lecture notes iii oxygen ion conducting ceramics
DESCRIPTION
Lecture Notes III Oxygen ion conducting ceramics. Oxygen senors Fuel Cells Oxygen pumps Heating elements. Oxygen ion conductors: defect reactions. [1]. [2]. [3]. [4]. [5]. [6]. Defect concentrations – p(O 2 ). Neutrality conditions:. p + 2[V O •• ] = n + 2[O i ″ ] + [Mf M ′ ]. - PowerPoint PPT PresentationTRANSCRIPT
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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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Content