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Ch. 4 Solidification and Imperfections
Growth of Crystals and Formation of Grain Structure
Nuclei growing into grainsForming grain boundaries
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Homogeneous Nucleation
Energy
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Total Energy
Gs surface energy
Gv Volume free energy
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Undercooling
Typical Undercooling for Homogeneous Nucleation
Element Undercooling Tm
Ga 76 30
Bi 90 271
Pb 80 327
Al 130 660
Ag 250 962
Cu 236 1085
Ni 480 1453
Fe 420 1538
Pt 332 1772
NaCl 169 801
H2O 40 0
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Heterogeneous Nucleation
fls
fsa
fla
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Typical Grains in Aluminum
Solidification
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Dendrites
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Dendritic Fraction
Chvorinov’s Rule
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Casting in Industries
Figure 4.8Direct‐Chill semicontinuousCasting unit for aluminum
Figure 4.9b
Continuous castingOf steel ingots
Grain Structure in Industrial castings
(a) (b)
Grain structure ofAluminum cast with (a) and without (b)grain refiners.
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Substrate makes a difference
Grain structure of Al onTa substrate (tantalum)
Grain structure of Alon TiN substrate
Same magnification level
Types of grains
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Solidification of Single Crystal
Metallic Solid Solutions = Alloys
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CuZn CuPb CuNi
Interstitial Solid Solution
Carbon atoms r=0.075nm
Iron atoms r00.129nm
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Imperfections
Point Defects – Vacancy
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Point Defects ‐ Interstitially
Point Defects in Ionic Crystals
Figure 4.17
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Edge Dislocation
Burgers vector
Burgers Vector
Trace around the defect, count number of lattice vectors traveled
Trace same path in an undistorted lattice.
The missing section is Burgers Vector (given in Direction indicies)and can be used to track dislocation magnitude and direction.
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Screw Dislocation
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Mixed Dislocation
Figure 4.21
TEM CMSX‐4 plain bar
Grain Boundaries
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Twin Boundaries
Twin
Twin Plane
Transmission Electron Microscope
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The Scanning Electron Microscope
Examples
640 nm polystyrenesphere coated with gold
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Scanning Tunneling Microscope
Constant height and current modes
Surface of platinum with defects
Atomic Force Microscope
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Observing Grain Boundaries ‐Metallography
Effect of Etching
Unetched Steel200 X
Etched Steel200 X
Unetched Brass200 X
Etched Brass200 X
Figure 4.28
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Measuring Grain Size
• ASTM grain size number ‘n’ is a measure of grain size.
N = 2 n‐1 N = Number of grains per
square inch of a polished
and etched specimen at 100 x.
n = ASTM grain size number.
200 X 200 X
1018 cold rolled steel, n=10 1045 cold rolled steel, n=8
n < 3 – Coarse grained4 < n < 6 – Medium grained7 < n < 9 – Fine grainedn > 10 – ultrafine grained
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Average Grain Diameter
• Average grain diameter
d = C/(nL * M)
C=1.5, and M =magnification
nL is the ratio of number of
grains intersected to length
of the line.
3 inches 5 grains.