1. Diffusion Chapter 5

2. Mechanics of Diffusion Primary method by which atoms mix Consider a drop of food coloring in a glass of water

3. Atoms are always in motion Bulk motion Random motion of individual atoms Vibration

4. Where does Diffusion Occur in Crystals? Through Interstitial Spaces At Defects Point Defects  Such as a vacancy Line Defects  Dislocations Surface Defects  Grain boundaries  Material surface Diffusion through defects is the primary form of diffusion in crystals Diffusion is slow in solids

5. Interstitial Diffusion There are holes between the atoms in the matrix If the atoms are small enough, they can diffuse through the interstitial holes Fast!!

12. If the interstitial atom is large, it has a harder time fitting through the spaces between the lattice atoms If its harder to do – it happens more slowly

13. Vacancy Diffusion Vacancies are holes in the crystal lattice All real materials have vacancies Vacancies are always moving An impurity can move into the vacancy Diffuse through the material

14. Vacancy Diffusion http://www.soton.ac.uk/~engmats/xtal/diffusion/diffusion.htm

15. Vacancy Diffusion

18. The vacancies appear to move, but of course it is really individual atoms just moving one position each

19. Diffusion along dislocations Notice the extra room available for atoms to squeeze through

20. Volume Diffusion Interstitial diffusion Vacancy diffusion Diffusion along dislocations Volume diffusion is the slowest of the types of diffusion we’ll study It is difficult to separate the effect of each of the types of volume diffusion from each other

21. Grain Boundary http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_2/backbone/r2_2_2.html You can affect the number of grains, and thus the total grain boundary area, by controlling the material processing

22. Surface Diffusion Surface diffusion occurs the most readily of the diffusion types

23. Activation Energy All the kinds of diffusion require a certain minimum energy to occur Called the activation energy The higher the activation energy, the harder it is for diffusion to occur

24. Activation Energy

25. Future state State now Activation Energy Activation energy is the amount required to get “over the hump” – whichever way you are going on the energy hill It’s the energy required to squeeze through a hole or to escape a position at one lattice point and move into another

26. Activation Energy The highest energy is for volume diffusion Vacancy Interstitial Grain Boundary diffusion requires less energy Surface Diffusion requires the least

27. Volume Diffusion Grain Boundary Diffusion Surface Diffusion Diffusion Activation Energy

28. Diffusion Rate High activation energy corresponds to low diffusion rates D = D 0 *exp(-Q/RT) Where D is the diffusivity, which is proportional to the diffusion rate Q is the activation energy R is the gas constant T is the absolute temperature Notice that the diffusivity increases, as the temperature increases This relationship is called the Arrhenius equation, and is seen regularly in chemistry and physics for a variety of processes

29. Fick’s First Law Diffusion is very similar to heat transfer Equations are the same Fick’s first law describes steady state diffusion J = - D (  C/  x)  J is the the rate of diffusion in atoms/area/time – called the flux  D is the diffusivity  C is the concentration  X is the distance

30. Steady state diffusion is rare in solids It takes a very long time for equilibrium to be established Can occur in very thin foils or polymeric membranes For example, the flow of small gas molecules through a membrane

31. Diffusivity Remember that D is a function of temperature Thus the flux (J) is also a function of temperature The flux goes up as the temperature goes up

32. Effect of Crystal Structure on Diffusion When all other things are equal, the rate of diffusion is higher in a BCC structure than in an FCC or HCP structure There is more open space in the BCC structure than the FCC structure

33. Low Temperature High Temperature Phase Change BCC FCC 910 0 C K -1 Iron Carbon

34. Fick’s Second Law Describes Transient Diffusion Non steady state Because diffusion in solids is slow, diffusion is almost always transient!

35. Carburizing Case Hardening Steel is sometimes surface hardened, by diffusing Carbon in from the surface The interior portion of the metal remains more ductile while the surface is hard and resistant to wear

36. Carburizing is a surface treatment – dependent on unsteady state diffusion

37. Planar Surface Solution

38. Planar Surface Unsteady State Diffusion Diffusion Direction CsCs C0C0 CxCx x

39. Error Function Integral of the Gaussian Curve The error function is part of one of the solutions to the second order partial differential equation, that describes non-steady state diffusion

40. Practically, you don’t really need to know how the error function works, just like you don’t need to know how sin is calculated to use it. Erf is not on most calculators – it is in Maple and MATLAB Need a table

41. Erf Values of Z and the erf of Z can be found in text books and on your CD

42. Error Function Table Zerf(Z) 0.000 0.100.1125 0.200.2227 0.300.3286 0.400.4284 0.500.5205 0.600.6039 0.700.6778 0.800.7421 0.900.7970 1.000.8427 1.500.9661 2.000.9953

43. Why is diffusion important in Materials Science? Diffusion can be used as part of a heat treatment Case Hardening/Carburizing Diffusion is important during the solidification process We’ll discussion this starting in Chapter 8 Diffusion is important in the aging process when very small components are used – for example in integrated circuits Diffusion is used to create integrated circuits!!

44. This is not the end! We will return to the topic of diffusion repeatedly as we continue through the course Please make sure that you understand the basic concepts!!