materials ch4
TRANSCRIPT
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CHAPTER 4Solidification andCrystalline Imperfections
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Crystalline Imperfections Learning Objectives
By the end of this chapter, you should be
able to
Describe the process of the solidificationof metals, distinguishing between
homogeneous and heterogeneous
nucleation.
Describe the two energies in volved in the
solidification process of a pure metal, and
write the equation for the total free-energychange associated with the
transformation of the liquid state to solid
nucleus.
Distinguish between equiaxed and
columnar grains and the advantage of the
former over the latter.
Distinguish between single crystal and
polycrystalline materials, and explain why
single crystal and polycrystalline forms of
the material have different mechanical
properties.
Describe various forms of metallic solid
solutions and explain the differences
between solid solution and mixture alloys. Classify various types of crystalline
imperfections, and explain the role of
defects on the mechanical and electrical
properties of crystalline materials.
Determine the ASTM grain size number
and average grain size diameter, anddescribe the importance of grain size and
grain boundary density on the behavior of
crystalline materials.
Learn how and why optical microscopy,
SEM, TEM, HRTEM, AFM, and STEM
techniques are used to understand moreabout the internal and surface structures
of materials at various magnifications.
Explain, in general terms, why alloys are
preferred materials over pure metals for
structural applications.
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Metals are:
1.Melted (liquefied)2.Cast (solidified)
3.Worked
Solidification of metals
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What does a perfect crystal look like?
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Tantalum metal single crystal
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Microscopically, a single crystal looks like this
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However, most materials are polycrystalline
Very ordered
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Solidification of Metals
There are two steps for solidifying molten metal:
1. Nucleation: Formation of stable nuclei.2. Growth of nuclei into crystals:Formation of grain structure.
Thermal gradients define the shape of each grain.
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Formation of Stable Nuclei
Two main mechanisms of nucleation:1. Homogenous nucleation
2. Heterogeneous nucleation
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Formation of stable nuclei: Homogeneous nucleation
Metal itself will
provide atoms to
form nuclei.
Metal, when significantly
undercooled, has
several slow moving
atoms which bond each
other to form nuclei.
If the cluster of atoms
reach critical size, they
grow into crystals. Else
they get dissolved.
Cooling
nuclei
Liquid metal Solid metal
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Formation of stable nuclei: Homogeneous nucleation
Clusters of atoms
below crit ic al size
is called embryo.
Clusters of atoms that
are greater than critical
size are called nuclei.
Cooling
nucleiembryo
WARNING: In this sense,nuclei does NOT refer to
the center of an atom!
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Energies involved in homogenous nucleation
Volume free energy GV
Released by liquid to solid
transformation.
Gv is change in free energy
per unit volume between liquidand solid (no formulaits a
material property).
Free energy change for a
spherical nucleus of radius r is
given by
Surface energy Gs
Required to form new solid
surface
Gs is energy needed to
create a surface. is specific surface free
energy.
Then
Gs is retarding energy.
2
s 4G r
vV GrG
3
3
4
Small v
Big V
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Total Free Energy: Embryo vs. nucleation
Total free energy is given by 23
4
3
4rGrG
vT
Nucleus
Above critical
radius r*
Below critical
radius r*
Energy
lowered by
growing into
crystals
Energy
lowered by
redissolving
VG
r
2
*Since when r=r*, d(GT)/dr = 0
G
+
- Gv
Gs
GT
r*
Releases energy
Needs energy
Radius of
particle (r)
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Critical Radius Versus Undercooling
The greater the degree of undercooling, the greater
the change in volume free energy GV
Gsdoes not change significantly.
As the amount of undercoolingT increases, critical
nucleus size decreases. That is, it is easier to
nucleate the metal as it gets colder.
Critical radius is related to undercooling by relation
TH
Tr
f
m
2
*
r* = critical radius of nucleus
= Surface free energy
Hf= Latent heat of fusion T = Amount of undercooling
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Heterogenous Nucleation
Nucleation occurs in a liquid on the surfaces of
structural material. Eg: Insoluble impurities. These structures, called nucleat ing agents, lower
the free energy required to form stable nuclei.
Nucleating agents also lower the critical size.
Smaller amount of undercooling is required to
solidify.
