1. Chapter 4 - 1 ISSUES TO ADDRESS... What types of defects arise in solids? Can the number and type of defects be varied and controlled? How do defects affect material properties? Are defects undesirable? Imperfections in Solids What are the solidification mechanisms?

2. Chapter 4 - 2 Solidification - result of casting of molten material –2 steps Nuclei form Nuclei grow to form crystals – grain structure Start with a molten material – all liquid Imperfections in Solids Crystals grow until they meet each other Adapted from Fig. 4.14(b), Callister & Rethwisch 8e. grain structure crystals growing nuclei liquid

3. Chapter 4 - 3 Polycrystalline Materials Grain Boundaries regions between crystals transition from lattice of one region to that of the other slightly disordered low density in grain boundaries –high mobility –high diffusivity –high chemical reactivity Adapted from Fig. 4.7, Callister & Rethwisch 8e.

4. Chapter 4 - 4 Solidification Columnar in area with less undercooling Shell of equiaxed grains due to rapid cooling (greater  T) near wall Grain Refiner - added to make smaller, more uniform, equiaxed grains. heat flow Grains can be- equiaxed (roughly same size in all directions) - columnar (elongated grains) Adapted from Fig. 5.17, Callister & Rethwisch 3e. ~ 8 cm

5. Chapter 4 - 5 Imperfections in Solids There is no such thing as a perfect crystal. What are these imperfections? Why are they important? Many of the important properties of materials are due to the presence of imperfections.

6. Chapter 4 - 6 Vacancy atoms Interstitial atoms Substitutional atoms Point defects Types of Imperfections Dislocations Line defects Grain Boundaries Area defects

7. Chapter 4 - 7 Vacancies: -vacant atomic sites in a structure. Self-Interstitials: -"extra" atoms positioned between atomic sites. Point Defects in Metals Vacancy distortion of planes self- interstitial distortion of planes

8. Chapter 4 -  8 Boltzmann's constant (1.38 x 10 -23 J/atom-K) (8.62 x 10 -5 eV/atom-K) N v N  exp  Q v kT      No. of defects No. of potential defect sites Activation energy Temperature Each lattice site is a potential vacancy site Equilibrium concentration varies with temperature! Equilibrium Concentration: Point Defects

9. Chapter 4 - 9 We can get Q v from an experiment.   N v N = exp  Q v kT      Measuring Activation Energy Measure this... N v N T exponential dependence! defect concentration Replot it... 1/T N N v ln - Q v /k/k slope

10. Chapter 4 - 10 Find the equil. # of vacancies in 1 m 3 of Cu at 1000  C. Given: A Cu = 63.5 g/mol  = 8.4 g/cm 3 Q v = 0.9 eV/atom N A = 6.02 x 10 23 atoms/mol Estimating Vacancy Concentration For 1 m 3, N = N A A Cu  x x1 m 3 = 8.0 x 10 28 sites = 2.7 x 10 -4 8.62 x 10 -5 eV/atom-K 0.9 eV/atom 1273 K  N v N  exp  Q v kT       Answer: N v =(2.7 x 10 -4 )(8.0 x 10 28 ) sites = 2.2 x 10 25 vacancies

11. Chapter 4 - 11 Low energy electron microscope view of a (110) surface of NiAl. Increasing temperature causes surface island of atoms to grow. Why? The equil. vacancy conc. increases via atom motion from the crystal to the surface, where they join the island. Reprinted with permission from Nature (K.F. McCarty, J.A. Nobel, and N.C. Bartelt, "Vacancies in Solids and the Stability of Surface Morphology", Nature, Vol. 412, pp. 622-625 (2001). Image is 5.75  m by 5.75  m.) Copyright (2001) Macmillan Publishers, Ltd. Observing Equilibrium Vacancy Conc. Island grows/shrinks to maintain equil. vancancy conc. in the bulk. Click once on image to start animation

12. Chapter 4 - 12 Two outcomes if impurity (B) added to host (A): Solid solution of B in A (i.e., random dist. of point defects) Solid solution of B in A plus particles of a new phase (usually for a larger amount of B) OR Substitutional solid soln. (e.g., Cu in Ni) Interstitial solid soln. (e.g., C in Fe) Second phase particle -- different composition -- often different structure. Imperfections in Metals (i)

13. Chapter 4 - 13 Imperfections in Metals (ii) Conditions for substitutional solid solution (S.S.) W. Hume – Rothery rule –1.  r (atomic radius) < 15% –2. Proximity in periodic table i.e., similar electronegativities –3. Same crystal structure for pure metals –4. Valency All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency

14. Chapter 4 - 14 Imperfections in Metals (iii) Application of Hume–Rothery rules – Solid Solutions 1. Would you predict more Al or Ag to dissolve in Zn? 2. More Zn or Al in Cu? Table on p. 118, Callister & Rethwisch 8e. ElementAtomicCrystalElectro-Valence Radius Structure nega- (nm) tivity Cu0.1278FCC1.9+2 C0.071 H0.046 O0.060 Ag0.1445FCC1.9+1 Al0.1431FCC1.5+3 Co0.1253HCP1.8+2 Cr0.1249BCC1.6+3 Fe0.1241BCC1.8+2 Ni0.1246FCC1.8+2 Pd0.1376FCC2.2+2 Zn0.1332HCP1.6+2

15. Chapter 4 - 15 Impurities in Solids Specification of composition –weight percent m 1 = mass of component 1 n m1 = number of moles of component 1 – atom percent

16. Chapter 4 - 16 are line defects, slip between crystal planes result when dislocations move, produce permanent (plastic) deformation. Dislocations: Schematic of Zinc (HCP): before deformation after tensile elongation slip steps Line Defects

17. Chapter 4 - 17 Imperfections in Solids Linear Defects (Dislocations) –Are one-dimensional defects around which atoms are misaligned Edge dislocation: –extra half-plane of atoms inserted in a crystal structure –b perpendicular (  ) to dislocation line Screw dislocation: –spiral planar ramp resulting from shear deformation –b parallel (  ) to dislocation line Burger’s vector, b: measure of lattice distortion

18. Chapter 4 - 18 Imperfections in Solids Fig. 4.3, Callister & Rethwisch 8e. Edge Dislocation

19. Chapter 4 - 19 Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession. Atomic view of edge dislocation motion from left to right as a crystal is sheared. (Courtesy P.M. Anderson) Motion of Edge Dislocation Click once on image to start animation

20. Chapter 4 - 20 Imperfections in Solids Screw Dislocation Adapted from Fig. 4.4, Callister & Rethwisch 8e. Burgers vector b Dislocation line b (a) (b) Screw Dislocation

21. Chapter 4 - VMSE: Screw Dislocation In VMSE: –a region of crystal containing a dislocation can be rotated in 3D –dislocation motion may be animated 21 Front ViewTop View VMSE Screen Shots

22. Chapter 4 - 22 Edge, Screw, and Mixed Dislocations Adapted from Fig. 4.5, Callister & Rethwisch 8e. Edge Screw Mixed

23. Chapter 4 - 23 Imperfections in Solids Dislocations are visible in electron micrographs Fig. 4.6, Callister & Rethwisch 8e.

24. Chapter 4 - 24 Dislocations & Crystal Structures Structure: close-packed planes & directions are preferred. view onto two close-packed planes. close-packed plane (bottom)close-packed plane (top) close-packed directions Comparison among crystal structures: FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none Specimens that were tensile tested. Mg (HCP) Al (FCC) tensile direction

25. Chapter 4 - 25 Planar Defects in Solids One case is a twin boundary (plane) –Essentially a reflection of atom positions across the twin plane. Stacking faults –For FCC metals an error in ABCABC packing sequence –Ex: ABCABABC Adapted from Fig. 4.9, Callister & Rethwisch 8e.

26. Chapter 4 - 26 Catalysts and Surface Defects A catalyst increases the rate of a chemical reaction without being consumed Active sites on catalysts are normally surface defects Fig. 4.10, Callister & Rethwisch 8e. Fig. 4.11, Callister & Rethwisch 8e. Single crystals of (Ce 0.5 Zr 0.5 )O 2 used in an automotive catalytic converter

27. Chapter 4 - 27 Microscopic Examination Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite large. –ex: Large single crystal of quartz or diamond or Si –ex: Aluminum light post or garbage can - see the individual grains Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.

28. Chapter 4 - 28 Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. Micrograph of brass (a Cu-Zn alloy) 0.75mm Optical Microscopy Adapted from Fig. 4.13(b) and (c), Callister & Rethwisch 8e. (Fig. 4.13(c) is courtesy of J.E. Burke, General Electric Co.) crystallographic planes

29. Chapter 4 - 29 Grain boundaries... are imperfections, are more susceptible to etching, may be revealed as dark lines, change in crystal orientation across boundary. Adapted from Fig. 4.14(a) and (b), Callister & Rethwisch 8e. (Fig. 4.14(b) is courtesy of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].) Optical Microscopy ASTM grain size number N = 2 n number of grains/in 2 at 100x magnification Fe-Cr alloy (b) grain boundary surface groove polished surface (a)

30. Chapter 4 - 30 Optical Microscopy Polarized light –metallographic scopes often use polarized light to increase contrast –Also used for transparent samples such as polymers

31. Chapter 4 - 31 Microscopy Optical resolution ca. 10 -7 m = 0.1  m = 100 nm For higher resolution need higher frequency –X-Rays? Difficult to focus. –Electrons wavelengths ca. 3 pm (0.003 nm) –(Magnification - 1,000,000X) Atomic resolution possible Electron beam focused by magnetic lenses.

32. Chapter 4 - 32 Atoms can be arranged and imaged! Carbon monoxide molecules arranged on a platinum (111) surface. Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995. Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”. Scanning Tunneling Microscopy (STM)

33. Chapter 4 - 33 Point, Line, and Area defects exist in solids. The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.) Defects affect material properties (e.g., grain boundaries control crystal slip). Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.) Summary

34. Chapter 4 - 34 Core Problems: Self-help Problems: ANNOUNCEMENTS Reading:

35. Chapter 4 - 35 ISSUES TO ADDRESS... How does diffusion occur? Why is it an important part of processing? How can the rate of diffusion be predicted for some simple cases? How does diffusion depend on structure and temperature? Chapter 5: Diffusion

36. Chapter 4 - 36 Diffusion Diffusion - Mass transport by atomic motion Mechanisms Gases & Liquids – random (Brownian) motion Solids – vacancy diffusion or interstitial diffusion

37. Chapter 4 - 37 Interdiffusion: In an alloy, atoms tend to migrate from regions of high conc. to regions of low conc. Initially Adapted from Figs. 5.1 and 5.2, Callister & Rethwisch 8e. Diffusion After some time

38. Chapter 4 - 38 Self-diffusion: In an elemental solid, atoms also migrate. Label some atoms Diffusion A B C D After some time A B C D

39. Chapter 4 - 39 Diffusion Mechanisms Vacancy Diffusion: atoms exchange with vacancies applies to substitutional impurities atoms rate depends on: -- number of vacancies -- activation energy to exchange. increasing elapsed time

40. Chapter 4 - 40 Simulation of interdiffusion across an interface: Rate of substitutional diffusion depends on: -- vacancy concentration -- frequency of jumping. (Courtesy P.M. Anderson) Diffusion Simulation This slide contains an animation that requires Quicktime and a Cinepak decompressor. Click on the message or image below to activate the animation.

41. Chapter 4 - 41 Diffusion Mechanisms Interstitial diffusion – smaller atoms can diffuse between atoms. More rapid than vacancy diffusion Adapted from Fig. 5.3(b), Callister & Rethwisch 8e.

42. Chapter 4 - 42 Adapted from chapter-opening photograph, Chapter 5, Callister & Rethwisch 8e. (Courtesy of Surface Division, Midland-Ross.) Case Hardening: -- Diffuse carbon atoms into the host iron atoms at the surface. -- Example of interstitial diffusion is a case hardened gear. Result: The presence of C atoms makes iron (steel) harder. Processing Using Diffusion

43. Chapter 4 - 43 Doping silicon with phosphorus for n-type semiconductors: Process: 3. Result: Doped semiconductor regions. silicon Processing Using Diffusion magnified image of a computer chip 0.5 mm light regions: Si atoms light regions: Al atoms 2. Heat it. 1. Deposit P rich layers on surface. silicon Adapted from Figure 18.27, Callister & Rethwisch 8e.

44. Chapter 4 - 44 Diffusion How do we quantify the amount or rate of diffusion? J  slope M = mass diffused time Measured empirically –Make thin film (membrane) of known surface area –Impose concentration gradient –Measure how fast atoms or molecules diffuse through the membrane

45. Chapter 4 - 45 Steady-State Diffusion Fick’s first law of diffusion C1C1 C2C2 x C1C1 C2C2 x1x1 x2x2 D  diffusion coefficient Rate of diffusion independent of time Flux proportional to concentration gradient =

46. Chapter 4 - 46 Example: Chemical Protective Clothing (CPC) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? Data: –diffusion coefficient in butyl rubber: D = 110 x10 -8 cm 2 /s –surface concentrations: C 2 = 0.02 g/cm 3 C 1 = 0.44 g/cm 3

47. Chapter 4 - 47 Example (cont). glove C1C1 C2C2 skin paint remover x1x1 x2x2 Solution – assuming linear conc. gradient D = 110 x 10 -8 cm 2 /s C 2 = 0.02 g/cm 3 C 1 = 0.44 g/cm 3 x 2 – x 1 = 0.04 cm Data:

48. Chapter 4 - 48 Diffusion and Temperature Diffusion coefficient increases with increasing T. D  DoDo exp        QdQd RT = pre-exponential [m 2 /s] = diffusion coefficient [m 2 /s] = activation energy [J/mol or eV/atom] = gas constant [8.314 J/mol-K] = absolute temperature [K] D DoDo QdQd R T

49. Chapter 4 - 49 Diffusion and Temperature Adapted from Fig. 5.7, Callister & Rethwisch 8e. (Date for Fig. 5.7 taken from E.A. Brandes and G.B. Brook (Ed.) Smithells Metals Reference Book, 7th ed., Butterworth-Heinemann, Oxford, 1992.) D has exponential dependence on T D interstitial >> D substitutional C in  -Fe C in  -Fe Al in Al Fe in  -Fe Fe in  -Fe 1000 K/T D (m 2 /s) C in  -Fe C in  -Fe Al in Al Fe in  -Fe Fe in  -Fe 0.51.01.5 10 -20 10 -14 10 -8 T(  C) 15001000 600 300

50. Chapter 4 - 50 Example: At 300ºC the diffusion coefficient and activation energy for Cu in Si are D(300ºC) = 7.8 x 10 -11 m 2 /s Q d = 41.5 kJ/mol What is the diffusion coefficient at 350ºC? transform data D Temp = T ln D 1/T

51. Chapter 4 - 51 Example (cont.) T 1 = 273 + 300 = 573 K T 2 = 273 + 350 = 623 K D 2 = 15.7 x 10 -11 m 2 /s

52. Chapter 4 - 52 Non-steady State Diffusion The concentration of diffusing species is a function of both time and position C = C(x,t) In this case Fick’s Second Law is used Fick’s Second Law

53. Chapter 4 - VMSE: Student Companion Site Diffusion Computations & Data Plots 53

54. Chapter 4 - 54 Non-steady State Diffusion Adapted from Fig. 5.5, Callister & Rethwisch 8e. B.C. at t = 0, C = C o for 0  x   at t > 0, C = C S for x = 0 (constant surface conc.) C = C o for x =  Copper diffuses into a bar of aluminum. pre-existing conc., C o of copper atoms Surface conc., C of Cu atoms bar s C s

55. Chapter 4 - 55 Solution: C(x,t) = Conc. at point x at time t erf (z) = error function erf(z) values are given in Table 5.1 CSCS CoCo C(x,t) Adapted from Fig. 5.5, Callister & Rethwisch 8e.

56. Chapter 4 - 56 Non-steady State Diffusion Sample Problem: An FCC iron-carbon alloy initially containing 0.20 wt% C is carburized at an elevated temperature and in an atmosphere that gives a surface carbon concentration constant at 1.0 wt%. If after 49.5 h the concentration of carbon is 0.35 wt% at a position 4.0 mm below the surface, determine the temperature at which the treatment was carried out. Solution: use Eqn. 5.5

57. Chapter 4 - 57 Solution (cont.): –t = 49.5 h x = 4 x 10 -3 m –C x = 0.35 wt%C s = 1.0 wt% –C o = 0.20 wt%  erf(z) = 0.8125

58. Chapter 4 - 58 Solution (cont.): We must now determine from Table 5.1 the value of z for which the error function is 0.8125. An interpolation is necessary as follows zerf(z) 0.900.7970 z0.8125 0.950.8209 z  0.93 Now solve for D

59. Chapter 4 - 59 To solve for the temperature at which D has the above value, we use a rearranged form of Equation (5.9a); from Table 5.2, for diffusion of C in FCC Fe D o = 2.3 x 10 -5 m 2 /s Q d = 148,000 J/mol  Solution (cont.): T = 1300 K = 1027ºC

60. Chapter 4 - 60 Example: Chemical Protective Clothing (CPC) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the breakthrough time (t b ), i.e., how long could the gloves be used before methylene chloride reaches the hand? Data –diffusion coefficient in butyl rubber: D = 110 x10 -8 cm 2 /s

61. Chapter 4 - 61 CPC Example (cont.) Time required for breakthrough ca. 4 min glove C1C1 C2C2 skin paint remover x1x1 x2x2 Solution – assuming linear conc. gradient Equation from online CPC Case Study 5 at the Student Companion Site for Callister & Rethwisch 8e (www.wiley.com/ college/callister) D = 110 x 10 -8 cm 2 /s Breakthrough time = t b

62. Chapter 4 - 62 Diffusion FASTER for... open crystal structures materials w/secondary bonding smaller diffusing atoms lower density materials Diffusion SLOWER for... close-packed structures materials w/covalent bonding larger diffusing atoms higher density materials Summary