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

2. Water droplet

3. Wave equation Waves

4. Diffusion

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

6. is a solution of Singularities decay immediately

7. Diffusion in semi-infinite space

8. Front at concentration c=10 -20 m -1 The velocity of light is reached at t = 5  10 -25 s if D=10 -8 m 2 /s. The jump time is, however, with a=0.1 nm Infinite diffusion :a little numerical exercise

9. Diffusion into a membrane of thickness L

10. Hydrogen near a metal surface, for example Pd

11. H in Nb Diffusion coefficients of various interstitials

13. Pd Cu Y Pd

14. Cu

15. Pd Cu Pd Cu

16. Pd Cu Y Pd Cu Y

17. Pd Cu Y Pd Cu Y

18. Pd Cu Pd Cu Pd Y

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

20. Cu atomic percent palladium Temperature o C

21. Diffusion coefficients of various interstitials

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

23. P-c isotherms and phase diagram

24. Fick’s law Equation of continuity dx ?

25. A real diffusion experiment

26. Kooij et al. 1999 Pressure-composition isotherm of YH x at T=293 K

27. Hydrogenography in Yttrium Den Broeder, van der Molen et al, Nature 394 (1998) 656 Y Y2O3Y2O3 Pd H

28. 1 H/Y 0 2 3  hcp- insulator  hcp- metal  

29. 1 H/Y 0 2 3  hcp- insulator  hcp- metal  

31. This picture demonstrates that instead of

32. Influence of the chemical factor

33. Y2O3Y2O3 Pd Y SiO 2 H V Switchable mirrors as indicators

34. SiO 2 VV Sample architecture

35. Pd 10 nm Y 50 nm SiO 2 VV Sample architecture

36. H Pd Y SiO 2 VV x x=0 Hydrogen loading

37. d V 25 nm 50 nm 75 nm 100 nm 125 nm 10 mm Pd YH 2 front x=0 x H-loading: 473K, 1mbar, 3h

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

39. Usual diffusion Real diffusion ?

40. Particles in a lattice gas X

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

42. Ds_1=0.1;%surface layer diffusion coefficient Ds_2=0.1; Ds=Ds_1; D1=0.1;%Ni NB 1 equals 10-5 cm^2/sc D2=0.1;%0.1Mg2Ni e1=-10;%0 Ni e2=-10;% -18Mg2Ni stmu_1=-2;% -5applied mu at top boundary START VALUE stmu_2=-20;% -5applied mu at top boundary ALTERNATIVE VALUE sizex=50; %sample length sizey=1; %DO NOT CHANGE this simulation is 1D t_surf=10;%thickness of surface layer trans=35;%position of boundary between two halfs must be >t_surf+2

43. Ds_1=0.1;%surface layer diffusion coefficient Ds_2=0.1; Ds=Ds_1; D1=0.1;%Ni NB 1 equals 10-5 cm^2/sc D2=0.1;%0.1Mg2Ni e1=-0;%0 Ni e2=-10;% -18Mg2Ni stmu_1=-2;% -5applied mu at top boundary START VALUE stmu_2=-20;% -5applied mu at top boundary ALTERNATIVE VALUE sizex=50; %sample length sizey=1; %DO NOT CHANGE this simulation is 1D t_surf=10;%thickness of surface layer trans=35;%position of boundary between two halfs must be >t_surf+2

44. Ds_1=0.1;%surface layer diffusion coefficient Ds_2=0.1; Ds=Ds_1; D1=0.1;%Ni NB 1 equals 10-5 cm^2/sc D2=0.1;%0.1Mg2Ni e1=-0;%0 Ni e2=-10;% -18Mg2Ni stmu_1=-2;% -5applied mu at top boundary START VALUE stmu_2=-20;% -5applied mu at top boundary ALTERNATIVE VALUE sizex=50; %sample length sizey=1; %DO NOT CHANGE this simulation is 1D t_surf=10;%thickness of surface layer trans=35;%position of boundary between two halfs must be >t_surf+2

45. Ds_1=0.1;%surface layer diffusion coefficient Ds_2=0.1; Ds=Ds_1; D1=0.1;%Ni NB 1 equals 10-5 cm^2/sc D2=0.1;%0.1Mg2Ni e1=-15;%0 Ni e2=-10;% -18Mg2Ni stmu_1=-2;% -5applied mu at top boundary START VALUE stmu_2=-20;% -5applied mu at top boundary ALTERNATIVE VALUE sizex=50; %sample length sizey=1; %DO NOT CHANGE this simulation is 1D t_surf=10;%thickness of surface layer trans=35;%position of boundary between two halfs must be >t_surf+2

46. K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Rb Sr Y Zr Nb Mo Tc Ru RhPd Ag Cd Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Heat of solution of metal-hydrides

47. Ni Ti Ni Ti Mg

48. Ni Ti Ni Ti Mg c = c(x,t)c H = f(t)

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

50. Ni-Mg bilayer c = c(x,t)c H = f(t)  =  (x,t) Fast loading, Very slow unloading

51. Ti-Mg bilayer Ds_1=0.1;%surface layer diffusion coefficient Ds_2=0.1; Ds=Ds_1; D1=0.1;%Ni NB 1 equals 10-5 cm^2/sc D2=0.1;%0.1Mg2Ni e1=-15;%0 Ni e2=-10;% -18Mg2Ni stmu_1=-2;% -5applied mu at top boundary START VALUE stmu_2=-20;% -5applied mu at top boundary ALTERNATIVE VALUE sizex=50; %sample length sizey=1; %DO NOT CHANGE this simulation is 1D t_surf=10;%thickness of surface layer trans=35;%position of boundary between two halfs must be >t_surf+2 c = c(x,t)c H = f(t)  =  (x,t) Relatively slow loading, Very fast unloading

52. Diffusion and Snell’s law

54. Random walk of a photon With v the velocity of light  a the absorption coefficient

55. SoSo The aquarium experiment

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

57. SiO 2 Pd 10 nm V 50 nm V 250 nm Y 50 nm Sample architecture

58. YH 2 YH 3 Pd 32 min 1 bar 373 K V 50 nm V 250 nm Hydrogen loading

59. YH 2 YH 3 Pd 110 min 1 bar 373 K

60. YH 2 YH 3 Pd 216 min 1 bar 373 K

61. YH 2 YH 3 Pd 442 min 1 bar 373 K

62. 2’32’55’110’216’332’442’90’ Time evolution of contours

63. Ray tracing along the phase – gradient at small angles A.Remhof, R. J. Wijngaarden, and B.R. Griessen, Refraction and reflection of diffusion fronts, C.Phys. Rev. Lett., 90 (2003) 145502 Snell’s law for diffusion !

64. Electromigration

65. In presence of an electric field

66. Usual diffusion Real electro-diffusion

67. Electromigration Electric field ONElectric field OFF

68. Electromigration of H in V Electric field ONElectric field OFF

69. Electromigration Den Broeder, van der Molen et al. Nature 394 (1998) 656 Pd Y Y2O3Y2O3 H H

70. Electro-diffusion of hydrogen in yttrium Den Broeder, van der Molen et al. Nature 394 (1998) 656 Pd Y Y2O3Y2O3 j=0 j=20 mA j=40 mA + _ H behaves like a negative ion H H