Used intensively in industries.
Liquid metal
Solid metal
Nucleating
agent
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Growth of Crystals and Formation of Grain Structure
Nuclei grow into crystals in different orientations.
Crystal boundar ies are formed when crystals jointogether at complete solidification.
Crystals in solidified metals are called grains.
Grains are separated by grain boundar ies.
More nucleation sites
yields more
grains.
Nuclei growing into grains
forming grain boundaries
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Types of Grains
Equiaxed Grains:
Small crystals which grow equally in all directions.
Formed at the sites of high concentration of the nuclei.
Example: Cold mold wall
Columnar Grains: Long thin and coarse.
Grow predominantly in one
direction.
Formed at the sites of slow cooling
and steep temperature gradient.
Example: Grains that are away
from the mold wall.
Columnar Grains
Equiaxed Grains
Mold
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Casting in Industries
In industries, molten metal is cast into either semi
finished or finished parts.
Direct-chill semicontinuous
casting unit for aluminum
Continuous casting
of steel ingots
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Video: Continuous casting of steel
http://www.youtube.com/watch?v=d-
72gc6I-_E
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Video: Iron Smelting
Please click on the following figure to open the video.
(This video has voice).
http://localhost/var/www/apps/conversion/tmp/scratch_6/iron_smelting_new.mpg -
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Grain Structure in Industrial castings
To produce cast ingots with fine grain size, grain
ref iners are added. Example: For an aluminum alloy, a small amount of
titanium, boron or zirconium is added.
(a) (b)
Grain structure of
Aluminum cast
without (a) and
with (b)
grain refiners.
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Solidification of a single crystal
Growth of single
crystal for turbine
airfoil.
For some applications (e.g.: Gas turbine blades-high
temperature environment), single crystals are needed. Single crystals have high temperature creep resistance.
Creep is the tendency of a solid material to slowly move or deform
permanently under the influence of stresses.
We will learn more about creep in Ch7.
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Silicon wafers are single crystal
A wafer is a thin slice of a silicon
single crystal used in the fabricationof integrated circuits.
The wafer serves as the substrate for
microelectronic devices, and
undergoes many microfabrication
process steps such as doping or ion implantation,
etching, deposition of various materials, and
photolithographic patterning.
Q:Why do you need a single crystal of silicon insteadof polycrystalline silicon, which is much easier to
make?
A:Uniformity, in a nutshell, to get the right electrical
processes to occur in the right place.
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Video: Czochralski Process
This method is used to
produce single crystalsilicon for electronic
wafers.
A seed crystal is dipped
in molten silicon androtated.
The seed crystal is
withdrawn slowly while
silicon adheres to theseed crystal and grows
as a single crystal.
http://www.youtube.com/
watch?v=LWfCqpJzJYM
http://www.youtube.com/watch?v=LWfCqpJzJYMhttp://www.youtube.com/watch?v=LWfCqpJzJYMhttp://www.youtube.com/watch?v=LWfCqpJzJYMhttp://www.youtube.com/watch?v=LWfCqpJzJYM -
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Metallic Solid Solutions
Most engineering applications use alloys instead of
pure metals. An alloy is a mixture of two or more metals and
nonmetals.
For example:
Cartridge brass is a binary alloy of 70% Cu and30% Zinc.
Inconel is a nickel based superalloy with about 10
elements.
Solid solutions are a simple type of alloy in whichelements are dispersed in a single phase.
Two types of metal solid solutions: substitutional and
interstitial
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Solid solution vs. liquid solution
Add a teaspoon of salt into a
glass of water and itdissolves.
Now it is a saline solution.
Solvent: water Solute: salt
Same thing with metals: in a
molten vat of metal A, mix in
metal B, and when it
solidifies, it becomes a metal
solid solution of both A and
B.
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Substitutional Solid Solutions
Solute atoms substitute for solvent atoms in a crystal lattice
and the crystal structure remains unchanged. The lattice might get slightly distorted due to the change in
diameter of the atoms.
The solute percentage in the solvent can vary from a
fraction of a percent up to 100%
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Substitutional Solid Solutions: Hume-Rothery rules
The solubility of solids is greater if:
The diameter of atoms do not differ by more than 15%
Crystal structures are similar.
