2012-04-09 1 Chapter 5: IMPERFECTIONS IN SOLIDS School of Mechanical Engineering Choi Hae Jin Chapter 4 - Choi, Hae-Jin Materials Science - Prof. Choi, Hae-Jin 1 ISSUES TO ADDRESS... • What are the solidification mechanisms? • What types of defects arise in solids? • Can the number and type of defects be varied and controlled? How do defects affect material properties? • What are the solidification mechanisms? Chapter 5 - 2 • How do defects affect material properties? • Are defects undesirable?
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2012-04-09
1
Chapter 5: IMPERFECTIONS IN SOLIDS
School of Mechanical Engineering
Choi Hae Jin
Chapter 4 -
Choi, Hae-Jin
Materials Science - Prof. Choi, Hae-Jin 1
ISSUES TO ADDRESS...
• What are the solidification mechanisms?
• What types of defects arise in solids?
• Can the number and type of defects be variedand controlled?
How do defects affect material properties?
• What are the solidification mechanisms?
Chapter 5 - 2
• How do defects affect material properties?
• Are defects undesirable?
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Imperfections in Solids
• Solidification- result of casting of molten material– 2 stepsp
• Nuclei form
• Nuclei grow to form crystals – grain structure
• Start with a molten material – all liquid
Chapter 5 - 3
• Crystals grow until they meet each otherAdapted from Fig. 5.19 (b), Callister & Rethwisch 3e.
grain structurecrystals growingnucleiliquid
Polycrystalline Materials
Grain Boundaries• regions between crystals• regions between crystals
• transition from lattice of one region to that of the other
• slightly disordered
• low density in grain
Chapter 5 -
boundaries– high mobility
– high diffusivity
– high chemical reactivity
4
Adapted from Fig. 5.12, Callister & Rethwisch 3e.
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SolidificationGrains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)~ 8 cm
Columnar in Shell of equiaxed grains
heat
flow
Chapter 5 - 5
area with less undercooling
equiaxed grains due to rapid cooling (greater T) near wall
Grain Refiner - added to make smaller, more uniform, equiaxed grains.
Adapted from Fig. 5.17, Callister & Rethwisch 3e.
Imperfections in Solids
There is no such thing as a perfect crystal.
• What are these imperfections?• What are these imperfections?
• Why are they important?
Many of the important properties of materials are due to the presence of
Chapter 5 -
materials are due to the presence of imperfections.
• Self-Interstitials:-"extra" atoms positioned between atomic sites.
Vacancydistortion of planes
lf
Chapter 5 - 8
self-interstitial
distortion of planes
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Equilibrium Concentration:Point Defects
• Equilibrium concentration varies with temperature!
Boltzmann's constant
( -23 / )
÷Nv
N exp Qv
kT
÷
No. of defects
No. of potential defect sites
Activation energy
Temperature
Chapter 5 - 9
(1.38 x 10-23 J/atom-K)
(8.62 x 10-5 eV/atom-K)
Each lattice site is a potential vacancy site
Measuring Activation Energy
• We can get Qv froman experiment.
÷Nv
N= exp
Qv
kT
÷N kT
• Measure this...
Nv
N
exponential
• Replot it...
N
Nvln
-Qv /k
slope
Chapter 5 - 10
T
exponential dependence!
defect concentration1/T
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Estimating Vacancy Concentration• Find the equil. # of vacancies in 1 m3 of Cu at 1000C.• Given:
ACu = 63.5 g/mol = 8.4 g/cm3
Qv = 0.9 eV/atom NA = 6.02 x 1023 atoms/mol
8 62 x 10-5 eV/atom-K
0.9 eV/atom
1273 K
÷Nv
N exp
Qv
kT
÷= 2.7 x 10-4
Chapter 5 - 11
For 1 m3 , N =N
A
ACu
x x 1 m3= 8.0 x 1028 sites8.62 x 10 eV/atom K
• Answer:
Nv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies
Observing Equilibrium Vacancy Conc.• Low energy electron
microscope view ofa (110) surface of NiAl.
• Increasing temperature• Increasing temperature causes surface island ofatoms to grow.
• Why? The equil. vacancyconc. increases via atommotion from the crystalto the surface, where they join the island
Reprinted with permission from Nature (K.F. McCarty, J A Nobel and N C Bartelt "Vacancies in
Chapter 5 - 12
they join the island. J.A. Nobel, and N.C. Bartelt, Vacancies inSolids and the Stability of Surface Morphology",Nature, Vol. 412, pp. 622-625 (2001). Image is5.75 m by 5.75 m.) Copyright (2001) Macmillan Publishers, Ltd.
Island grows/shrinks to maintain equil. vancancy conc. in the bulk.
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Point Defects in Ceramics (i)• Vacancies
-- vacancies exist in ceramics for both cations and anions
• Interstitialsinterstitials exist for cations-- interstitials exist for cations
-- interstitials are not normally observed for anions because anions are large relative to the interstitial sites
Cation Interstitial
Chapter 5 - 13
Adapted from Fig. 5.2, Callister & Rethwisch 3e. (Fig. 5.2 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.)
