Transport of O-2 ions through the electrolyte towards the electrolyte/anode interface – ionic conduction.

• Anode: Transport of gaseous fuel (H2 or H2 + CO) through the porous anode towards the anode/electrolyte interface –diffusion/convection. Transport of electrons.

• Anode: Reaction of fuel (H2 or H2 + CO) with O-2 ions to form H2O or H2O + CO2 and release of electrons for transport through the external circuit, through the load, to the cathode – electrochemical reaction of oxidation.

10

A Simplified Equivalent Circuit for SOFC

Current Flow

Ref. ‘Fuel Cells and Fuel Batteries’, H. A. Liebhafsky and E. J. Cairns

Fuel cell is essentially a primary battery where fuel is continuallysupplied to the anode, and oxidant is continually supplied to thecathode. The free energy of the oxidation of fuel is convertedinto electrical energy. The operation of the fuel cell is one way. Thus, it is not limited by the Carnot cycle, unlike a cyclic process, such asa heat engine. Being a battery, it can be represented by an equivalent circuit using a voltage source and, in the simplest case,using an internal resistance. When a load is connected in the external circuit, work is derived.

CathodeAir

AnodeFuel

Electrolyte

LoadElec

tron

Flow

Fuel Cell

+-Ri

RLLoad

Internal resistance

Nernst Potential

Equivalent Circuit

Elec

tron

Flow

E

= fuelO

airO

p

pF

RTE2

2ln4

Electron FlowCurrent Flow

+-

Ri

Load Represented by a battery

E

V

V<E

+-

11

Voltage vs. Current (or Current Density)

+-Ri

RLLoad

Internal resistance

Nernst Potential

Equivalent Circuit

Elec

tron

Flow

E

= fuelO

airO

p

pF

RTE2

2ln4

Current Flow

Voltage acrossLoad or Cell

Li RREI+

=Current

LIRV =

iIREV −=

Thus, by load we meaneither RL or I Current, I

Vol

tage

, V

Slope = -Ri

E

Power ( )VI

RRRE

RVRI

Li

L

LL =

+=== 2

222

Power

12

Fuel Cell with Hydrogen as the Fuel

The chemical reaction with H2 as the fuel isH2 + 1/2O2 H2O

In a fuel cell, the reaction occurs electrochemically.In what follows, we will assume the electrolyte to be an oxygen ion conductor. Then, the reactions at the two electrodes are:

Cathode: ½O2 + 2e’ O-2

O-2 ions transport through the electrolyte towards the anode.

Anode: H2 + O-2 H2O + 2e’The electrons transport through the external circuit performing useful work. The overall reaction is the sum of the two.

The Overall Reaction: H2 + 1/2O2 H2OoG∆ :Standard free energy change

G∆ : Free energy change(partial pressures differentfrom 1 atm).

Reduction of O atoms into O-2 ions

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Fuel Cell Efficiency (Standard State, Reversible)Standard Gibbs Free Energy Change for the Reaction

oo FEG 2−=∆

ooo STHG ∆−∆=∆

Standard Gibbs Free Energy Change in terms of the Nernst Voltage

Maximum Work (reversible process) in standard state is given by

All partial pressures are at 1 atm

ooo FEGw 2'max =∆−=

o

o

o

o

o

oorev

HFE

Hw

H

G

∆=

∆=

∆

∆=

2'maxη

∆Ho = Standard enthalpy (H) change (H of one mole of H2O at T and 1 atm. partialPressure – H of one mole of H2 at T and 1 atm. partial pressure – H of ½ mole of O2 at TAnd 1 atm. partial rpessure)∆So = Standard entropy change.

‘Introduction to Thermodynamics of Materials’, D. R. Gaskell

When operated reversibly, the power is nearly zero.

Eo = 0.972 at800oC (1073 K)

F: Faraday constant (96,487 Coulombs/mol.)

Introduction to Thermodynamicsof Materials D. R. Gaskell

Thermodynamic Efficiency when the cell is operated reversibly, and in standard state

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Fuel Cell Efficiency (Non-Standard State, Reversible)Gibbs Free Energy Change for the reaction when Reactants and products not in Standard States

STHG ∆−∆=∆ Partial pressures different from 1 atm.

Gibbs Free Energy Change in terms of the Nernst VoltageFEG 2−=∆

Maximum Work (reversible process) is given byFEGw 2'max =∆−=

Thermodynamic Efficiency when the cell is operated reversibly

orevHFE

HFE

Hw

HG

∆=

∆=

∆=

∆∆

=22'

maxη

For the assumption of an ideal gas, oHH ∆=∆However, oSS ∆≠∆

222ln H

oHH pRSS −= and similarly for other species.

SoH2 = Partial molar entropy of hydrogen in the standard state

15

Thermodynamic Efficiency=∆−∆=∆ ooo STHG -247,500 + 55.85 T j/mol. From Gaskell

oH∆oG∆

o

oo

H

G

∆

∆=η

G∆

airOp

2

97.003.0

2

2 =

fuelH

fuelOH

p

p

HG

∆

∆=η

Temp.K

1073

973

873

773

673

573

StandardEnthalpy(J/mol.)

-247,500

-247,500

-247,500

-247,500

-247,500

-247,500

StandardFreeEnergy(J/mol.)

-187,573

-193,158

-198,743

-204,328

-209,913

-215,498

Standard TherrmodynamicEfficiency(%)

76%

78%

80%

82.5%

85%

87%

= 0.21

-211,623

-214,967

-218,310

-221,654

-224,997

-228,341

Thermo-dynamicEfficiency(%)

85.5%

86.9%

88.2%

89.6%

90.9%

92.3%

Efficiencyat 0.8 V(%)

78%

78%

78%

78%

78%

78%

HF∆×

=8.02

8.0η

++−∆−∆=∆−∆=∆ air

OfuelH

fuelOH

oo pRpRpRSTHSTHG222

ln21lnln

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Free Energy and Reversible Work

+∆=∆

airO

fuelH

fuelOHo

pp

pRTGG

22

2lnFree Energy Change

−=−=∆

fuelO

fuelH

fuelOH

eqo

pp

pRTKRTG

22

2lnln

Standard Free Energy and the Equilibrium Constant

−=

−=∆ fuel

O

airO

fuelO

airO

p

pRT

p

pRTG

2

2

2

2 ln21ln

Free Energy Change in terms of Oxygen Partial Pressures

=∆−= fuel

O

airO

FC p

pRTGw

2

2ln21'max

Maximum (Reversible) Work Maximum work is the same as reversible, isothermal expansion of half a mole of oxygen gas.

In the fuel itself , the reactionH2(fuel) +1/2O2(fuel) H2O(fuel)Is in equilibrium. Thus,∆G = 0 = ∆Go + RTlnKeq

--(1)

--(2)

--(3)

Substitute for ∆Go from (2) into (1)

(air)21(fuel)(fuel)

-

222

reactantsproducts

OHOH GGG

GGG

−−=

=∆

iGi

ofenergy freemolar partialor potential Chemical=

∫ ∫−==p

dpRTpdVw

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Isothermal Reversible Expansion of an Ideal Gas

=∆−= fuel

O

airO

FC p

pRTGw

2

2ln21'max

Piston

Cylinder

Gas Resisting ForceHeat Reservoir

18

Free Energy and Reversible Work (contd.)Maximum (Reversible) Work for a Carnot Cycle

( )

−=

1

2max ln21

PPTTRw coldhotCarnot

Figure: A p-V diagram comparing a fuel cell and a Carnot engine.Reversible work during a Carnot cycle = Area ABCDAReversible work during a fuel cell operation = Area ABB’A’A

A

B

C

D

B’A’ Volume

Pres

sure

Thot

Tcold

=

1

2max ln21

PPRTw hotFuelCell

( )

−= fuel

O

airO

coldhotCarnot p

pTTRw

2

2ln21max

maxmaxCarnotFuelCell ww >

2PPA =

1PPB =

'2PPD =

'1PPC =

1

2'

1

'2

PP

PP

=

19

An Illustration

( )

