1. Transport
Zuoan Li
NorFERM-2008

2. Outline Diffusion basis ▲ Diffusion mechanism
▲ Mathematics of diffusion
▲ D vs. T
Diffusion in electric gradient (conductivity)
Transport in electrochemical gradient

3. Diffusion
Cu-Ni diffusion couple
Before
heat treatment
After

4. Diffusion Mechanism
Vacancy diffusion

5. Interstitial diffusion

6. Interstitialcy diffusion
Collinear jump

7. Free transport mechanism (Grotthuss mechanism)
Proton diffusion
Vehicle mechanism
Free transport mechanism (Grotthuss mechanism)

8. BaCeO3
Kreur, Annu. Rev. Mater. Res. 2003

9. Mathematics of diffusion J: flux of particles across plane with area A
Fick’s 1st law c x A
J: flux of particles across plane with area A

10. Fick’s 2nd law

11. Solution to Fick’s 2nd law
Thin film
Thin layer of radioactive isotopes is located at x=0 of a semi-infinite sample (self-exhausting source).
Boundary conditions:
Concentration after time t:

12. Deposition
Annealing
Cutting

13. Error function
The concentration of tracer at x=0 is kept constant after diffusion (non-exhausting source).
Boundary conditions:
Concentration after time t:

14. O18 depth profile

15. Activation energy of diffusion coefficient
Random diffusion:
frequency of successful jumps
: probability that jump can overcome energy barrier
: probability of site being ready for jump

16. DHm

17. : probability of site for jump
Vacancy
Interstitial
Defects
Interstitial solute
Constituents
T, defect structure, and pO2

18. ci Di Defects Constituents
small & variable
large & constant
Constituents

19. Constant or frozen vacancy
Vacancy diffusion in elemental solids or
Constant or frozen vacancy

20. Predominant oxygen vacancy (MaOb-d) Constant oxygen vacancy
Vacancy diffusion in oxides
Predominant oxygen vacancy (MaOb-d)
Constant oxygen vacancy

21. Jump depends on oxygen-oxygen distance
Protons
Rotation is easy
Jump depends on oxygen-oxygen distance
Large soft lattices

22. H/D isotope effects
Classical effects:
Non-classical effects:

23. Electrical potential gradient
Transport
Electrical potential gradient

24. Nernst-Einstein relationship
Activation energy

25. Conductivity
Solid ionic conductor

26. Electronic conductivity
Intrinsic semiconductor
Intrinsic ionization

27. Extrinsic semiconductor (n-type)
Low temperature
Log n
1/T, K
Intermediate temperature
High temperature
intrinsic

28. Non-stoichiometric semiconductor
Defect equilibrium, T, P

29. un & up
Magnitude
Non-polar solids
Polar oxides

30. Electrochemical potential gradient
Transport
Electrochemical potential gradient

31. Voltage over a sample Neutral form itot= 0 → transport number (EMF)
itot≠ 0 → fuel cell

32. Flux of a specific species
Steady state

33. Some diffusion terms Self diffusion Tracer diffusion Defect diffusion
Chemical diffusion
Ambipolar diffusion

34. Nonstoichiometric (defects)
Defect Chemistry
Summary
Intrinsic (n=p)
Extrinsic (n≠p)
Nonstoichiometric (defects)

35. Thank you for your attention!
Organization committee
Thank you for your attention!