Chap2 IBT

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Chapter 2

Overview on BasicMaterials’ Properties

Reference: William F. Smith, Javad Hashemi, 2006,

“Foundations of Materials Science and Engineering”,

4th ed., McGraw-Hill

Only for Teaching

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• Metallic Materials

---Inorganic and have crystalline structure.

---Good thermal and electric conductors.

• Polymeric (Plastic) Materials

Organic giant molecules and mostly noncrystalline.

Some are mixtures of crystalline and noncrystalline regions.

Poor conductors of electricity and hence used as insulators.

Strength and ductility vary greatly.

Low densities and decomposition temperatures.

Examples :- Poly vinyl Chloride (PVC), Polyester.

Applications :- Appliances, DVDs, Fabrics etc.

Materials’ Categories

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• Ceramic Materials Metallic and nonmetallic elements are chemically

bonded together.

Inorganic but can be either crystalline, noncrystallineor mixture of both.

High hardness, strength and wear resistance.

Very good insulator. Hence used for furnace lining for

heat treating and melting metals.

Also used in space shuttle to insulate it during exit and

reentry into atmosphere.

Other applications : Abrasives, construction materials,utensils etc.

Example:- Porcelain, Glass, Silicon nitride.


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• Composite MaterialsMixture of two or more materials.

Consists of a filler material and a binding material.

Materials only bond, will not dissolve in each other.Mainly two types :-

---Fibrous: Fibers in a matrix

---Particulate: Particles in a matrix

---Matrix can be metals, ceramic or polymer

Examples :-

Fiber Glass ( Reinforcing material in a polyester orepoxy matrix)

Concrete ( Gravels or steel rods reinforced in cementand sand)

Applications:- Aircraft wings and engine, construction.


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Electronic Materials

Not Major by volume but very important.

Silicon is a common electronic material.

Its electrical characteristics are changed by adding impurities.

Examples:- Silicon chips, transistors

Applications :- Computers, Integrated Circuits, Satellites etc.

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• Atoms, arranged in repetitive 3-Dimensional pattern, in long rangeorder (LRO) give rise to crystal structure.

• Properties of solids depends upon crystal structure and bonding

force.

• An imaginary network of lines, with atoms at intersection of lines,

representing the arrangement of atoms is called space lattice.

Unit Cell

Space Lattice• Unit cell is that block of

atoms which repeats itself

to form space lattice.

• Materials arranged in

short range order are

called amorphous materials

Space Lattice & Unit Cells

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• Only seven different types of unit cells are

necessary to create all point lattices.

• According to Bravais (1811-1863) fourteenstandard unit cells can describe all possible lattice

networks.

• The four basic types of unit cells are Simple

Body Centered

Face Centered

Base Centered

Crystal Systems and Bravais Lattice

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• Cubic Unit Cell• a = b = c

• =β =γ = 90

• Tetragonal

• a =b c• =β =γ = 90

Simple Body Centered Face centered

Simple Body CenteredRef: W.G. Moffatt, G.W. Pearsall, & J. Wulff,

“The Structure and Properties of Materials,” vol. I: “Structure,” Wiley, 1964, p.47.)

Unit Cells

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• Orthorhombic• a b c

• =β =γ = 90

• Rhombohedral• a =b = c

• =β =γ 90

Simple Base Centered

Face Centered Body Centered

Simple

Unit Cells

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• Hexagonal

a = b =a c

=β = 900,γ = 1200

• Monoclinic

a b c

=γ = 900,β 900

• Triclinic a b c

β γ 900

Simple

Simple

Simple

BaseCentered

Unit Cells

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• Determine direction indices of the given vector.Origin coordinates are (3/4 , 0 , 1/4).

Emergence coordinates are (1/4, 1/2, 1/2).

Subtracting origin coordinates

from emergence coordinates,

(3/4 , 0 , 1/4) - (1/4, 1/2, 1/2)= (-1/2, 1/2, 1/4)

Multiply by 4 to convert all

fractions to integers

4 x (-1/2, 1/2, 1/4) = (-2, 2, 1)

Therefore, the direction indices are [ 2 2 1 ]

Direction Indices

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• Miller Indices are used to refer to specific latticeplanes of atoms.

• They are reciprocals of the fractional intercepts (with

fractions cleared) that the plane makes with the

crystallographic x,y and z axes of three nonparallel

edges of the cubic unit cell.

Miller Indices =(111)

Miller Indices

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• Metals exist in more than one crystalline form. This iscalled polymorphism ( 質形體) or allotropy ( 素異形體).