∆

=

=

∆−=

RTG

p

pp

pp

pRTGK

o

oH

oOHfuel

O

fuelO

oH

oOH

o

eq

2exp

exp

2

2/1

2

22

22

2 =airOp

2

=fuelOp

2

Fuel: H2=97%, H2O=3%: 1 atm. poH2=0.97 atm, po

H2O = 0.03 atmOxidant: Air (21% O2): 1 atm. po

O2 = 0.21 atm, T = 800oC = 1073 K

Standard Free Energy of H2(g) + 1/2O2(g) H2O(g)∆Go = ∆Ho –T∆So = -247,500 +55.85T

0.21 atm

5.23x10-22 atm

Nernst voltage:

V1.0966

1023.521.0ln

96487410733144.8ln

4 222

2

=

×××

=

= −fuel

O

airO

p

pF

RTE

Data from book on thermodynamics,e.g. Gaskell

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Free Energy, Work and Efficiency

+∆+∆−= fuel

OH

airO

fuelHoo

FC p

ppRSTHw

2

22lnmax

Fuel Cell Maximum (Reversible) Work and EMF

F

p

ppRSTH

FGE

fuelOH

airO

fuelHoo

2

ln

22

22

+∆+∆−

=∆

−=

Nernst Voltage

max2 FCFC wFVw <=Work when the cell is operated irreversibly

ChangeEnthalpy DerivedWork 2

=∆−

=H

FVη

Thermodynamic Efficiency Voltage Efficiency

ChangeEnergy Free GibbsDerivedWork

==EV

vη

The objective is to maximize ηv for a given power level, or maximizepower at a given ηv.

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Maximize Power at Given Efficiency or Efficiency at Given Power

Current Density

Vol

tage

Pow

er D

ensi

ty

Current DensityV

olta

ge

Pow

er D

ensi

ty

Power Density at a Given Efficiency Efficiency at a Given Power Density

Either way, the lower the cell resistance, the better

Low Cell Resistance

High Cell Resistance

Low Cell Resistance

High Cell Resistance

Higher Power Higher Efficiency

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Thermodynamics in Terms of Cell Parameters and Load

An Equivalent CircuitAll sources of voltage losses inThe cell are lumped into Ri.

Voltage vs. Current Plot

I

E

V

- Ri

Slope

(This is a simplification, made just forthe sake of simplified discussion. TheV-I curve is rarely linear).

( )LiLi RRFG

RREI

+∆

−=+

=2

iL IREIRV −==Voltage,

Current,

ERi

RL Load

ERi

Equivalent circuitfor the cell

The above is idealized. Usually, the V-I trace is nonlinear. I

V

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Thermodynamics in Terms of Cell Parametersand Load (contd.)E

Ri

RL Load VIP = Li RREI+

=

iRIQ 2' =o

iRIVIQP 2' +=+o

iIREV −=

dtdqEEIQP ==+

o

'

( )E

FRRt Li 2+=

( )2

22'

Li

ii

RRRERIQ

+==

oPower Voltage Current

Internal Rate of Heat Dissipationinto work or heat

Work Done

Time Required to Consume One Mole of Hydrogen

Rate of Free Energy Conversion

Heat Dissipated

The Sum GFEQw ∆−==+ 2''

( ) ( )Li

L

Li

LRR

RGRR

FERFVVItPtw+

∆−=+

====22'

( ) ( )Li

i

Li

iRR

RGRR

FERtQQ+

∆−=+

==2''

o

Equivalent Circuit

Recall

∆G < 0

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Thermodynamics in Terms of Cell Parametersand Load (contd.)

12 UUwQU −=−=∆

irrSTQSSS ∆+=−=∆ 12

( ) irrSTSSTQ ∆−−= 12

( )12' VVPww −+=

11122212 TSPVUTSPVUGGG +−−−+=−=∆

'wSTG irr −∆−=∆

irrSTGw ∆−∆−='

FEG 2−=∆

irrSTFEw ∆−= 2'

First Law Q = Heat absorbed by the systemw = Work done by the system

Isothermal Process

Isobaric ProcessFor an Isothermal-Isobaric Process

The above gives

( ) ( )Li

i

Li

LRR

RFEFERR

FERFVVItPtw+

−=+

==== 2222'We also have

‘Introduction to the Thermodynamicsof Materials’ D. R. Gaskell

Maximum possible work Loss – degree of irreversibility.

25

Thermodynamics in Terms of Cell Parametersand Load (contd.)

Degree of Irreversibility

Rate of Irreversible Entropy Production

( ) ( )2

2

22

Li

i

LiLi

iirrirr

RRTRE

RRFE

RRR

TFE

tS

dtdS

+=

+×

+

=∆

=

Thermodynamic Efficiency

+

∆−=

+

=∆Li

i

Li

iirr RR

RTG

RRR

TFES 2

+∆

∆=

+

=

+∆

=∆

=Li

L

Li

Lrev

Li

LRR

RHG

RRR

RRR

HFE

HFV ηη 22

Need toLower Ri

Need toLower Ri

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Rate of Heat Exchange with the Surroundings

( ) ( )

+

−−=∆−−=Li

iirr RR

RFESSTSTSSTQ 21212

( )( )( ) ( )2

212

22Li

i

LiLi RRRE

RRFSST

ERRF

QtQQ

+−

+−

=+

==o

Heat produced per mole of hydrogen consumed

Rate of heat production (exothermic)

Note that ∆S = S2 – S1 < 0.

Need toLower Ri

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What Does this all Mean For an SOFC?

1) Magnitude of free energy of the reaction (with free energy < 0) must be as high as possible to achieve the highest possible conversion of chemical energy into electrical energy. With H2(or CO) as the fuel, this implies, the lower the temperature, the higher is the thermodynamic efficiency.

2) The internal cell resistance must be as small as possible. Thus, every effort must be made to lower the overall cell resistance. Since the V-I relationship is usually nonlinear, it is necessary to address voltage losses (polarizations) at both electrodes as well. The higher the temperature, the lower the resistance.

Now we will devote next several slides on understanding what arethe main contributions to the cell ‘resistance’, and how to lower the cell resistance, which is in fact the main part of this part of this lecture

28

Solid Oxide Fuel Cells: General

2 W/cm)( iiη=

Power: Rate of Work Derived

Rate of Heat Generation byPolarization

2 W/cm)( iiV=

Objective: Lower η(i) to as low a value as possible.

(Open Circuit Voltage (OCV))

Load

Cell

Voltage

Cur

rent

Polarization or OverpotentialV

i

V(i)

E

Current Density

Vol

tage

Voltage AvailableFor Useful Work

Short CircuitCurrent Density

η(i)

OperatingCurrent Density

nFGE

∆−=

η(i)Typical Operating Point, V = 0.7E

Loss of voltage – Polarizationor Overpotential

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Topic 2: SOFC Materials: Electrolyte, Cathode, Anode; Cell Architecture on the Basis of Support

• Electrolyte: A dense (no open, connected porosity) Yttria Stabilized Zirconia (YSZ) A solid solution between ZrO2 and Y2O3 (~8 mol.% Y2O3, ~92 mol.% ZrO2).

• Anode: A porous, two-phase composite of Ni + YSZ.

• Cathode: A porous, two-phase composite of LSM + YSZ. (LSM: Sr-doped LaMnO3; typical composition – La0.8Sr0.2MnO(3-δ)).

Anode

Cathode

Electrolyte

30

YSZ Electrolyte: Defect Chemistry

[ ] [ ]••= OZr VY 2'

YxZr(1-x)O(2-x/2)

Over the temperature and oxygen partial pressure ranges of interest, thepredominant point defects are oxygen vacancies. The electroneutralitycondition is given by

For this reason, YSZ is predominantly an oxygen ion conductor.

31

LSM Cathode: Defect Chemistry

LSM: La(1-x)SrxMnO(3-δ) is a perovskite

Mn is predominantly in +3 state. Sr substitution on the A-site (La-site) leads to the creation of oxygen vacancies. This further leads to the absorption of oxygen by oxidizing Mn from +3 to +4 states. Chargecompensation is achieved by the formation of electron holes. Thus, LSM is predominantly a p-type material.

•×•• +→+ hOgOV OO 2)(21

2

4/12Oel p∝σElectronic conductivity

32

Other SOFC Materials

• Electrolyte: Rare earth oxide doped CeO2 (e.g. Gd2O3-CeO2 - GDC); Sr-doped and Mg-doped LaGaO3 (LSGM).

