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Zr 0.85 Ca 0.15 O 1.85

The Nernst-Einstein equation indicates that the ratio β /D for a given material varies only with temperature. Calculate β /D for oxygen ions in Zr 0.8 Y 0.2 O 1.9 at 800°C.

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Zr 0.85 Ca 0.15 O 1.85

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  1. The Nernst-Einstein equation indicates that the ratio β /D for a given material variesonly with temperature. Calculate β/D for oxygen ions in Zr0.8Y0.2O1.9 at 800°C.

  2. The Nernst-Einstein equation indicates that the ratio β /D for a given material variesonly with temperature. Calculate β/D for oxygen ions in Zr0.8Y0.2O1.9 at 800°C.

  3. Simpson and Carter (J. Am. Ceram. Soc. 49 (1966) 139) measured the self diffusion coefficient for oxygen in Zr0.85Ca0.15O1.85 and found it to be DO = 2.0·10-7 cm2/s at 1100°C. Calculate the electrical mobility and conductivity of oxygen ions based on this. Assume density of Zr0.85Ca0.15O1.85 5.7g/cm3 and molecular weight 113.15g/mole.

  4. O O O O O O Zr Zr Zr Zr Zr Zr O O O O Zr O Zr Zr Zr Zr Zr O O O O O Zr Zr Zr Zr Zr Zr O O O O O O Zr Zr Zr Zr Zr Zr O O O O O O Zr Ca Zr Zr ZrO2 Ca Zr O O O O O O Zr Zr Zr Zr Zr Zr Zr0.85Ca0.15O1.85 O O O Zr Zr Zr O O O Zr Zr Zr O O O Zr Zr Zr O O Zr Zr Zr O O O Zr Ca Zr O O O Zr Zr Zr SI

  5. Simpson and Carter (J. Am. Ceram. Soc. 49 (1966) 139) measured the self diffusion coefficient for oxygen in Zr0.85Ca0.15O1.85 and found it to be DO = 2.0·10-7 cm2/s at 1100°C. Calculate the electrical mobility and conductivity of oxygen ions based on this. Assume density of Zr0.85Ca0.15O1.85 5.7g/cm3.

  6. Electrical conductivity Zahl der Zr0.85Ca0.15O1.85-Einheiten per m3

  7. For intrinsic silicon, the room-temperature electrical conductivity is 410-4 Ω-1m-1; the electron and hole mobilities are, respectively, 0.14 and 0.048 m2V-1s-1. Compute the electron and hole concentrations at room temperature.

  8. Solution: For intrinsic silicon, the room-temperature electrical conductivity is 410-4 Ω-1m-1; the electron and hole mobilities are, respectively, 0.14 and 0.048 m2V-1s-1. Compute the electron and hole concentrations at room temperature.

  9. Calculate concentration of the charge carriers in intrinsic Si in a function of temperature. (mole fractions) Temperature dependence: Eg=1.14 eV energy gap, k=8.63∙10-5 eV/K

  10. Intrinsic Silicon (mole fractions) Temperature dependence: Eg=1.14 eV energy gap, k=8.63∙10-5 eV/K

  11. Zr(Y) O Fluoritstruktur (CaF2-Typ) What is the number of the oxygen vacancies in the unit cell of Zr0.8Y0.2O1.9? Assuming the lattice parameter of (cubic) YSZ is 0.54 nm, calculate a concentration of the oxygen vacancies (number per m3).

  12. Zr(Y) O Fluoritstruktur (CaF2-Typ) In Zr0.8Y0.2O1.9, how many oxygen vacancies are there per unit cell? If the lattice parameter of (cubic) YSZ is 0.54 nm, calculate the density of vacancies (number per m3) Formula VO per unit cell Vc =0.543∙10-27m3

  13. Defektkonzentration n/N0 bei verschiedenen Temperaturen

  14. Write the Kröger-Vink notation for the following fully charged species in MgO: • Cation and anion on their normal sites • Oxygen vacancy • Magnesium vacancy • Interstitial magnesium ion

  15. Write the Kröger-Vink notation for the following species in ZrO2: • Cation and anion on their normal sites • Oxygen vacancy • Zirkonium vacancy • Yttrium dopant substituting Zr • Nitrogen ion (N3-) substituting for oxygen ion • Write the Kröger-Vink notation for the following fully charged species in CaTiO3: • Calcium vacancies • Titanium vacances • Oxygen vacances • Ti ions on Ca sites and vice versa • Ti interstitials

  16. Write the Kröger-Vink notation for the following species in ZrO2: • Cation and anion on their normal sites • Oxygen vacancy • Zirkonium vacancy • Yttrium dopant substituting Zr • Nitrogen ion (N3-) sobstituting for oxygen ion • Write the Kröger-Vink notation for the following fully charged species in CaTiO3: • Calcium vacancies • Titanium vacances • Oxygen vacances • Ti ions on Ca sites and vice versa • Ti interstitials

  17. Write the electroneutrality condition for defects in silicon : • pure • boron-doped • phosphorous-doped

  18. Write the electroneutrality condition for MO1-x Write the electroneutrality condition for MO1+x (oxygen interstitial sites) Write the electroneutrality condition for M1-xO Write the electroneutrality condition for M1+xO (metal interstitial sites) 18

