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CHAPTER

4 Solidification

and Crystalline Imperfections

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Solidification of Metals

• Metals are melted to produce finished and semi-finished parts.

• Two steps of solidification  Nucleation : Formation of stable nuclei.  Growth of nuclei : Formation of grain structure.

• Thermal gradients define the shape of each grain.

Liquid

Nuclei

Crystals that will Form grains

Grain Boundaries

Grains

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Formation of Stable Nuclei

• Two main mechanisms: Homogenous and heterogeneous.

• Homogenous Nucleation :  First and simplest case.  Metal itself will provide atoms to form nuclei.  Metal, when significantly undercooled, has several slow

moving atoms which bond each other to form nuclei. Cluster of atoms below critical size is called embryo.  If the cluster of atoms reach critical size, they grow into

crystals. Else get dissolved.  Cluster of atoms that are grater than critical size are called

nucleus.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Energies involved in homogenous nucleation.

Volume free energy Gv

• Released by liquid to solid transformation.

• ΔGv is change in free energy per unit volume between liquid and solid.

• free energy change for a spherical nucleus of radius r is given by

Surface energy Gs

• Required to form new solid surface

• ΔGs is energy needed to create a surface.

• γ is specific surface free energy.

Then

• ΔGs is retarding energy.

γπ 2s 4G r=∆

vGrr ∆= 3

3 4

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Total Free Energy

• Total free energy is given by γππ 23 4 3 4

rGrG vT +∆=∆

Nucleus

Above critical radius r*

Below critical radius r*

Energy lowered by

growing into crystals

Energy Lowered by redissolving

VG r

∆ −=

γ2 *Since when r=r*, d(ΔGT)/dr = 0

r* r

ΔG

- ΔGv

ΔGs

ΔGT

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Critical Radius Versus Undercooling

• Greater the degree of undercooling, greater the change in volume free energy ΔGv

• ΔGs does not change significantly. • As the amount of undercooling ΔT increases, critical

nucleus size decreases. • Critical radius is related to undercooling by relation

TH T

r f

∆∆ =

γ2 *

r* = critical radius of nucleus γ = Surface free energy ΔHf = Latent heat of fusion Δ T = Amount of undercooling.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Homogenous Nucleation

• Nucleation occurs in a liquid on the surfaces of structural material. Eg:- Insoluble impurities.

• These structures, called nucleating agents, lower the free energy required to form stable nucleus.

• Nucleating agents also lower the critical size. • Smaller amount of undercooling is required to solidify. • Used excessively in industries.

Liquid

Solid

Nucleating agent

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Growth of Crystals and Formation of Grain Structure

• Nucleus grow into crystals in different orientations. • Crystal boundaries are formed when crystals join together

at complete solidification. • Crystals in solidified metals are called grains. • Grains are separated by grain boundaries. • More the number of

nucleation sites available, more the number of grains formed.

Nuclei growing into grains Forming grain boundaries

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Types of Grains

• Equiaxed Grains:  Crystals, smaller in size, grow equally in all directions.  Formed at the sites of high concentration of the nuclie.  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

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

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

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Iron Smelting: Video

• Please click on the following figure to open the video. (This video has voice).

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

YouTube videos

• http://www.youtube.com/watch?v=9l7Jq onyoKA (Steel making)

• http://www.youtube.com/watch?v=vWxs 7ZV5Ly8 (iron smelting)

• http://www.youtube.com/watch?v=wz4L dX6UJcE (crystal defects)

http://www.youtube.com/watch?v=9l7JqonyoKA

http://www.youtube.com/watch?v=vWxs7ZV5Ly8

http://www.youtube.com/watch?v=wz4LdX6UJcE

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Grain Structure in Industrial castings

• To produce cast ingots with fine grain size, grain refiners are added.

• Example:- For aluminum alloy, small amount of Titanium, Boron or Zirconium is added.

(a) (b)

Grain structure of Aluminum cast with (a) and without (b) grain refiners.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Solidification of Single Crystal

• For some applications (Eg: Gas turbine blades-high temperature environment), single crystals are needed.