• Cathode: Single Phase - Sr-doped LaCoO3 (LSC), Sr-doped LaFeO3 (LSF), LSCF, etc.; Composite – LSM + Rare earth oxide doped CeO2 – e.g. GDC, LSM + LSGM; LSF + GDC, LSCF + GDC, etc.

• Anode: Ni + Rare earth oxide doped CeO2 – GDC; Cu + CeO2; La-doped SrTiO3, etc.

Many of these materials are currently being explored as they offercertain advantages over the state of the art materials; e.g. LSGMhas higher ionic conductivity than YSZ. However, there alsoare associated challenges. Thus, state of the art materials stated earlier (or small variations from them) continue to be widely used.

33

SOFC Designs Based on Relative Thicknesses

Cathode Current Collector or Support

Anode Functional Layer

Anode Support orAnode Current Collector

Electrolyte

Cathode Functional Layer

ELECTROLYTE-SUPPORTED CATHODE-SUPPORTED

ANODE-SUPPORTED

34

Types and Approximate Magnitudes of Conductivities (Resistivities) of the Various Layers (800oC)

• Anode Support or Current Collector: Electronic ~1,000 S/cm (~0.001 Ωcm).

• Anode Functional Layer: Electronic ~500 S/cm (~0.002 Ωcm).

• Electrolyte: Ionic ~0.033 S/cm (~30 Ωcm).• Cathode Functional Layer: Electronic ~50 S/cm (0.02

Ωcm).• Cathode Current Collector or Support: Electronic ~100

S/cm (~0.01 Ωcm).

35

Calculations of the Approximate Ohmic Area Specific Resistance (ASR) at 800oC for the Three Types of Designs

Electrolyte-Supported: High ASRElectrode-supported: Low ASR

Electrolyte Ionic Resistivity: eρ = 30 ΩcmCathode (Both Layers) Electronic Resistivity: cρ = 0.01 ΩcmAnode (Both Layers) Electronic Resistivity: aρ = 0.005 Ωcm Electrolyte Thickness: el (cm)Cathode (Total) Thickness: cl (cm)

Anode (Total) Thickness: al (cm)

Ohmic Area Specific Resistance (ASR): aacceeiR lll ρρρ ++= Ωcm2

Electrolyte Supported: (30x0.015+0.01x0.01+0.005x0.01) = 0.4502 Ωcm2

Cathode Supported: (30x0.001+0.01x0.2+0.005x0.01) = 0.0321 Ωcm2

Anode Supported: (30x0.001+0.01x0.01+0.005x0.1) = 0.0306 Ωcm2

Cell Resistance = ASR (Ωcm2)/Cell Area (cm2) = Ω (ohms)

36

A Typical, Five Layer Anode-Supported Cell: Various Layers and their Functions

• Anode support: Ni + YSZ, ~0.3 to ~1 mm, ~40% porosity, Coarse microstructure: Electronic conduction, fuel gas transport.

• Anode Functional Layer: Ni + YSZ, ~10 to ~20 microns, ~25% porosity, fine microstructure: Mixed Ionic (YSZ) and Electronic (Ni) conduction, fuel gas transport - electrochemical reaction.

• Electrolyte: YSZ, ~5 to 10 microns, dense (no connected porosity), fine microstructure: Ionic conduction.

• Cathode Functional Layer: LSM + YSZ, ~10 to ~20 microns, ~25% porosity, fine microstructure: Mixed Ionic (YSZ) and Electronic (LSM) conduction, oxidant gas transport – electrochemical reaction.

• Cathode Current Collector: LSM, ~50 to ~150 microns, ~40% porosity, Coarse microstructure: Electronic conduction, oxidant gas transport.

Anode Support

Anode Functional LayerElectrolyteCathode Functional LayerCathode Current Collector

37

An SEM Micrograph of an Anode-Supported Cell (Microstructure)

Electrolyte

Anode Support

Anode Functional Layer

Cathode Functional Layer

Cathode Current Collector

50 µm~0.6 mm

~15 µm~8 µm

~20 µm

High porosity foreasy air transport

High porosity foreasy fuel transport

Fine porous structure foreasy electrocatalysis – oxygen reduction

Fine porous structure foreasy electrocatalysis – fuel oxidation

38

Attributes of Anode-Supported Design

• Easy fabrication with Ni + YSZ as starting materials.• NiO and YSZ neither dissolve in each other nor react with

each other.• The presence of two phases helps maintain the microstructure

fine.• The electrolyte/anode bi-layer or cathode/electrolyte/anode

tri-layer can be fabricated in a single firing step. • The presence of a large amount of Ni improves heat transfer.• Cell is quite robust.

39

Topic 3: Sources of various voltage losses, and their dependence on cell parameters and test conditions.

• Voltage loss associated with ‘resistance’ to gas transport through porous anode – Anode Concentration Polarization or Concentration Overpotential.

• Voltage loss associated with ‘resistance’ to gas transport through porous cathode – Cathode Concentration Polarization or Concentration Overpotential.

• Voltage loss associated with the ‘resistance’ to electrochemicaloxidation of fuel at the anode – Anode Activation Polarization or Activation Overpotential.

• Voltage loss associated with the ‘resistance’ to electrochemicalreduction of oxygen at the anode – Cathode Activation Polarization or Activation Overpotential.

• Voltage loss associated with resistance to ion transport through the electrolyte, electron transport through electrodes – Ohmic Loss.

40

Gas Transport through Electrodes

Flux of oxygen through cathode depends upon: (1) Binary O2-N2 diffusivity.(2) Porosity. (3) Pore size. (4) Tortuosity. (5) Thickness. (6) Partial pressureof oxygen in the oxidant, poO2.

FiNjjj A

OOHH 22

222===

Fluxes of hydrogen and water vapor through anode depend upon: (1) Binary H2-H2O Diffusivity. (2) Porosity. (3) Pore size. (4) Tortuosity. (5) Thickness. (6) Partial pressure of hydrogen in the fuel, poH2.

( )(int)222 H

oHH ppj −∝

( )(int)222 O

oOO ppj −∝

oOp

2

Ano

de su

ppor

t

Ano

de in

terla

yer

Elec

troly

te

Cat

hode

inte

rlaye

r

Cat

hode

cur

rent

co

llect

or

)(')(2ip iOH)()(2

ip iH

)(')(2

ip iH

)(2 iOp

)(')(2

ip iO

oHp

2

)(')(2

ip iOH

oOHp

2

H2 + O-2 H2O + 2e Anode Interlayer 1/2O2 + 2e O-2 Cathode Interlayer

Fluxes in #/cm2.s

41

Fluxes and Current Density

AIi =

=I Current in Amps (A)

=A Active Cell Area (cm2)=i Current Density (A/cm2)

=2Hj Flux of Hydrogen (moles/(sec.cm2))

For every one mole of H2 passed (consumed) per unit time per unit area2 moles of electrons are passed in the external circuit; that is 2Fwhere F = Faraday constant (96,487 Coulombs/mole). Thus,

22 HFji =

Also, for every one mole of H2 consumed per unit time per unit areahalf a mole of O2 is consumed per unit time per unit area and one mole of H2O is formed per unit time per unit area. Thus,

222422 OOHH jFjFjFi ===

42

Gas Transport and Voltage Loss

oOp

2

Ano

de su

ppor

t

Ano

de in

terla

yer

Elec

troly

te

Cat

hode

inte

rlaye

r

Cat

hode

cur

rent

co

llect

or

)(')(2ip iOH)()(2

ip iH

)(')(2

ip iH

)(2 iOp

)(')(2

ip iO

oHp

2

)(')(2

ip iOH

oOHp

2

)(2

coOp

)(2

aoOp )('

2

aOp

)('2

cOp

)()('22

coO

cO pp <

)()('22

aoO

aO pp >

Note

= )('

)(''

2

2ln4 a

O

cO

p

p

FRTE

= )(

)(

2

2ln4 ao

O

coO

p

p

FRTE

Nernst Voltages

Thus, 'EE >

Loss of voltage = 'EE −

Concentration polarization orconcentration overpotentialat the anode + cathode

E’ = Nernst voltage across theelectrolyte when cell is underload (finite non zero current)

43

Electrode Design for Minimizing Concentration Polarization

• For a given current density, minimize partial pressure variations through the electrodes.