Cation Vacancy
Anion Vacancy
Point Defects in Ceramics (ii)
• Frenkel Defect-- a cation vacancy-cation interstitial pair.
Sh ttk D f t• Shottky Defect-- a paired set of cation and anion vacancies.
Adapted from Fig. 5.3, Callister & Rethwisch 3e. (Fig. 5.3 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure John Wiley and Sons
Shottky Defect:
Chapter 5 - 14
• Equilibrium concentration of defects
Structure, John Wiley and Sons, Inc., p. 78.)
Frenkel Defect
/kTQDe
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Imperfections in Metals (i)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 newh ( ll f l t f B)
OR
Substitutional solid soln.(e.g., Cu in Ni)
Interstitial solid soln.(e.g., C in Fe)
Chapter 5 - 15
phase (usually for a larger amount of B)
Second phase particle-- different composition-- often different structure.
Imperfections in Metals (ii)
Conditions for substitutional solid solution (S.S.)
• W. Hume – Rothery ruley– 1. r (atomic radius) < 15%
– 2. Proximity in periodic table • i.e., similar electronegativities
– 3. Same crystal structure for pure metals
– 4. Valency
Chapter 5 -
• All else being equal, a metal will have a greater tendency to dissolve a metal of higher valency than one of lower valency
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Imperfections in Metals (iii)
Application of Hume–Rothery rules – Solid Solutions
Element Atomic Crystal Electro- ValenceS
1. Would you predictmore Al or Ag to dissolve in Zn?
• Comparison among crystal structures:FCC: many close-packed planes/directions;HCP: only one plane, 3 directions;BCC: none
Chapter 5 - 28
• Specimens that were tensiletested.
Mg (HCP)
Al (FCC)tensile direction
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Planar Defects in Solids
• One case is a twin boundary (plane)– Essentially a reflection of atom positions across the twin
lplane.
Adapted from Fig. 5.14,
Chapter 5 -
• Stacking faults– For FCC metals an error in ABCABC packing sequence– Ex: ABCABABC
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Callister & Rethwisch 3e.
Catalysts and Surface Defects
• A catalyst increases the rate of a chemical reaction without beingreaction without being consumed
• Active sites on catalysts are normally surface defects
Fig. 5.15, Callister & Rethwisch 3e.
Chapter 5 - 30
Fig. 5.16, Callister & Rethwisch 3e.
Single crystals of (Ce0.5Zr0.5)O2
used in an automotive catalytic converter
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Microscopic Examination
• Crystallites (grains) and grain boundaries. Vary considerably in size Can be quite largeVary 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
Chapter 5 -
) ymicroscope.
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Optical Microscopy• Useful up to 2000X magnification.• Polishing removes surface features (e.g., scratches)• Etching changes reflectance, depending on crystal
i t tiorientation.
Adapted from Fig. 5.18(b) and (c), Callister & Rethwisch 3e. (Fig. 5.18(c) is courtesyof J.E. Burke, General Electric Co.)
crystallographic planes
Chapter 5 - 32
Micrograph ofbrass (a Cu-Zn alloy)
0.75mm
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Optical MicroscopyGrain boundaries...
• are imperfections,• are more susceptible
to etchingto etching,• may be revealed as
dark lines,• change in crystal
orientation across boundary. Adapted from Fig. 5.19(a)
and (b), Callister & Rethwisch 3e.ASTM grain
grain boundary
surface groove
polished surface
(a)
Chapter 5 - 33
(Fig. 5.19(b) is courtesyof L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
gsize number
N = 2n-1
number of grains/in2
at 100x magnification
Fe-Cr alloy(b)
Optical Microscopy
• Polarized light t ll hi ft l i d– metallographic scopes often use polarized
light to increase contrast
– Also used for transparent samples such as polymers
Chapter 5 - 34
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Electron MicroscopyOptical resolution ca. 10-7 m = 0.1 m = 100 nm
For higher resolution need higher frequency
– Electrons• wavelengths ca. 3 pm (0.003 nm)
– (Magnification - 1,000,000X)
• Atomic resolution possible
• Electron beam focused by magnetic lenses.
S i El t Mi (SEM)
Chapter 5 -
• Scanning Electron Microscopy (SEM) – reflected electron beam
• Transmission Electron Microscopy (TEM) – transmitted electron beam
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Scanning Tunneling Microscopy(STM)
• Atoms can be arranged and imaged!
Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995.
I t d
Chapter 5 - 36
Iron atoms arranged on a copper (111)
surface. These Kanji characters represent
the word “atom”.Schematic view of an STM (http://wikipedia.org)
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Summary
• Point, Line, and Area defects exist in solids.
Th b d t f d f t b i d• The number and type of defects can be variedand controlled (e.g., T controls vacancy conc.)
• Defects affect material properties (e.g., grainboundaries control crystal slip).
• Defects may be desirable or undesirable(e g dislocations ma be good or bad depending
Chapter 5 - 37
(e.g., dislocations may be good or bad, dependingon whether plastic deformation is desirable or not.)