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Lecture Notes III Oxygen ion conducting ceramics

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 ′ ].

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Lecture Notes III Oxygen ion conducting ceramics

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  1. Lecture Notes III Oxygen ion conducting ceramics Oxygen senors Fuel Cells Oxygen pumps Heating elements

  2. Oxygen ion conductors:defect reactions [1] [2] [3] [4] [5] [6]

  3. Defect concentrations – p(O2) Neutrality conditions: p + 2[VO••] = n + 2[Oi″] + [MfM′] Regions in Brouwer plot: n = 2[VO••] [MfM′] = 2[VO••] p = [MfM′] p = 2[Oi″]

  4. 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 p p prop. to p(O2) +1/6 Eq. 4: KAF = [Oi″] [VO••] [Oi″] prop. to p(O2)+1/6

  5. Oxygen ion conductors: Brouwer plot high pressure low pressure Ion conductor n-conductor p-conductor

  6. Conductivity plot σtotal = σion+ σn+ σp ti = 1 Transport number: ti + tn + tp = 1

  7. Influence of temperature Conductvity: ionic and n and p conduction Domain boundaries

  8. Total conductivity σtotal = σion + σn + σp σtotal = 2e[VO••](VO••) + enn + epp Note: mobility of electronic defects much bigger than for ions Transport numbers: tion+ tn+ tp = 1

  9. Dependence on temperature Both carrier concentration and mobility are thermally activated. Arrhenius equation describe tthe temperature dependence of both ionic and electronic conduction: σ = σ0exp(-Q/kT)* Where: σ0 factor depending on temperature,Q activation energy k Boltzmann constant T absolute temperature *correct formula is: σ T = σ0exp(-Q/kT)

  10. Typical oxygen conductors

  11. Influence of temperature on domain boundaries

  12. Domain boundaries of stabilized zirconia Pp Ionic domain P0 Pn

  13. Practice:Calculate oxygen ion conductivity

  14. Answers to practice:Calculate oxygen ion conductiviy

  15. What determine the ionic condutivity • Several factors are important: • Host oxide • Type and concentration of dopant; • Temperature;

  16. Host Oxides/dopants Fluorite Oxides – structure fcc (face centered cubic) Examples: ZrO2, ThO2, CeO2 doped with Y2O3, CaO

  17. Free defects vs bound defects

  18. Activation energy for conduction of free defects σion T = C [VO••] exp ( - ΔHm/kT)

  19. 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)

  20. 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)

  21. Comparison of activation energies for free and bound defects Free defects ΔHm (CaZr″ VO••)x ΔHm + ΔH(Ax)/2 (YZr′ VO•• )•ΔHm + ΔH(A•)

  22. Binding energies of defect clusters M2O3 - dopants

  23. Dependence on defect concentrations

  24. Conductivity data: Ce(Y)O2-x

  25. Conductivity data: Ce(Ca)O2-x High temperatures

  26. Conductivity data for Ce(Ca)O2-x Low temperatures – 500 K

  27. Practice

  28. Answers to practice

  29. Content

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