• Single crystals have high temperature creep resistance. • Latent head of solidification is conducted through

solidifying crystal to grow single crystal. • Growth rate is kept slow so that temperature at solid-

liquid interface is slightly below melting point.

Growth of single crystal for turbine airfoil.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Czochralski Process

• This method is used to produce single crystal of silicon for electronic wafers.

• A seed crystal is dipped in molten silicon and rotated. • The seed crystal is withdrawn slowly while silicon

adheres to seed crystal and grows as a single crystal.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Metallic Solid Solutions

• Alloys are used in most engineering applications. • Alloy is an mixture of two or more metals and nonmetals. • Example:

 Cartridge brass is binary alloy of 70% Cu and 30% Zinc.  Iconel is a nickel based superalloy with about 10 elements.

• Solid solution is a simple type of alloy in which elements are dispersed in a single phase.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Substitutional Solid Solution

• Solute atoms substitute for parent solvent atom in a crystal lattice.

• The structure remains unchanged. • Lattice might get slightly distorted due to change in

diameter of the atoms. • Solute percentage in solvent

can vary from fraction of a percentage to 100%

Solvent atoms

Solute atoms

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Substitutional Solid Solution (Cont..)

• The solubility of solids is greater if  The radius of atoms not differ by more than 15%  Crystal structures are similar.  No much difference in electronegativity (else compounds will

be formed).  Have some valence.

• Examples:- System

Atomic radius

Difference

Electron- egativity

difference

Solid Solibility

Cu-Zn 3.9% 0.1 38.3%

Cu-Pb 36.7% 0.2 0.17%

Cu-Ni 2.3% 0 100%

W. Hume – Rothery Rule

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Interstitial Solid Solution

• Solute atoms fit in between the voids (interstices) of solvent atoms.

• Solvent atoms in this case should be much larger than solute atoms.

• Example:- between 912 and 13940C, interstitial solid solution of carbon in γ iron (FCC) is formed.

• A maximum of 2.8% of carbon can dissolve interstitially in iron.

Carbon atoms r=0.075nm

Iron atoms r00.129nm

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Crystalline Imperfections

• No crystal is perfect. • Imperfections affect mechanical properties,

chemical properties and electrical properties. • Imperfections can be classified as

 Zero dimension point deffects.  One dimension / line deffects (dislocations).  Two dimension deffects.  Three dimension deffects (cracks).

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Point Defects – Vacancy

• Vacancy is formed due to a missing atom. • Vacancy is formed (one in 10000 atoms) during

crystallization or mobility of atoms. • Energy of formation is 1 ev. • Mobility of vacancy results in cluster of

vacancies. • Also caused due

to plastic defor- -mation, rapid cooling or particle bombardment.

Vacancies moving to form vacancy cluster 21

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Point Defects - Interstitials

• Atom in a crystal, sometimes, occupies interstitial site.

• This does not occur naturally. • Can be induced by irradiation. • This defects caused structural distortion.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi



Equilibrium Concentration: Point Defects

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!

Courtesy: Callister et. al., Wiley productions

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Estimating Vacancy Concentration

• Find the equil. # of vacancies in 1 m3 of Cu at 1000°C. • Given:

ACu = 63.5 g/molρ = 8.4 g/cm 3

Qv = 0.9 eV/atom NA = 6.02 x 10 23 atoms/mol

For 1 m3, N = N

A A

ρ x x 1 m3= 8.0 x 1028 sites

= 2.7 x 10-4

8.62 x 10-5 eV/atom-K

0.9 eV/atom

1273 K

 Nv N

= exp −Qv kT



 



 

• Answer: Nv = (2.7 x 10-4)(8.0 x 1028) sites = 2.2 x 1025 vacancies

Courtesy: Callister et. al., Wiley productions

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Point Defects in Ionic Crystals

• Complex as electric neutrality has to be maintained. • If two appositely charged particles are missing, cation-

anion divacancy is created. This is scohttky imperfection. • Frenkel imperfection is created when cation moves to

interstitial site. • Impurity atoms are

also considered as point defects.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

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

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Edge Dislocation

• Created by insertion of extra half planes of atoms.