Not much difference in electronegativity (or else
compounds will be formed).
The two elements should have the same valence.
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Substitutional Solid Solutions (Cont.)
Examples:
SystemAtomic radius
difference
Electro-
negativity
difference
Solid solubility
Cu-Zn 3.9% 0.1 38.3%
Cu-Pb 36.7% 0.2 0.17%
Cu-Ni 2.3% 0 100%
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Interstitial Solid Solutions
Solute atoms fit in between the voids
(interstices) of the solvent atoms.
Solvent atoms are much larger than solute
atoms.
Solvent atoms
Solute atoms
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Interstitial Solid Solutions: Steel
Example: between 912 and 1394C,
interstitial solid solution of carbon in iron(FCC) is formed.
A maximum of 2.8% of carbon can dissolve
interstitially in iron.
Different
radii
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Substitutional vs. interstitial alloys
C lli I f i
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Crystalline Imperfections
No crystal is perfect.
Imperfections affectmechanical, chemical,
and electrical properties.
Imperfections can be
classified as: Zero-dimensional point
defects.
One-dimensional / line
defects (dislocations). Two-dimensional
defects.
Three-dimensional
defects (cracks).
P i t D f t V
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Point Defects: Vacancy
A vacancy is formed due to a missing atom in the
crystal lattice. The vacancy is formed (~1:10,000 atoms) during
crystallization or movement of atoms.
Energy of formation is on
the order of 1 eV.
Mobile vacancies cluster
together.
Also caused due to
plastic deformation,
rapid cooling, or
particle bombardment.Vacancies move to form vacancy
clusters
P i t D f t I t titi l
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Point Defects: Interstitial
Sometimes an atom in a crystal occupies
an interstitial site. This does not occur naturally.
Can be induced by irradiation.
This defect causes structural distortion.
P i t D f t i I i C t l
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Point Defects in Ionic Crystals
are more complicated because electrical
neutrality has to be maintained.
Schottky imperfection: if two oppositely charged
particles are missing, a cation-anion divacancy is
created.
Frenkel imperfection:
when a cation moves
to an interstitial site.
Impurity atoms arealso considered as
point defects.
Li D f t Di l ti
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Line Defects: Dislocations
Lattice distortions are centered
around a line.
Formed during:
Solidification
Permanent deformation Vacancy condensation
Different types of line defects are:
Edge dislocation
Screw dislocation
Mixed dislocation
Li D f t Ed Di l ti
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Line Defects: Edge Dislocation
Created by insertion of extra half planes of atoms.
Positive edge dislocation
Negative edge dislocation
Burgers vector
shows displa-
cement ofatoms (slip).
Burgers vector
Li D f t S Di l ti
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Line Defects: Screw Dislocation
Created due to shear stresses applied to regions
of a perfect crystal separated by cutting plane. Distortion of lattice in form of a spiral ramp.
Burgers vector is parallel to dislocation line.
Li D f t Mi d Di l ti
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Line Defects: Mixed Dislocation
Most dislocations in crystals
have components of both
edge and screw dislocations.
Since dislocations have
irregular atomic arrangement,
they will appear as dark lineswhen observed in an electron
microscope.
Dislocation structure of iron
deformed 14% at1950
C
Planar Defects
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Planar Defects
Grain boundar ies, twins, low/high angle
boundaries, twists and stacking faults
A free surface is also a defect : Since it is
bonded to atoms on only one side, it has
a higher state of energy Highlyreactive
Nanomaterials have small clusters of
atoms and hence are highly reactive.
Grain Boundaries
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Grain Boundaries
Grain boundaries separate grains.
Formed due to simultaneously growing crystalsmeeting each other.
Width = 2-5 atomic diameters.
Atoms in grain boundaries have higher energy.
Grain boundaries restrict plastic flow and prevent
dislocation movement.
3D view of
grains
Grain boundaries
in 1018 steel
Grain Boundaries
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Grain Boundaries
Twin Boundaries
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Twin Boundaries
Twin: A region in which mirror image of
structure exists across a boundary.
Formed during plastic deformation and
recrystallization.
Strengthens the metal. Explained in Chapter 6.5
Twin
Twin
Plane
Other Planar Defects
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Other Planar Defects
Small angle tilt boundary:Array of edge
dislocations tilts two regions of a crystal by < 10
Stacking faults: Piling up faults during
recrystallization due to collapsing.
