Purpose of this talk

1. Purpose of this talk Diffusion Ronald Griessen ACTS workshop May 24, 2007

2. Water droplet

3. Waves Wave equation

4. Diffusion

5. Fick’s law Equation of continuity J dx C(x,t)

6. Singularities decay immediately is a solution of

7. Diffusion in semi-infinite space

8. Diffusion into a membrane of thickness L

9. Hydrogen near a metal surface, for example Pd

10. Diffusion coefficients of various interstitials H in Nb

11. Diffusion coefficients of various interstitials

12. Cu Pd Y Pd

13. Cu Pd

14. Cu Pd Cu Pd

15. Cu Pd Cu Y Pd Y

16. Cu Pd Cu Y Pd Y

17. Cu Pd Cu Y Pd Pd

18. Fast H diffusion in bcc Pd-Cu Y Pd Cu Pd

19. Fast H diffusion in bcc Pd-Cu Temperature oC Cu atomic percent palladium

20. Diffusion coefficients of various interstitials

21. Fick’s law Equation of continuity ? ? dx Is this true Is this true

22. P-c isotherms and phase diagram

23. Fick’s law Equation of continuity dx ?

24. A real diffusion experiment

25. Pressure-composition isotherm of YHx at T=293 K Kooij et al. 1999

26. H Hydrogenography in Yttrium Y2O3 Pd Y Den Broeder, van der Molen et al, Nature 394 (1998) 656

27. 3 g hcp- H/Y g hcp- 2 b metal insulator 1 a 0

28. 3 g hcp- H/Y g hcp- 2 b metal insulator 1 a 0

30. This picture demonstrates that instead of

31. Switchable mirrors as indicators H Y2O3 Pd Y V SiO2

32. Sample architecture SiO2 V V

33. Sample architecture Pd 10 nm Y 50 nm SiO2 V V

34. Hydrogen loading Pd Y SiO2 V V H x=0 x

35. H-loading: 473K, 1mbar, 3h Pd x=0 10 mm dV 25 nm 50 nm 75 nm 100 nm 125 nm YH2 front x

36. Diffusion in a multilayer The chemical potential MUST be continuous The concentration MAY have discontinuities

37. ? Usual diffusion Real diffusion

38. Particles in a lattice gas X

39. Usual diffusion Real diffusion However, the chemical potential MUST be continuous

40. Ni Ni Mg Mg Ti Ti

41. c = c(x,t) cH = f(t) Ni Ni Mg Mg Ti Ti

42. c = c(x,t) cH = f(t) Ni Ni Mg Fast loading, Very slow unloading Mg Ti Ti Relatively slow loading, Very fast unloading

43. Diffusion and Snell’s law

45. Random walk of a photon With vthe velocity of light athe absorption coefficient

46. The aquarium experiment So

47. O’Leary et al., Phys. Rev. Lett. 69 (1992) 2658

48. Sample architecture Y 50 nm V 250 nm SiO2 V 50 nm Pd 10 nm

49. Hydrogen loading 32 min 1 bar 373 K V 250 nm V 50 nm YH2 YH3 Pd

50. 110 min 1 bar 373 K YH2 YH3 Pd