• Positive edge dislocation

• Negative edge dislocation

• Burgers vector Shows displa- cement of atoms (slip).

Burgers vector

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

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.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Mixed Dislocation

• Most crystal have components of both edge and screw dislocation.

• Dislocation, since have irregular atomic arrangement will appear as dark lines when observed in electron microscope.

Dislocation structure of iron deformed 14% at –1950C

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Planar Defects

• Grain boundaries, twins, low/high angle boundaries, twists and stacking faults

• Free surface is also a defect : Bonded to atoms on only one side and hence has higher state of energy Highly reactive

• Nanomaterials have small clusters of atoms and hence are highly reactive.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Grain Boundaries

• Grain boundaries separate grains. • Formed due to simultaneously growing crystals meeting

each other. • Width = 2-5 atomic diameters. • Some atoms in grain boundaries have higher energy. • Restrict plastic flow and prevent dislocation movement.

3D view of grains

Grain Boundaries In 1018 steel

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Twin Boundaries

• Twin: A region in which mirror image pf structure exists across a boundary.

• Formed during plastic deformation and recrystallization.

• Strengthens the metal.

Twin

Twin Plane

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Other Planar Defects

• Small angle tilt boundary: Array of edge dislocations tilts two regions of a crystal by < 100

• Stacking faults: Piling up faults during recrystallization due to collapsing.

 Example: ABCABAACBABC FCC fault

• Volume defects: Cluster of point defects join to form 3-D void.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Observing Grain Boundaries - Metallography

• To observe grain boundaries, the metal sample must be first mounted for easy handling

• Then the sample should be ground and polished with different grades of abrasive paper and abrasive solution.

• The surface is then etched chemically.

• Tiny groves are produced at grain boundaries.

• Groves do not intensely reflect light. Hence observed by optical microscope.

After M. Eisenstadt, “Introduction to Mechanical Properties of Materials,” Macmillan, 1971, p.126 34

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Virtual Lab Modules

• Click on the following figures to open the virtual lab modules related to polishing the specimen for Metallography.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Effect of Etching

Unetched Steel 200 X

Etched Steel 200 X

Unetched Brass 200 X

Etched Brass 200 X

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Virtual Lab Modules

• Click on the following figures to open the virtual lab modules related to etching the specimen.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Virtual Lab Modules

• Click on the following figures to open the virtual lab modules related to metallographic observation.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Grain Size

• Affects the mechanical properties of the material

• The smaller the grain size, more are the grain boundaries.

• More grain boundaries means higher resistance to slip (plastic deformation occurs due to slip).

• More grains means more uniform the mechanical properties are.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

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 grained 4 < n < 6 – Medium grained 7 < n < 9 – Fine grained N > 10 – ultrafine grained

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Measuring ASTM Grain Size Number

• Click the Image below to play the tutorial.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

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 to length of

line, nL is determined.

d = C/nLM C=1.5, and M is magnification

3 inches 5 grains.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Virtual Lab Module

• Click on the following figures to open the virtual lab modules related to grain size measurement.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Transmission Electron Microscope

• Electron produced by heated tungsten filament.

• Accelerated by high voltage (75 - 120 KV)

• Electron beam passes through very thin specimen.

• Difference in atomic arrangement change directions of electrons.

• Beam is enlarged and focused on fluorescent screen.

Collagen Fibrils of ligament as seen in TEM

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

TEM (..Cont)

• TEM needs complex sample preparation • Very thin specimen needed ( several hundred

nanometers) • High resolution TEM (HRTEM) allows

resolution of 0.1 nm. • 2-D projections of a crystal with accompanying

defects can be observed. Low angle boundary As seen In HTREM

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

The Scanning Electron Microscope

• Electron source generates electrons.

• Electrons hit the surface and secondary electrons are produced.

• The secondary electrons are collected to produce the signal.

• The signal is used to produce the image.

TEM of fractured metal end 46

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

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.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Scanning Tunneling Microscope

• Tip placed one atom diameter from surface. • Voltage applied across tip and surface. • Electrons tunnel the gap and produce current. • Current produced is proportional to change in

gap. • Can be used only for conductive materials.

Constant height and current modes Surface of platinum with defects 48

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Atomic Force Microscope

• Similar to STM but tip attached to cantilever beam.

• When tip interacts with surface, van der waals forces deflect the beam.

• Deflection detected by laser and photodetector.

• Non-conductive materials can be scanned.

• Used in DNA research and polymer coating technique.

Foundations of Materials Science and Engineering, 5th Edn. Smith and Hashemi

Definitions

Crystalline defect: a lattice irregularity having one or more of its dimensions on the order of an atomic diameter Nuclei: small particles of new phase formed by phase transformation or solidification. Grain: a single crystal of a polycrystalline material Polycrystalline material: a material made of many crystals or grains. Alloy: a mixture of two or more metals. Solid solution: a single phase atomic structure of an alloy of two metals. Substitutional solid solution: solute atoms of one element replace those of solvent atoms of other element occupying regular lattice positions. Interstitial solid solution: when solute atoms occupy interstitial sites or holes inside the solvent crystal lattice. vacancy: a point defect/imperfection in a crystal lattice where an atom is missing from a regular lattice site in a crystal structure. Self interstitial: is an atom from the crystal that is crowded into an interstitial site. Frenkel defect: a point defect in an ionic crystal in which a cation vacancy is associated with an interstitial cation. Schottky defect: a point defect in an ionic crystal in which a cation vacancy is associated with anion vacancy. Dislocation: a linear or one dimensional defect around which some of the atoms are misaligned. Edge dislocation: a linear defect that centers on the line that is defined along the end of extra half plane of atoms. Screw dislocation: a dislocation produced by skewing a crystal by one atomic spacing so that a spiral ramp is produced. Burger’s vector: a direction and distance that a dislocation moves in each step. Grain boundary: a surface or two dimensional defect that separates grains or crystals of different orientation. Twist boundary: an array of screw dislocations creating mismatch inside a crystal. Twin boundary: is a special type of grain boundary across which there is a specific mirror lattice symmetry. Phase boundary: exists in multiphase materials in which a different phase exists on each side of boundary. Stacking fault: a surface defect formed due to improper (out of plane) stacking of atomic planes. Microstructure: the grain size and shape of a material. Grain size: the average size of a grain of a material.

CHAPTER �4
Solidification of Metals
Formation of Stable Nuclei
Energies involved in homogenous nucleation.
Total Free Energy
Critical Radius Versus Undercooling
Homogenous Nucleation
Growth of Crystals and Formation of Grain Structure
Types of Grains
Casting in Industries
Iron Smelting: Video
YouTube videos
Grain Structure in Industrial castings
Solidification of Single Crystal
Czochralski Process
Metallic Solid Solutions
Substitutional Solid Solution
Substitutional Solid Solution (Cont..)
Interstitial Solid Solution
Crystalline Imperfections
Point Defects – Vacancy
Point Defects - Interstitials
Equilibrium Concentration: Point Defects
Estimating Vacancy Concentration
Point Defects in Ionic Crystals
Line Defects – (Dislocations)
Edge Dislocation
Screw Dislocation
Mixed Dislocation
Planar Defects
Grain Boundaries
Twin Boundaries
Other Planar Defects
Observing Grain Boundaries - Metallography
Virtual Lab Modules
Effect of Etching
Virtual Lab Modules
Virtual Lab Modules
Grain Size
Measuring Grain Size
Measuring ASTM Grain Size Number
Average Grain Diameter
Virtual Lab Module
Transmission Electron Microscope
TEM (..Cont)
The Scanning Electron Microscope
Scanning Probe Microscopy
Scanning Tunneling Microscope
Atomic Force Microscope
Definitions