• Minimize the thicknesses of the electrodes – consistent with sufficient in-plane electrical conduction (low sheet resistance) and mechanical ruggedness.

• Increase porosity – again consistent with in-plane electrical conduction and mechanical ruggedness.

• Increase pore size.

Materials Processing procedures required to ensure that thedesired microstructures at the desired places are realized

44

Gas Transport through Porous Bodies

• Binary diffusion: (Anode:H2, H2O; Cathode: O2,N2).• Knudsen diffusion (if the pore size is comparable to the

mean free path).• Viscous flow.• Surface diffusion.

From the standpoint of cell design, need parameters that canbe readily measured. Assumptions:1) Viscous flow neglected. 2) Surface diffusion neglected.3) Transport by effective binary diffusion – treat tortuosity

factor as a fitting parameter - not valid if the pore size isvery small (less than about 0.25 microns).

Modes of Transport

Important Microstructural Parameters(a)Volume Fraction Porosity, (b)Pore Size, (c) Tortuosity

For more details, see: ‘Dusty Gas Model’ Mason and Malinauskas

45

Effective DiffusivitiesEffective Diffusivity through the Anode:

OHHa

avaeff D

VD

22

)()( −=

τ

22

)()( NO

c

cvceff D

VD −=

τ

Effective Diffusivity through the Cathode:

= Anode Tortuosityaτ

cτ = Cathode Tortuosity

= Binary DiffusivityOHHD22 −

= Binary Diffusivity22 NOD −

22 NOD −OHHD22 − , : From handbooks or calculations

= Anode Volume Fraction Porosity)(avV

= Cathode Volume Fraction Porosity)(cvV

)(avV )(cvV, : From measurements

aτ cτ, : No direct way to measure

)()( , ceffaeff DD : Can bemeasured in principle.

46

Some Values of Binary Diffusivities

( )Ω

+×=

−

2

2/12/33 /1/11086.1

AB

BAAB p

MMTDσ

BA MM ,

T

Chapman Enskogg Model for Binary Diffusivity

cm2/s

= Molecular weights

= Temperature (K) p = Pressure (in atmospheres)

ABσ = Average Molecular Diameter (in Angstroms)

Ω = Collision Integral

Values at 800oC

OHHD22 − ~6.52 cm2/s

22 NOD − ~1.28 cm2/s

Depending upon the porosity andtortuosity, these numbers can be lower by more than an order of magnitude. Design of electrodemicrostructure (porosity) is important.

‘Mass Transfer in Fluids’E. L. Cussler

Higher binary diffusivity of H2-H2O is another reason for choosing anode-supported.

47

Measurement of Effective Diffusivities:An Electrochemical Method

Pump

Sensor

Porous LSM disk

Glass seal

Pt lead

Zirconia disk

V

A

Platinum paste Power supply

x = 0 x = l

PorousLSMDisc

p = p0

p = pi

0.15 0.20 0.25 0.30 0.35 0.40 0.450.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

Effe

ctiv

e di

ffusi

vity

(cm

2 /s)

Open porosity

Experimentally measured effective O2-N2diffusivity at 800oC as a function of porosity

1) Measure current – relate gaseous flux to it.2) Measure Nernst voltage – pO2 in the chamber3) Estimate efefctive diffusivity

48

How is the Voltage vs. Current Density Polarization Curve Influenced by Transport through Porous Electrodes?

asi

Current Density

Vol

tage

Limiting Current Density

csi = Cathode limiting current density (oxygen partial pressure at thecathode/electrolyte approaching zero)

= Anode limiting current density (hydrogen partial pressure at theanode/electrolyte approaching zero)

Voltage vs. current behavior when partial pressure of hydrogen at anode/electrolyte interface, or partialpressure of oxygen at cathode/electrolyte interfaceis nearly zero – limiting current density

49

Schematic of pH2 Variation as a Function of Current Density: Limiting Behavior

)(')(2ip iOH

Ano

de

oHp 2 )('

2 ipH

Elec

troly

te

At the limiting condition, )('22 ipp H

oH >> . This leads to a limiting flux.

That is, oHH

HoHH

pj

ippj

22

'222 ))((

∝

−∝

In the above schematic, the anode functional layer is ignored.or when )('

22 ipp HoH >>

Current Density

Vol

tage

Limiting Current Density

ias

50

Anode Limiting Current Density Behavior

)(22~ aeff

a

oH

as Dl

pRT

Fi

oHp

2 : Partial pressure of hydrogen just outside the anode

al : Anode thickness

Under most operating conditions, this behavior is not observed. However, a cell can be operated using a diluted fuel (low partialpressure of hydrogen in the fuel) to induce this type of behavior.The purpose is to experimentally determine the effectivediffusivity, which is usually not a strong function of the relativeamounts of H2 and H2O.

51

Cell Performance in Fuels with Different Hydrogen Partial Pressures

Vol

tage

Current DensityPo

wer

Den

sity

High pH2

Low pH2

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.50.0

0.2

0.4

0.6

0.8

1.0

Current Density (A/cm2)

Vol

tage

(V)

0.0

0.5

1.0

1.5

2.0

H2 15% H2O+H2

32% H2O+H2

45% H2O+H2

50% H2O+H2

66% H2O+H2

80% H2O+H2

Power D

ensity (W/cm

2)

Schematic

Data on a button cell at 800oC

asiasi

asi

In a stack of cells, portion of thecell at the inlet is exposed to a highpH2, while that near the outlet isexposed to low pH2, as the fuel gasbecomes depleted in H2.

Tests conducted under flooded conditions

Cell performance in a stack near outletCell performance in a stack near inlet

52

Anode Concentration Polarization or OverpotentialVoltage loss associated with fuel gas transport through the porous anodeis known as anode concentration polarization or overpotential. It depends onthe anode porosity, anode tortuosity, anode thickness; effective diffusivity,partial pressure of hydrogen in the fuel (how depleted is the fuel), and temperature.

−= '

)(2

)(2)( ln

4aO

oaO

aconc p

p

FRTη

−= '

22

'22

)( ln2 OH

oH

Ho

OHaconc pp

ppF

RTη

+

−

−=

as

asaconc

ii

ii

FRT

1

1ln

2)(η

)(22~ aeff

a

oH

as Dl

pRT

Fi

)(2

aoOp

oOp

2

Ano

de su

ppor

t

Ano

de in

terla

yer

Elec

troly

te

Cat

hode

inte

rlaye

r

Cat

hode

cur

rent

co

llect

or

)(')(2ip iOH)()(2

ip iH

)(')(2

ip iH

)(2 iOp

)(')(2

ip iO

oHp

2

)(')(2

ip iOH

oOHp

2

)(2

coOp

)('2

aOp

)('2

cOp

53

Experimental Evidence on the Effect of Anode Concentration Polarization on Cell Performance

Only Anode Support Porosity variedOnly Anode Support Thickness varied

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.2

0.4

0.6

0.8

1.0

1.2


Vol

tage

(V)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

800 oCElectrolyte thickness: 8 µmAnode support porosity: 48 vol%Cathode interlayer: 20 µm

Anode support thickness: 0.50 mm 1.00 mm 1.45 mm 2.45 mm

Power D

ensity (W/cm

2)

2.45 mm

0.5 mm

)(22~ aeff

a

oH

as Dl

pRT

Fi

+

−

−=

as

asaconc

ii

ii

FRT

1

1ln

2)(η

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.2

0.4

0.6

0.8

1.0

1.2

Anode support porosity 76% 57% 48% 32%

800 oCAnode support thickness: 1.0 mmElectrolyte thickness: 8 µmCathode interlayer: 20 µm


Vol

tage

(V)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Power D

ensity (W/cm

2)

32%

57%,76%

48%

F. Zhao and A. Virkar, J. Power Sources, 141 79-95 (2005)

54

Anode Concentration Polarization - Calculations

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

50

100

150

200

Ano

de C

once

ntra

tion

Pola

rizat

ion

(mV

)


0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0



PH

2 at anode/electrolyte interface (atm)

Only Anode Support Porosity VariedOnly Anode Support Thickness Varied

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

50

100

150

200

250

300

Ano

de C

once

ntra

tion

Pola

rizat

ion

(mV

)




0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

PH

2 at anode/electrolyte interface (atm)

These calculations assume poH2 = 0.97. Downstream in a stack, the poH2 << 0.97,due to depleted fuel. Thus, anode concentration polarization downstream is even greater.

55

Cathode Concentration Polarization or Overpotential

oOp

2

Ano

de su

ppor

t

Ano

de in

terla

yer

Elec

troly

te

Cat

hode

inte

rlaye

r

Cat

hode

cur

rent

co

llect

or

)(')(2ip iOH)()(2

ip iH

)(')(2

ip iH

)(2 iOp

)(')(2

ip iO

oHp

2

)(')(2

ip iOH

oOHp

2

)(2

coOp

)(2

aoOp

)('2

aOp

)('2

cOp

−= )(

2

)('2

)( ln4 co

O

cO

cconcp

p

FRTη

Cathode concentration polarization can be similarly estimated. In anode-supportedcells this contribution is usually small, as long as the cathode is thin enough and porous enough. However, depending upon other design criteria, this may besignificant.

c

ceffco

O

coO

cs lD

pp

pp

RTFi )(

)(2

)(24~

−

Cathode Limiting Current Density

22)(

)( NOc

cvceff D

VD −=

τIn anode-supported cells, for typical cathode porosities and thicknesses, and overthe range of operating conditions, the cathode concentration polarization loss isusually small – about 10 mV.

Slightly different equationthan ias due to jN2 = 0

56

Voltage Loss Associated with Electrochemical Reactions at the Electrodes: Activation Polarization• Cathode Reaction: 1/2O2 + 2e’ O-2

• Anode Reaction: H2 + O-2 H2O + 2e’• Species in the Gas Phase: O2(cathode), H2(anode), H2O(anode)• Species in YSZ: O-2

• Mobile Species in Electrode Materials: e’(LSM-cathode, Ni-anode)

The above gives only the overall electrode reactions. These compriseof many series and parallel steps. These include: (a) Adsorption,(b) Dissociation, (c) Surface Diffusion, (d) Electron Transfer. If anyone of the series steps is much slower than the other, one can describethe mechanism in terms of a rate-limiting step (RDS). Experimentally, thisis very difficult to determine – and the literature is full of many differentRDS. This underscores the difficulty in isolating such steps unequivocally.We will not much dwell on this topic. Our focus will be on identifying thosematerial/microstructural parameters which influence electrode reactions, andcan be experimentally measured and directly related to cell performance.

57

ηact – voltageloss

Activation Polarization or Overpotential: This is associated with the actualCharge transfer reaction, which in solid state electrochemistry generally occurs at a Three Phase Boundary (Electrolyte-Electrocatalyst-Gas Phase) (TPB).

1/2O2(g)

2e’

O-2

Oxidant (e.g. air)ElectrocatalystParticle(e.g. LSM)

Electrolyte(e.g. YSZ) O-2

H2(g)H2O(g)

2e’ Fuel(e.g. H2)

Electrolyte(e.g. YSZ)

ElectrocatalystParticle(e.g. Ni)

Cathode Anode2

2 '2)(21 −→+ OegO '2)()( 22

2 egOHgHO +→+−

actη : Voltage loss associated with the charge transfer reaction. This isusually a thermally activated process. A phenomenological equation,known as the Butler-Volmer equation, originally developed for aqueouselectrochemistry, is often used to describe it.

ηact – voltageloss

Three PhaseBoundary (TPB)

Three PhaseBoundary (TPB)

Activation Polarization

58

The Cathode Reaction

YSZ

LSM1/2O2

2e’

O-2

Air

YSZ

LSM

2e’

O-2

Air

Adsorbed‘O’ Atom

Three Phase Boundary (TPB)

ε

δView from top

TPB

ct

TPB

ctpR

ll

ρδ

ερ==

'

δερ ,,'ct -cannot be measured

independently

ctTPBpR ρ,,l -can be measuredindependentlyTPBl -Three Phase Boundary (TPB)

Length/unit area (cm-1) pR - Ωcm2

59

Monolithic (Screen-Printed) vs. Composite Cathode

From current collector

In a non-composite cathode, there are insufficient TPB’s. Thus, the resistanceto charge transfer (electrochemicalreaction) is large. Traditionally, LSMhas been used until recently. The importanceof using a composite cathode is nowbeing recognized by the SOFC community.

O-2 O-2 O-2 O-2

YSZ Electrolyte

1/2O22e’

PorosityIn the CompositeCathode

1/2O22e’


O-2 O-2 O-2 O-2

YSZ Electrolyte

O-2 YSZ

LSM

These LSM particles are not effectiveas electrocatalyst – they only carry electronic current.

Electrocatalysisoccurs onlyat the TPBs.Very lowTPB

LSM Cathode LSM + YSZ Cathode

Isolated

Much larger TPB in composite cathodes

60

Composite Cathode Features

• The cathode functional layer is a mixture of an ionic (YSZ) and an electronic (LSM) conductor. This increases the total TPB and extends the reaction zone.

• YSZ must be contiguous – to carry ionic current.• LSM must be contiguous – to carry electronic current.• Porosity must be contiguous – for gaseous transport.• There must be large TPB length – that is LSM should not

completely cover YSZ particles.

1/2O22e’


O-2 O-2 O-2

YSZ Electrolyte

O-21) J. S. Newman and C. Tobias, J. Electrochem. Soc., 109 1183 (1962).2) T. Kenjo, S. Osawa, and K. Fujikawa, J. Electrochem. Soc., 138

349 (1991).3). C. W. Tanner, K-Z. Fung, and A. V. Virkar, J. Electrochem. Soc.,

144 21 (1997).

61

Role of Cathode TPB on Performance

Maximum Power density at 800oC was ~0.33 W/cm2.

Maximum Power density was ~1.1 W/cm2 at 800oC.

Cell 1 Cell 2

Black – PoresWhite – YSZRed or Blue – LSM

Color-Coded Electron Micrographs (taken on an Electron Microprobe)

62

Good CathodeEPMA Micrograph

Three Phase Boundaries (TPB)

Not a TPB5 µm

MaximumPower density Of this cell was~1.1 W/cm2 at800oC.

Pore

YSZ

YSZ

LSM

TPB

TPB

63

Poor CathodeEPMA Micrograph

Three Phase Boundaries (TPB)

No TPB5 µm

Maximumpowerdensity at800oC was~0.33 W/cm2.

LSM

YSZ

Pore

No TPB

64

Quantitative Features of the Composite CathodeParameters

• Ionic conductivity (σi) or resistivity (ρi = 1/σi) of the ionic conductor in the functional layer YSZ.(S/cm or Ω-1cm-1)

• Particle size of the YSZ (d) in the functional layer (cm).• Porosity of the functional layer (Vv).• Charge transfer resistivity (ρct). This is a function of

temperature and oxygen partial pressure (local) (Ωcm).• Three phase boundary length (lTPB) (cm-1).• Thickness of the functional layer (h). Essentially no

dependence for h>>d.

Assumptions: (a) Electronic conductivity of LSM is much greater than ionicConductivity of YSZ. (b) Gas diffusion is fast (so porosity is not too low).

65

A Simple ModelLSM particles

Log(h)

Rp R

ct

( ) ( ) )1(11 viTPB

ct

vi

ct

v

ctip V

dVdR

VdRR

−=

−=

−≈

σρ

σρ

l

Illustrative calculation:Rct = 1 Ωcm2 ρi = 50 Ωcm d = 1 µm Vv = 0.3

Then, Rp = 0.0845 Ωcm2 – a twelve-fold decrease in polarization resistance through microstructural design!

ρi = Ionic resistivity of the electrode

C. W. Tanner et al.J. Electrochem Soc., 144 21-30 (1997).

Screen-printed LSM

hcr ~10d

All parameters can be measured.

Fundamental parameter which governs electrochemical reaction is ρct

h

2e’

O-2 O-2 O-2

YSZ Electrolyte

O-2 h

66

How to Measure Charge Transfer Resistivity, ρct?

• Not very easily.• Need to make electrodes

with well-defined and varying three phase boundary length, lTPB.

• This requires methods from microlithography.

• Measure area specific charge transfer resistance using methods such as impedance spectroscopy.

