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### Oxygen Ion Conductors: Theory, Applications, and Conductivity Analysis ###

This lecture explores the intricate workings of oxygen ion conducting ceramics, essential for various applications including oxygen sensors, fuel cells, oxygen pumps, and heating elements. We delve into defect reactions, concentrations, and the conditions of neutrality that govern ionic conductivity. Key topics include the influence of temperature on defect mobilities, Brouwer plots for conductivity assessment, and the calculation of oxygen ion conductivity. Discussion on typical oxygen conductors, factors influencing ionic conductivity, and practical exercises are also included to enhance understanding. ###

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### Oxygen Ion Conductors: Theory, Applications, and Conductivity Analysis ###

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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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