![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 = 2n-1
number of grains/in2
at 100x
magnification
Fe-Cr alloy
(b)
grain boundary
surface groove
polished surface
(a)](https://image.slidesharecdn.com/ch04-230720083848-f93272e9/85/ch04-ppt-ppt-29-320.jpg)
ch04.ppt.ppt
- 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? Chapter 4: 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) Nv N = exp Qv 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 Qv from an experiment. Nv N = exp Qv kT Measuring Activation Energy • Measure this... Nv N T exponential dependence! defect concentration • Replot it... 1/T N Nv ln -Qv /k slope
- 10. Chapter 4 - 10 • Find the equil. # of vacancies in 1 m3 of Cu at 1000C. • Given: ACu = 63.5 g/mol r = 8.4 g/cm3 Qv = 0.9 eV/atom NA = 6.02 x 1023 atoms/mol Estimating Vacancy Concentration For 1 m3 , N = NA ACu r x x 1 m3 = 8.0 x 1028 sites = 2.7 x 10-4 8.62 x 10-5 eV/atom-K 0.9 eV/atom 1273 K Nv N = exp Qv kT • Answer: Nv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 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 mm by 5.75 mm.) 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. Element Atomic Crystal Electro- Valence Radius Structure nega- (nm) tivity Cu 0.1278 FCC 1.9 +2 C 0.071 H 0.046 O 0.060 Ag 0.1445 FCC 1.9 +1 Al 0.1431 FCC 1.5 +3 Co 0.1253 HCP 1.8 +2 Cr 0.1249 BCC 1.6 +3 Fe 0.1241 BCC 1.8 +2 Ni 0.1246 FCC 1.8 +2 Pd 0.1376 FCC 2.2 +2 Zn 0.1332 HCP 1.6 +2
- 15. Chapter 4 - 15 Impurities in Solids • Specification of composition – weight percent 100 x 2 1 1 1 m m m C = m1 = mass of component 1 100 x 2 1 1 ' 1 m m m n n n C = nm1 = 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 View Top 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 (Ce0.5Zr0.5)O2 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 = 2n-1 number of grains/in2 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 mm = 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: