Materials Ch4

8/12/2019 Materials Ch4

1/62

CHAPTER 4Solidification andCrystalline Imperfections


2/62

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.


3/62

Metals are:

1.Melted (liquefied)2.Cast (solidified)

3.Worked

Solidification of metals


4/62

What does a perfect crystal look like?


5/62

Tantalum metal single crystal


6/62

Microscopically, a single crystal looks like this


7/62

However, most materials are polycrystalline

Very ordered


8/62

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.


9/62

Formation of Stable Nuclei

Two main mechanisms of nucleation:1. Homogenous nucleation

2. Heterogeneous nucleation


10/62

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


11/62

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!


12/62

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


13/62

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)


14/62

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


15/62

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


16/62

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


17/62

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


18/62

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


19/62

Video: Continuous casting of steel

http://www.youtube.com/watch?v=d-

72gc6I-_E


20/62

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


21/62

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.


22/62

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.


23/62

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.


24/62

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


25/62

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


26/62

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.


27/62

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%


28/62

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.


29/62

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%


30/62

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


31/62

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


32/62

Substitutional vs. interstitial alloys

C lli I f i


33/62

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


34/62

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


35/62

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


36/62

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


37/62

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


38/62

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


39/62

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


40/62

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


41/62

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


42/62

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


43/62

Grain Boundaries

Twin Boundaries


44/62

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


45/62

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


46/62

Volume Defects

Volume defects: Cluster of point defects join to

form 3-D void.

Metallography: Technique of Observing Grain Boundaries


47/62

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


48/62

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


49/62

Effect of Etching

Unetched

Steel200 X

Etched

Steel200 X

Unetched

Brass

200 X

Etched

Brass

200 X

Virtual Lab Modules


50/62

Virtual Lab Modules


modules related to etching the specimen.

Virtual Lab Modules
http://localhost/var/www/apps/conversion/tmp/scratch_6/ETCHING.htm


51/62

Virtual Lab Modules


modules related to metallographic observation.

Grain Size
http://localhost/var/www/apps/conversion/tmp/scratch_6/brassmag.htm


52/62

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


53/62

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


54/62

Measuring ASTM Grain Size Number

Click the Image below to play the tutorial.

Average Grain Diameter
http://localhost/var/www/apps/conversion/tmp/scratch_6/Grain_size.html


55/62

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


56/62

Virtual Lab Module


modules related to grain size measurement.

Transmission Electron Microscope
http://localhost/var/www/apps/conversion/tmp/scratch_6/grainsize.htm


57/62

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.)


58/62

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


59/62

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


60/62

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.


61/62

Atomic Force Microscope


62/62

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.

Documents

Materials Ch4