YSZSubstrate

LSMFilm

TPB

Slope = 1/ρct

Working Electrode

Reference Electrode

100 µm

Photo Microlithography

67

Activation Polarization at High Current Densities• Polarization ‘resistance’ we described so far, including the effect of

electrode microstructure, is applicable only at very low currentdensities – linear (not ohmic) relation between current and voltage (overpotential).

• At high current densities, relationship between current and voltage (overpotential) is not linear. The most commonly used phenomenological equation is known as the Butler-Volmer equation.

• In either low or high current density regime, the relationship is thermally activated – hence the term activation polarization.

• Experimentally, it is very difficult, if not impossible to determine the relationship between current and voltage. Hence, fitting to cell test data is the only practical approach – if the objective is to design a cell.

• The simplest approach is to use a limiting case of the Butler-Volmer equation, known as the Tafel equation, applicable at high current densities. The use of Tafel equation also allows one to lump activation polarizations at both the cathode and the anode into a single expression.

68

Butler Volmer Equation and the Low Current Density Regime

( )

−

−

−=

RTzF

RTzFii actact

oηαηα 1expexp

z: Number of electrons participating in the reaction.F: Faraday constant (96,487 Coulombs/mole).R: Gas constant (8.3144 J/mol.).T: temperature (K).α: Transfer coefficient (0 < α < 1.0).io: Exchange current density (Amp/cm2) (thermally activated).

We see that the Butler-Volmer equation gives the current density, i, as afunction of the activation polarization, ηact, and not ηact as an explicitfunction of i. For very small values of the current density, the above simplifies to

iRizFiRT

po

act ≈≈η

whereo

p zFiRTR = is the charge transfer resistance (Ωcm2), a measure of the

resistance to the electrochemical reaction.

1)‘Electrochemical EngineeringPrinciples’ G. Prentice2) ‘Electrochemistry, P. H. Rieger

Linearized: Note; linear does not mean ohmic.

Ωcm2

69

Butler-Volmer Equation and the High Current Density Regime

( )

−

−

−=

RTzF

RTzFii actact

oηαηα 1expexp

The Butler-Volmer equation

At high ηact, that is

1>>RT

zF actη

1>>−RT

zF actη

ibaizF

RTizF

RToact lnlnln +=−≈

ααη

Or, for

ibaizF

RTizF

RToact lnln

)1(ln

)1(+=

−+

−−≈

ααη

Tafel Equation

Tafel Equation

The Tafel equation is usually applicable for i >> io. In an SOFC, both ofthe electrode activation polarizations can be usually described by theTafel equation at high overpotentials.

70

Exchange Current Density

GA

GA

Fast Electrode ProcessHigh Exchange Current Density

Slow Electrode ProcessLow Exchange Current Density

GA: Activation Energy

71

Understanding Exchange Current DensityVirtually no holes

Negligible exchange of water between compartments

Larger holes

Greater water exchange between compartments

Very fine holes

Some water exchange between compartmentsEquivalent to low exchange current density

Equivalent to higher exchange current density

Equivalent to negligible exchange current density

72

Activation Polarization: Summary Points

• Activation Polarization exists at both electrodes – cathode and anode.

• The general phenomenological equation used is the Butler-Volmer equation.

• In the general case, no simple relation can be given for the sum of activation polarization at the two electrodes as a function of current density.

• In the low current density regime, the relationship between overpotential, ηact, and current density, i, is linear. Thus, the activation polarization at the two electrodes can summed and expressed as a function of current density.

• In the high current density regime, the Tafel equation is assumed to be applicable. The ηact depends linearly on lni. Thus, in this case also, the activation polarization at the two electrodes can be summed and expressed as a function of the logarithm of current density.

73

What to do for Designing a Good Cathode with a Functional Layer?

• YSZ Particle should be fine (~0.5 µm or finer). Commercially available YSZ with 8 mol.% Y2O3 is satisfactory.

• LSM particle size should be fine (~0.5 µm or finer).• Mix YSZ and LSM in approximately 50:50 ratio.• Apply on the YSZ electrolyte surface. Approximate

thickness 10 to 20 microns. The porosity should be ~25%.• Apply a layer of LSM over this layer. Thickness of this

current collector layer should be ~50 to ~100 microns. Porosity should be about 45% or somewhat higher.

• Heat to ~1100 to 1200oC for 1 hour.

74

A Simple Analytical Model for SOFC Performance

Minimum number of parameters required is 5 to describe performance. Unfortunately,voltage – current density plots are of very simple shapes, which can be fit with threearbitrary parameters. Thus, it is generally not possible to obtain a unique set of parameters by fitting to cell performance data.

+

−

+

−+−−−=

as

as

csio

ii

ii

FRT

ii

FRTibaiREiV

1

1ln

21ln

4ln)(

OCV ActivationPolarization(assumes theTafel limit)-both electrodes

CathodeConcentrationPolarization

AnodeConcentrationPolarization

OhmicLoss

+

+−−−=

)(

)(ln

2)(

ln4

ln)( ')(

')(

')(

22

22

2

2

ipp

pipF

RTp

ipF

RTibaiREiViOH

oH

oOHiH

oO

iOio

Anode or CathodeLimiting Behavior

J. Electrochem. Soc., 146 [1] 69-78 (1999))()( iEiV o η−=

V(i)

i

75

Schematics of Various Polarizations


Vol

tage

(V)

Ohmic Polarization

Cathode Activation Polarization

Anode Activation Polarization

Cathode Concentration Polarization

Anode Concentration PolarizationVoltage AcrossLoad

Eo

Load

Ohmic Cathode Con Anode con. Cathode Act Anode Act

Eo Equivalent Circuit

76

Curve Fitting: Anode Support Thickness Varied

)1(22

effOHHD − = 0.68 cm2/s

)2(22

effOHHD − = 0.08 cm2/s

)1(22

effNOD − = 0.14 cm2/s

)2(22

effNOD − = 0.04 cm2/s

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

Ri 0.101a 0.098b 0.11Deff(1)

O2-N2

0.14

Deff(2)O2-N2

0.04

Deff(1)H2-H2O

0.68

Deff(2)H2-H2O

0.08

Experimental Curve-fitted

Vol

tage

(V)


Anode thickness = 0.5 mm

0.5 mm

0.0 0.5 1.0 1.5 2.0 2.5 3.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2


Ri 0.104a 0.094b 0.11Deff(1)

O2-N2

0.14

Deff(2)O2-N2

0.04

Deff(1)H2-H2O

0.68

Deff(2)H2-H2O

0.08


Vol

tage

(V)


1.0 mm

0.0 0.5 1.0 1.5 2.0 2.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2



Ri 0.135

a 0.105b 0.12Deff(1)

O2-N2

0.139

Deff(2)O2-N2

0.04

Deff(1)H2-H2O

0.68

Deff(2)H2-H2O

0.079

Vol

tage

(V)


1.5 mm

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.40.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2



Ri 0.148

a 0.12b 0.118Deff(1)

O2-N2

0.14

Deff(2)O2-N2

0.04

Deff(1)H2-H2O

0.68

Deff(2)H2-H2O

0.08

Vol

tage

(V) 2.45 mm

0.5 mm

1.0 mm

1.45 mm

2.45 mm

Only anode support thickness varied. Note all polarization curves fitted with the same four effectivediffusivities – experimental validation of the model

Divergence at low currentdensities since Tafel is not applicable at low i

77

Topic 4: Cell Design for Enhanced Performance

• A five layer anode-supported cell with standard materials (YSZ, LSM, Ni).

• Anode support of Ni + YSZ, approximately 50% of each by volume, porosity in excess of ~45% , coarse structure – pore size several microns; thickness as small as possible – practical 0.3 to 0.5 mm.

• Anode functional layer of Ni + YSZ, approximately ~60 vol.% YSZ,~40 vol.% Ni, porosity ~25%, thickness ~5 to 20 microns; particle sizes on the order of 0.5 to 1 micron. If particle size is much smaller than 0.5 µm, reduce thickness to ~2-3 µm. Microstructure well-developed – good inter-particle contact.