  19. Write the electroneutrality condition for MO1-x

  20. Write the electroneutrality condition for MO1+x (oxygen interstitial sites)

  21. Write the electroneutrality condition for M1-xO

  22. Write the electroneutrality condition for M1+xO (metal interstitial sites)

  23. At a certain temperature T and oxygen partial pressure 10-9 atm, concentration of oxygen vacancies is 10-3. Make a plot showing dependence of point defects concentration ( ) on oxygen partial pressure at T. Identify the charge carriers and regions of intrinsic and extrinsic conductivity. , and Metal oxide MeO2 is doped with Mf2O3 at the doping level

  24. -1/6 -1/4 0 extrinsic intrinsic Brouwer (Patterson)-Diagramm T=const

  25. Cobalt oxide: The electronic conductivity of Co1-yO at 1350°C and pO2 = 0.1 atm is 25 S/cm. Thermogravimetric measurements show that y = 0.008 under the same conditions. It is assumed that singly charged cobalt vacancies are the dominating point defects. Identify the charge carriers responsible for the conductivity and calculate their charge mobility. (Assume that the density of CoO at 1350°C equals that at room temperature, 6.4 g/cm3. Atomic weights MCo = 58.93; MO = 16.00; q=1.6∙10-19 C) Platzverhältnis Die Anzahl an Kationenplätzen (K) einer Verbindung KxAy muss immer im richtigen Verhältnis zur Anzahl der Anionenplätze (A) stehen

  26. Holes mobility

  27. Nickel oxide: Assume that doubly charged nickel vacancies and holes are the dominating defects in Ni1-yO under oxidising conditions. At 1245°C and pO2 = 1 atm we know the following for the compound: The self diffusion coefficient for nickel: DNi = 9∙10-11 cm2/s Electrical conductivity: σ = 1.4 S/cm (Data from M.L. Volpe and J. Reddy, J. Chem. Phys., 53 (1970) 1117) Nickel vacancy concentration, in site or mole fraction: [VNi’’] = 2.510-4 (Data from W.C. Tripp and N.M. Tallan, J. Am. Ceram. Soc., 53 (1970) 531) (Atomic weights MNi = 58.71, MO = 16.00, density of NiO = 6.67 g/cm3) a) Calculate the charge mobility of the nickel vacancies and the ionic conductivity under the conditions referred to above (Nernst-Einstein Gleichung) b) Calculate the concentration of electron holes under the given conditions, given as site fraction and as volume concentration ( number/m3). c) Calculate the charge mobility of the holes. q=1.6∙10-19 C k=1.38∙10-23 J/K

  28. Nernst-Einstein Point „a“

  29. are not dominating carriers a) nickel vacancies Compare the obtained value with σ = 1.4 S/cm =140 S/m

  30. b) holes site fraction Volume concentration

  31. c) holes σ for nickel vacances

  32. 1. Calculate EMF (EMK) at 500 and 1100K for fuel cells in which Methane (CH4) or Hydrogen is used as a fuel. Assume that the partial pressures of all the gaseous reactants are equal 1 bar (pure oxygen at the cathode!). 2. Calculate what will be change of EMF at 1100K in the case of CH4 fuel, assuming total pressure of the gases at both the electrodes 1 bar (pure oxygen at the cathode!) and composition at anode 50%H2O, 25%CO2 and 25%CH4. I. Barin, O. Knacke, „Thermochemical properties of inorganic substances“, Springer-Verlag, 1973

  33. 500K G=-80.965-(-15.996)-0.5·(-24.910)=-52.514 kcal/mol -52.514·1000·4.184=-219719 J/mol E=-(-219719)/(2·96486)=1.139V -187816 J/mol -44.889 kcal/mol 1100K 0.973V ½ O2 + H2  H2O Anode: O2- + H2  H2O + 2e- Kathode: ½ O2 + 2e-  O2-

  34. 2O2 + CH4  2H2O+CO2 Anode: 4O2- + CH4  2H2O + CO2+8e- Kathode: 2O2 + 8e-  4O2- 1100K G =-801864 J/mol Eo=-(-801864)/(8·96486)=1.039V V

  35. n-type n p On the diagram show the doping regions for intrinsic and doped silicon at room temperature. (mole fractions)

  36. Doped silicon • 1. Phosphorus is added to high-purity silicon to give a concentration of 1023m-3 of charge carriers at room temperature. • Is the material n-type or p-type? • Calculate the room-temperature conductivity of this material, assuming that electron and hole mobilities (respectively, 0.14 and 0.048 m2V-1s-1) are the same as for the intrinsic material Density of Si 2.33 g/cm3; molecular weight 28.09 g/mol (mole fractions) q=1.6∙10-19 C

  37. 1. a) Phosphorus- V group, will act as a donor in silicon b) 1023 m-3 electron concentration is greater than that for the intrinsic case (mole fractions)

  38. Doped silicon • 2. The room-temperature conductivity of intrinsic silicon is 410-4 Ω-1m-1. An extrinsic n-type silicon material is desired having a room-temperature conductivity of 150 Ω-1m-1. • a) Specify a donor element type that may be used and its concentration in atom percent. • b) Calculate the equilibrium hole concentration • Assume that electron and hole mobilities (respectively, 0.14 and 0.048 m2V-1s-1) are the same as for the intrinsic material, and that at room temperature the donor atoms are already ionized. • Density of Si 2.33 g/cm3, molecular weight 28.09 g/mol. (mole fractions) Eg=1.14 eV, k=8.63∙10-5 eV/K

  39. 2. a) P, As, Sb

  40. 2. b)

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