![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. 4.15 (b), Callister & Rethwisch 9e.
grain structure
crystals growing
nuclei
liquid
[Photomicrograph
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.)]](https://image.slidesharecdn.com/5imperfection-defects-250808161618-016de031/85/5-imperfection-defects-types-of-defects-2-320.jpg)
![Chapter 4 - 16
Imperfections in Solids
Screw Dislocation
Adapted from Fig. 4.5, Callister & Rethwisch 9e.
[Figure (b) from W. T. Read, Jr.,Dislocations in Crystals,
McGraw-Hill Book Company, New York, NY, 1953.]
Burgers vector b
Dislocation
line
b
(a)
(b)
Screw Dislocation](https://image.slidesharecdn.com/5imperfection-defects-250808161618-016de031/85/5-imperfection-defects-types-of-defects-16-320.jpg)
![Chapter 4 - 19
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. 4.11, Callister & Rethwisch 9e.
Fig. 4.12, Callister & Rethwisch 9e.
[From W. J. Stark, L. Mädler, M. Maciejewski, S. E.
Pratsinis, and A. Baiker, “Flame Synthesis of
Nanocrystalline Ceria/Zirconia: Effect of Carrier
Liquid,” Chem. Comm., 588–589 (2003). Reproduced
by permission of The Royal Society of Chemistry.]
Single crystals of
(Ce0.5Zr0.5)O2
used in an automotive
catalytic converter](https://image.slidesharecdn.com/5imperfection-defects-250808161618-016de031/85/5-imperfection-defects-types-of-defects-19-320.jpg)
![Chapter 4 - 22
Grain boundaries...
• are imperfections,
• are more susceptible
to etching,
• may be revealed as
dark lines,
• change in crystal
orientation across
boundary. Fig. 4.15(a) & (b), Callister &
Rethwisch 9e.
[Fig. 4.15(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/5imperfection-defects-250808161618-016de031/85/5-imperfection-defects-types-of-defects-22-320.jpg)
5 imperfection- defects. types of defects.
- 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. 4.15 (b), Callister & Rethwisch 9e. grain structure crystals growing nuclei liquid [Photomicrograph 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.)]
- 3. Chapter 4 - 3 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.
- 4. Chapter 4 - 4 • Vacancy atoms • Interstitial atoms • Substitutional atoms Point defects Types of Imperfections • Dislocations Line defects • Grain Boundaries Area defects
- 5. Chapter 4 - 5 • 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
- 6. Chapter 4 - 6 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
- 7. Chapter 4 - 7 • 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
- 8. Chapter 4 - 8 • Find the equil. # of vacancies in 1 m3 of Cu at 1000C. • Given: ACu = 63.5 g/mol ρ= 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 ρ x x 1 m3 = 8.0 x 1028 sites • Answer: Nv = (2.7 x 10-4 )(8.0 x 1028 ) sites = 2.2 x 1025 vacancies = 2.7 x 10-4 8.62 x 10-5 eV/atom-K 0.9 eV/atom 1273 K Nv N = exp - Qv kT
- 9. Chapter 4 - 9 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)
- 10. Chapter 4 - 10 Imperfections in Metals (ii) Conditions for substitutional solid solution (S.S.) • W. Hume – Rothery rule – 1. Δr (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
- 11. Chapter 4 - 11 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. 135, Callister & Rethwisch 9e. 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
- 12. Chapter 4 - 12 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
- 13. Chapter 4 - 13 • 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
- 14. Chapter 4 - 14 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
- 15. Chapter 4 - 15 Imperfections in Solids Edge Dislocation Fig. 4.4, Callister & Rethwisch 9e. (Adapted from A. G. Guy, Essentials of Materials Science, McGraw-Hill Book Company, New York, NY, 1976, p. 153.)
- 16. Chapter 4 - 16 Imperfections in Solids Screw Dislocation Adapted from Fig. 4.5, Callister & Rethwisch 9e. [Figure (b) from W. T. Read, Jr.,Dislocations in Crystals, McGraw-Hill Book Company, New York, NY, 1953.] Burgers vector b Dislocation line b (a) (b) Screw Dislocation
- 17. Chapter 4 - 17 Imperfections in Solids Dislocations are visible in electron micrographs Fig. 4.7, Callister & Rethwisch 9e. (Courtesy of M. R. Plichta, Michigan Technological University.)
- 18. Chapter 4 - 18 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. 4.10, Callister & Rethwisch 9e.
- 19. Chapter 4 - 19 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. 4.11, Callister & Rethwisch 9e. Fig. 4.12, Callister & Rethwisch 9e. [From W. J. Stark, L. Mädler, M. Maciejewski, S. E. Pratsinis, and A. Baiker, “Flame Synthesis of Nanocrystalline Ceria/Zirconia: Effect of Carrier Liquid,” Chem. Comm., 588–589 (2003). Reproduced by permission of The Royal Society of Chemistry.] Single crystals of (Ce0.5Zr0.5)O2 used in an automotive catalytic converter
- 20. Chapter 4 - 20 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.
- 21. Chapter 4 - 21 • 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) 0.75 mm Optical Microscopy Fig. 4.14(b) & (c), Callister & Rethwisch 9e. crystallographic planes Courtesy of J.E. Burke, General Electric Co.
- 22. Chapter 4 - 22 Grain boundaries... • are imperfections, • are more susceptible to etching, • may be revealed as dark lines, • change in crystal orientation across boundary. Fig. 4.15(a) & (b), Callister & Rethwisch 9e. [Fig. 4.15(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)
- 23. Chapter 4 - 23 • Point, Line, and Area defects exist in solids. • The number and type of defects can be varied and controlled (e.g., temperature controls vacancy concentration). • 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