• Electrolyte, approximately ~ 8 to 10 microns thick, dense.• Cathode functional layer of LSM + YSZ, approximately ~60 vol.%

YSZ, ~40 vol.% LSM, porosity ~25%, thickness ~5 to 20 microns; particle sizes on the order of 0.5 to 1 micron. If particle size is much smaller than 0.5 µm, reduce thickness to ~2-3 µm. Microstructure well-developed – good inter-particle contact.

• Cathode current collector, LSM, coarse structure, porosity ~45 or 50%;pore size several microns; thickness ~50 to 200 microns (0.05 to 0.2 mm).

78

Rationale for the Choices of Various Cell Microstructural/Geometric Parameters

• Anode Support: Minimize concentration polarization, even at low pH2(high fuel utilization) – maximize ias. Ensure sufficient strength (not too thin – not too porous), sufficient electrical conductivity.

• Anode Functional Layer: Minimize activation polarization, even at low pH2 – large TPB length, small YSZ particle size, connected YSZ and connected Ni, modest porosity – thick enough to spread out electrochemical zone – thin enough to minimize concentration polarization.

• Electrolyte: Thickness not too critical, as long as below about 10 microns. Thick enough to be pinhole free.

• Cathode Functional Layer: Minimize activation polarization, even at low pO2 – large TPB length, small YSZ particle size, connected YSZ and connected LSM, modest porosity – thick enough to spread out electrochemical zone – thin enough to minimize concentration polarization.

• Cathode Current Collector: Minimize concentration polarization, even at low pO2 (high oxidant utilization) – maximize ics. Ensure sufficient electrical conductivity – minimize sheet resistance.

79

Topic 5: Cell Design – Thermo-mechanical Considerations

• All three components (anode, cathode, electrolyte) and the cell are brittle – can break, not bend.

• Strength is largely determined by the strength of the anode in anode-supported cells (thickest component). Typical strength is ~120 to ~150 MPa, sometimes even lower.

• Strength requirement is important from the standpoint of handling, thermal cycling, stresses due to non-uniform temperature distribution.

• Anode strength depends upon the relative amounts of Ni and YSZ, porosity, etc.

• Fracture toughness is another important fracture mechanical property.

80

100

150

200

250

0 10 20 30 40 50 60 70 80

Zirconia Content in ZrO2/NiO, vol.%

Flex

ural

Str

engt

h, M

Pa

8YSZ/Ni4YTZP/Ni3YTZP/Ni

Four-Point Bend Strength of Zirconia/Ni Anode-Supports as a Function of Zirconia Content

(after reducing at 800oC for 24 hours under 5 liter/min of 10% H2 + 90% N2)

81

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80Zirconia Content in ZrO2/NiO, vol.%

8YSZ/Ni4YTZP/Ni3YTZP/Ni

Frac

ture

Tou

ghne

ss, K

IC, M

Pa √

m

Fracture Toughness of Zirconia/Ni Anode-Supports as a Function of Zirconia Content

(Measured Using Single Edge Notch Bending (SENB) Technique, after reducing at 800oC for 24 hours under 5 liter/min of 10% H2 + 90% N2)

82

Thermo-mechanical Issues – Stresses in PEN• PEN stands for the cell (Positive electrode – Electrolyte – Negative

electrode).• Thermal expansion coefficients of the three components are in general

different.• Elastic moduli (e.g. Young’s) of the three components are in general

different.• At the sintering or cathode firing temperature, there are negligible

stresses in the PEN structure. • When cooled to room temperature, different components tend to shrink

to different sizes – dictated by their thermal expansion coefficients.• However, they are bonded together. Thus, the unit as a whole needs to

shrink as one body – without causing cracks or delaminations. This leads to the establishment of stresses.

• Stresses are the highest at room temperature – lower at the operating temperature.

• Objective is to design cells such that minimum possible damage occurs.

83

Thermo-Mechanical Considerations

• Differences in coefficients of thermal expansion.• Differences in elastic properties, and component

thicknesses.• Cracking or delamination of layers. • Flatness of the cell.• Criteria for the selection of the best cell design.

84

What Happens when an Electrolyte-Anode Bi-layer is Cooled from the Fabrication Temperature?

Net Resulta) Electrolyte under bi-axial

compressionb) Anode under bi-axial

mild tensionc) The bi-layer exhibits

a convex up bow

Anode Thickness >> Electrolyte ThicknessElectrolyte ThermalShrinkage if it were free

Anode ThermalShrinkage if it were free

At High Temperature

At Room Temperature

But anode and electrolyte are bonded across the interface

Shrinkages and bow are shown exaggerated

InterfaceDelaminationcan occur

Cell assumed flat at hightemperature

85

Electrolyte/Anode Bi-Layer Structure

X

Y

A

L1 L2

B

CD

Anode

Electrolyte

α1 = Coefficient of thermal expansion of the electrolyte = 10.5 E-06/ °Cα2 = Coefficient of thermal expansion of the anode = 13 E-06/°CE1 = Modulus of elasticity of the electrolyte = 210 GPaE2 = Modulus of elasticity of the anode = 170 GPa

A Crack

Objective: To identify conditions under which a crack may develop – then in practice avoidsuch situations

86

Finite Element Analysis of Anode-Supported Cells

Finite Element Analysis of Delamination

Delamination Crack

Delamination Crack

Delamination Cracks

Anode

Cathode

Electrolyte

YSZ film in biaxial compression

Light violet color indicates the presence ofa compressive stress in the electrolyte. If a crack forms,stress in the cracked part of the electrolyte is relieved.This is shown in white.

In this case, delamination crack is assumed to occur along the cathode-electrolyte interface. Thus, stress from the cracked part of thecathode is relieved – shown in light blue.

87

Compressive Stress

Tensile Stress

Electrolyte

Anode YSZ electrolyte film in biaxial compressionNi + YSZ anode inmild biaxial tension

Bi-Layer without a Delamination Crack

High Stress

88

What Happens if Crack Develops along the Interface?

Stress Relief by Cracking

A delamination crack

Note negligiblestresses in the YSZ film and theNi + YSZ anodein the delaminatedregion.

89

Release of Strain Energy by Cracking along Interface

y = 927557x + 1.2986R2 = 0.999

0

5

10

15

20

25

30

35

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

2.50E-05

3.00E-05

3.50E-05

Electrolyte Thickness in m

G in

J m

^2

Electrolyte Thickness (µm)

G (J m^2)

7 7.5

10 10.6

15 15.5

20 20.1

25 24.6

30 28.8

Low Tendency forDelamination High Tendency for

Delamination

G: Strain Energy Released when a Delamination Crack forms

Conclusion: For an anode-supported cell design, the thickerThe YSZ film, the greater is the tendency for crackingMessage: Make the electrolyte as thin as possible from the standpointof mechanical integrity – fortunately, this good for resistance as well

90

An Illustration: An Estimation of the Maximum Electrolyte Thickness in Anode-Supported Cells

≈elE 200 GPa

≈elα 10 x 10-6 /oC

≈anα 13 x 10-6 /oC

≈hT 1200oC = 1473 K

25oC = 298 K≈lT

30 J/m2 (rather approximate – could be off 20%)

( )m 24~2

2int µ

αγ

TEt

elel

∆∆<

Maximum allowable electrolyte thickness

Typical electrolyte thickness ~5 to 10 µm

Typical Values

Bending Neglected

91

Complete Cathode-Electrolyte-Anode (PEN) Structure

Electrolyte

Anode

Cathode

50 mm

1 mm

10 µm

50 - 300µm

Stress Analysis of the complete tri-layer structure can be similarly done usingFinite Element Analysis (FEA) using commercial software (e.g. ANSYS). DataRequired are: (a) Elastic properties of the three layers (or as many layers are there),(b) Thermal expansion properties of the three (or as many) layers, and (c) Thicknessesof the three (or as many) layers.

Results of some calculations

92

X

Y

A

L1 L2

B

CD

Anode Electrolyte

Cathode

α1 = Coefficient of thermal expansion of the electrolyte = 10.5 E-06/ °Cα2 = Coefficient of thermal expansion of the anode = 13 E-06/°Cα3 = Coefficient of thermal expansion of the cathode = 13 E-06/°C E1 = Modulus of elasticity of the electrolyte = 210 GPaE2 = Modulus of elasticity of the anode = 170 GPaE3 = Modulus of elasticity of the cathode = 50 GPa

Cathode-Electrolyte-Anode Tri-layer: Crack Along Electrolyte-Anode Interface: Cathode matched with Anode

93

Tensile Stress

Cathode

ElectrolyteCompressive stress

Anode

Note mildtensile stressesin both the anodeand the cathode

Stress State in the Absence of a Crack:Cathode Matched with Anode

94

Tensile stress

Compressive stressNote relaxed stresses inthe delaminated regions. Also note bending of thecathode-electrolyte bi-layerin the delaminated region.