Example: ABCABAACBABC FCC fault
Volume Defects
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Volume Defects
Volume defects: Cluster of point defects join to
form 3-D void.
Metallography: Technique of Observing Grain Boundaries
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Metallography: Technique of Observing Grain Boundaries
To observe grain boundaries, the metal
sample should be ground and polished withdifferent grades of abrasive paper andabrasive solution.
The surface is then etched chemically.
Tiny grooves are produced at grainboundaries.
Grooves do not intensely reflect light.
Hence they can be observed by opticalmicroscope.
After M. Eisenstadt, Introduction to Mechanical Properties of Materials, Macmillan, 1971, p.126
Virtual Lab Modules
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Virtual Lab Modules
Click on the following figures to open the virtual lab
modules related to polishing the specimen forMetallography.
Effect of Etching
http://localhost/var/www/apps/conversion/tmp/scratch_6/polishing.htm -
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Effect of Etching
Unetched
Steel200 X
Etched
Steel200 X
Unetched
Brass
200 X
Etched
Brass
200 X
Virtual Lab Modules
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Virtual Lab Modules
Click on the following figures to open the virtual lab
modules related to etching the specimen.
Virtual Lab Modules
http://localhost/var/www/apps/conversion/tmp/scratch_6/ETCHING.htm -
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Virtual Lab Modules
Click on the following figures to open the virtual lab
modules related to metallographic observation.
Grain Size
http://localhost/var/www/apps/conversion/tmp/scratch_6/brassmag.htm -
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Grain Size
Affects the mechanical properties of the
material. The smaller the grain size, the more grain
boundaries there are.
More grain boundaries means higher
resistance to slip (plastic deformationoccurs due to slip).
More grains means more uniform the
mechanical properties are.
Measuring Grain Size
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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 persquare 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 < 3Coarse grained
4 < n < 6Medium grained
7 < n < 9Fine grained
n > 10ultrafine grained
Measuring ASTM Grain Size Number
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Measuring ASTM Grain Size Number
Click the Image below to play the tutorial.
Average Grain Diameter
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Average Grain Diameter
Average grain diameter more directly
represents grain size. Random line of known length is drawn on
photomicrograph.
Number of grains intersected is counted.
Ratio of number of grains intersected tolength of line, nLis determined.
d = C/nLMC=1.5, and M is
magnification 3 inches 5 grains.
Virtual Lab Module
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Virtual Lab Module
Click on the following figures to open the virtual lab
modules related to grain size measurement.
Transmission Electron Microscope
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Transmission Electron Microscope
Electrons are
produced by heatedtungsten filament.
Accelerated by highvoltage (75 - 120 KV)
Electron beam
passes through verythin specimen.
Difference in atomicarrangement changes
directions ofelectrons.
Beam is enlargedand focused onfluorescent screen.
CollagenFibrils
of ligament as
seen in TEM
TEM (Cont.)
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TEM (Cont.)
TEM needs complex sample preparation
Very thin specimen needed (several hundrednanometers)
High resolution TEM (HRTEM) allows resolution of
0.1 nm.
2-D projections of a crystal with accompanyingdefects can be observed.
Low angle
boundaryAs seen
In HTREM
The Scanning Electron Microscope
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The Scanning Electron Microscope
Electron source
generates electrons. Electrons hit the surface
and secondary
electrons are produced.
The secondaryelectrons are collected
to produce the signal.
The signal
is used toproduce
the image.
SEM of fractured metal end
Scanning Probe Microscopy
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Scanning Probe Microscopy
Scanning Tunneling Microscope (STM) and
Atomic Force Microscope (AFM). Sub-nanometer magnification.
Atomic scale topographic map of surface.
STM uses extremely sharp tip. Tungsten, nickel, platinum
- iridium or carbon nanotubes
are used for tips.
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Atomic Force Microscope
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Atomic Force Microscope
Similar to STM but tip attached to cantilever
beam. When tip interacts with surface, van der Waals
forces deflects the beam.
Deflection detected by laserand photodetector.
Non-conductive materials
can be scanned. Used in DNA research and
polymer coating technique.