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Lecture Notes III Oxygen ion conducting

ceramics

Oxygen senors

Fuel Cells

Oxygen pumps

Heating elements

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Oxygen ion conductors:

defect reactions

[1]

[2]

[3]

[4]

[5]

[6]

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Defect concentrations – p(O2)

Regions in Brouwer plot:

Neutrality conditions:

p + 2[VO••] = n + 2[Oi

″] + [MfM′]

n = 2[VO••]

[MfM′] = 2[VO

••]p = [MfM

′]p = 2[Oi

″]

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Calculation for region n = 2[VO

••]

Eq. 2: K(VO

••) = [VO••] n2 p(O2)1/2 ;

[VO••] prop. to p(O2)-1/6 ; n prop. to p(O2)-1/6

Eq. 5:Ki = n pp prop. to p(O2) +1/6

Eq. 4:KAF = [Oi

″] [VO••]

[Oi″] prop. to p(O2)+1/6

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Oxygen ion conductors: Brouwer plot

n-conductor p-conductor

Ion conductor

low pressure high pressure

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Conductivity plot

Transport number: ti + tn + tp = 1

ti = 1

σtotal = σion+ σn+ σp

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Influence of temperature

Conductvity: ionic and n and p conduction

Domain boundaries

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Total conductivity

σtotal = σion + σn + σp

σtotal = 2e[VO••](VO••) + enn + epp

Transport numbers: tion+ tn+ tp = 1

Note: mobility of electronic defects much bigger than for ions

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Dependence on temperatureBoth carrier concentration and mobility are thermally activated.

Arrhenius equation describe tthe temperature dependenceof both ionic and electronic conduction:

σ = σ0exp(-Q/kT)*Where:σ0 factor depending on temperature,Q activation energyk Boltzmann constantT absolute temperature

*correct formula is: σ T = σ0exp(-Q/kT)

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Typical oxygen conductors

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Influence of temperature on domain boundaries

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Domain boundaries of stabilized zirconia

Ionic domain

Pp

Pn

P0

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Practice:Calculate oxygen ion conductivity

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Answers to practice:Calculate oxygen ion conductiviy

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What determine the ionic condutivity

Several factors are important:- Host oxide- Type and concentration of dopant;- Temperature;

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Host Oxides/dopantsFluorite Oxides – structure fcc (face centered cubic)

Examples: ZrO2, ThO2, CeO2 doped with Y2O3, CaO

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Free defects vs bound defects

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Activation energy for conduction of free defects

σion T = C [VO••] exp ( - ΔHm/kT)

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Activation energies for conduction of bound defects

Dopants with +3 cations, e.g. Y3+, in host with +4 cations, e.g. ZrO2

Defect cluster: (YZr′ VO

••)•

σionT = C exp (- (ΔHm + ΔH(A•))/kT)

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Activation energy for conduction of bound defects

Dopants with +2 cations, e.g. Ca2+, in host with +4 cations, e.g. ZrO2

Defect cluster: (CaZr″ VO

••)x

σionT = CM1/2 C1 exp((- (ΔHm+ ΔH(Ax)/2)/kT)

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Comparison of activation energies for free and bound defects

Free defects ΔHm

(CaZr″ VO

••)x ΔHm + ΔH(Ax)/2

(YZr′ VO

•• )• ΔHm + ΔH(A•)

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Binding energies of defect clusters

M2O3 - dopants

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Dependence on defect concentrations

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Conductivity data: Ce(Y)O2-x

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Conductivity data: Ce(Ca)O2-x

High temperatures

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Conductivity data for Ce(Ca)O2-xLow temperatures – 500 K

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Practice

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Answers to practice

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