Stresses when Delamination Crack forms between Anode and Electrolyte: Cathode Matched with Anode

95

Elastic Energy Release Rate Cathode Matched with Anode

Plot of G vs cathode thickness

y = 600x + 0.0031R2 = 0.9996

y = -15120x + 8.0647R2 = 0.9724

012345678

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04

Cathode Thickness in m

G in

J m

^2

G for crackbetween anodeand ElectrolyteG for crackbetween cathodeand electrolyteDelamination

Crack

Elastic energy release rate, G, is the energy released per unit area of the interfaceIF a crack forms. For a crack to form, this must exceed a certain materialAnd structure (PEN) parameter – here 2γint. That is, if G > 2γint, crack will form.Thus, the lower the G, the lower the tendency for crack formation.

The above implies that crack will most likely occur along electrolyte/anode interface,And not along cathode/electrolyte interface, assuming the γint is the nearly the samefor both interfaces. But note the rather low values of G.

96

α1 = Coefficient of thermal expansion of the electrolyte = 10.5 E-06/°Cα2 = Coefficient of thermal expansion of the anode = 13 E-06/°Cα3 = Coefficient of thermal expansion of the cathode = 10.5 E-06/°CE1 = Modulus of elasticity of the electrolyte = 210 GPaE2 = Modulus of elasticity of the anode = 170 GPaE3 = Modulus of elasticity of the cathode = 50 GPa

X

Y

A

L1 L2

B

CD

Anode Electrolyte

Cathode

Cathode-Electrolyte-Anode Tri-layer Crack Along Electrolyte-Anode Interface

Cathode matched with Electrolyte

97

Compressive Stress

Anode

CathodeElectrolyte

Tensile Stress

Stress State in the Absence of a CrackCathode Matched with Electrolyte

98

Electrolyte

Anode

Cathode

Compressive Stress

Tensile Stress

Stresses when Delamination Crack forms between Anode and Electrolyte Cathode Matched with Electrolyte

99

Elastic Energy Release RateCathode Matched with Electrolyte

y = 185324x + 14.411R2 = 0.9874

y = 184955x + 24.681R2 = 0.9874

0

10

20

30

40

50

60

70

80

90

0.00E+00 1.00E-04 2.00E-04 3.00E-04 4.00E-04

Cathode Thickness in m

G in

J- m

^2

G for crack between anode andelectrolyte

G for crack betweencathodeand electrolyte

Delamination Crack

Note: The G is high for cracks along both interfaces. Thus, cracking may occur along either interface. Also, the G is higher in this case (cathode matched with electrolyte) than in the previous case (cathode matched with anode).

Message: For anode-supported cells, better to matchCathode with anode – not with the electrolyte

100

Effect of Properties on Cell Flatness

• So far, we have neglected the role of bending stresses –which is actually significant.

• Bending occurs due to differences in stresses in the various layers. Bending can be calculated using equilibrium conditions; Sum of forces = 0, Sum of moments = 0.

• Since thermal expansion coefficients are of the various layers are different, the level of bending (bow) will vary with temperature.

• Whether or not cells are flat is important in both stack assembly procedure used, and stresses that are generated.

• By choosing appropriate values of thermal expansion coefficients, elastic properties, and thicknesses, bow can be minimized.

101

Bending Stresses: How Flat is the Cell?

E1 = Electrolyte Modulus = 210 GPa α1 = Electrolyte Th. Ex. Coeff. = 10.5 x 10-6/oCE2 = Anode Modulus = 170 GPa α2 = Anode Th. Ex. Coeff. = 13 x 10-6 /oCE3 = Cathode Modulus = 50 GPa α3 = Cathode Th. Ex. Coeff. = 10 to 15 x 10-6 /oC

Thus, for αcathode ~14 x 10-6 /oC, for the chosen values, the cellwill be flat at room temperature.

R2 = 0.9994

-0.3-0.25

-0.2-0.15

-0.1-0.05

00.05

0.1

9.00E-06

1.00E-05

1.10E-05

1.20E-05

1.30E-05

1.40E-05

1.50E-05

1.60E-05

Coeff. of thermal expansion for cathode /oC

Dis

plac

emen

t in

Y di

rect

ion

in

mm

FlatCellanode

cathode

102

Topic 6: Cell FabricationCell fabrication by tape-casting followed by sintering is described in thissection. This is probably the most common method of cell fabrication,although there likely are significant differences among developers insofar asthe details are concerned. What is described is one of the approaches, and byno means the only approach. Also, it is to be emphasized that many details and variations from the process described here that are actually implemented inour process, are not given due to the proprietary nature of the work.

103

Cell Fabrication Steps

1) Raw materials and formulation2) Tape casting the anode support, cutting to desired size3) Applying the anode functional layer4) Applying the electrolyte5) Bisquing to ~1000oC for binder burnout 6) Application of the electrolyte layer7) Sintering (1300 to 1500oC)8) Applying the cathode functional layer9) Applying the cathode current collector layer10) Firing at ~1200oC

Processes have been developed for co-sintering the complete cell in a singlehigh temperature step

104

Topic 7: Cell Testing1) Button size cells (typical cathode area of 1 to 2 cm2) are typically tested for

general cell characterization.2) Cells are tested under flooded conditions (high flow rates for both fuel and

oxidant) – thus during such tests, fuel and oxidant utilizations are very small. In such cases, the measured parameters correspond to a given set of fuel and oxidant utilization (depending upon gas compositions).

3) Cell is secured (using either glass or compression seals) in a test fixture, placed inside a furnace.

4) Cell is heated to ~700oC, and a mixture of H2 + N2 is passed over anode to reduce NiO to Ni – leads to the creation of porosity. Then the fuel is passed over the anode (H2 + H2O mixtures), and air (or O2 + N2 mixtures).

5) An electronic load box and/or a resistor box is used for testing.6) Voltage vs. current data are collected. Usually, voltage (y-axis) is plotted

vs. current density (x-axis). 7) Using a fast response electrochemical measuring instrument, sudden change

in voltage that occurs immediately after interrupting the current is measured. This gives a measure of the ohmic contribution from the cell.

105

A Test Fixture for Testing Button Cells

Air

Single Cell

Current Collector

Seal Al2O3 Tube

Out

A

V

Silver Wire

Silver Wire

106

Current Interruption

Ohmic Contribution = ∆V

Electrode Processes (slow)50 µs

iVRi

∆=Ohmic Area Specific Resistance Ωcm2

An oscilloscope trace

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.00

20

40

60

80

100

120

140

160

180

200

Mea

sure

d oh

mic

vol

tage

dro

p (m

V)

Current density (A/cm2)

2cm 103.0 Ω≈iRSlope

107

Effect of Various Cell Parameters on Performance

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.2

0.4

0.6

0.8

1.0

1.2


Vol

tage

(V)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4



Power D

ensity (W/cm

2)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2


Vol

tage

(V)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Electrolyte thickness: 4 µm 8 µm 15 µm 20 µm

800 oCAnode Support Thickness: 1.0 mmAnode Support Porosity: 48 vol%Cathode Interlayer: 20 µm

Power D

ensity (W/cm

2)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00.0

0.2

0.4

0.6

0.8

1.0

1.2




Vol

tage

(V)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Power D

ensity (W/cm

2)

Anode Support Porosity Varied

Electrolyte Thickness Varied Anode Support Thickness Varied

The phenomenological equation statedearlier can be used to fit to the data. Some of the parameters can be obtained through separate, out of cell, measurements.

108

Summary Statements

• I have tried to give some material on fundamental concepts for designing high performance, robust cells.The material given here is by no means complete. It is hoped that this might be useful as a starting point for someone interested in the subject. There are numerous articles in the literature one should read for further learning.

materials challenges in solid oxide fuel cells1 materials challenges in solid oxide fuel cells anil...

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