• Temperature and pressure leads to change in crystalline

forms.

• Example:- Iron exists in both BCC and FCC form

depending on the temperature.

-2730C 9120C 13940C 15390C

Iron

BCC

γ Iron

FCC

δ

Iron

BCC

Liquid

Iron

Polymorphism or Allotropy

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• Crystal planes of target metal act asmirrors reflecting X-ray beam.

• If rays leaving a set of planes

are out of phase (as in case of

arbitrary angle of incidence)

no reinforced beam isproduced.

• If rays leaving are in phase,

reinforced beams are

produced.

X-Ray Diffraction

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• For rays reflected from different planes to be in phase, the extradistance traveled by a ray should be a integral multiple of wave

lengthλ .

nλ

= MP + PN (n = 1,2…)

n is order of diffraction

If dhkl is interplanar distance,

Then MP = PN = dhkl

.Sinθ

Therefore, λ

= 2 dhkl.Sinθ

Ref: A.G. Guy and J.J. Hren, “Elements of Physical Metallurgy,” 3d ed., Addison-Wesley, 1974, p.201.)

XRD

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λ

= 2 dhkl.Sinθ

H-Y Chang et al, Nanotechnology 14 (2003) 603–608

Example of XRD

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• Solute atoms substitute for parent solvent atom in acrystal 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

Substitutional Solid Solution

S b i i l S lid S l i

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• The solubility of solids is greater if The diameter of atoms not differ by more than 15%

Crystal structures are similar.

No much difference in electronegativity (else compoundswill be formed).

Have some valence.

• Examples:-

System

Atomic

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%

Substitutional Solid Solution

I i i l S lid S l i

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

• Solvent atoms in this case should be much larger than

solute atoms.• Example:- between 912 and 13940C, interstitial solid

solution of carbon inγ iron (FCC) is formed.

• A maximum of 2.8%of carbon can dissolve

interstitially in iron.

Carbon atoms r=0.075nm

Iron atoms r=0.129nm

Interstitial Solid Solution

C t lli I f ti

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Crystalline Imperfections

• No crystal is perfect.

• Imperfections affect mechanical properties,

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

Zero dimension point defects.

One dimension / line defects (dislocations). Two dimension defects (planar defects).

Three dimension defects (cracks).

P i t D f t V

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• 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 deformation,

rapid cooling or particle

bombardment.

Point Defects – Vacancy

Figure: Vacancies moving to form vacancy cluster

P i t D f t I t titi ll

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

• This does not occur naturally.

• Can be induced by irradiation.

• This defects caused structural distortion.

Point Defects - Interstitially

Point Defects in Ionic Cr stals

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• Complex as electric neutrality has to be maintained.

• If two oppositely charged particles are missing, cation-

anion divacancy is created. This is Schottky imperfection.

• Frenkel imperfection is created when cation moves tointerstitial site.

• Impurity atoms are

also considered as

point defects.

Point Defects in Ionic Crystals

Dislocations

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＊Line Defects (Dislocations)—

＊Edge Dislocation---

＊Screw Dislocation---

＊Mixed Dislocation---

Dislocations

Grain Boundaries (GB)

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• 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

(ref:A.G. Guy, “ Essentials of materials Science,” McGraw-Hill, 1976.)

Grain Boundaries (GB)

Planar Defects

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• Grain boundaries, twins, low/high angleboundaries, 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.

Planar Defects

Atomic Diffusion in Solids

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• Diffusion is a process by which a matter is

transported through another matter.

• Examples:

---Movement of smoke particles in air : Very fast.

---Movement of dye in water : Relatively slow.

---Solid state reactions : Very restricted movement due

to bonding.

Atomic Diffusion in Solids

Diffusion mechanism

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• Atoms diffuse in solids if

Vacancies or other crystal defects are present

There is enough activation energy

• Atoms move into the vacancies present.

• More vacancies are created at higher temperature.

• Diffusion rate is higher at high temperatures.

Diffusion mechanism

Substitutional Diffusion

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• Example: If atom ‘A’

has sufficient activation

energy, it moves into the

vacancy self diffusion.

• As the melting point increases, activation energy also

increases

Activation

Energy of

Self diffusion

Activation

Energy to

form a

Vacancy

Activation

Energy to

move a

vacancy

= +

Substitutional Diffusion

Interstitial Diffusion mechanism

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• Atoms move from one

interstitial site to another.

• The atoms that move mustbe much smaller than the

matrix atom.

• Example:

Carbon interstitially

diffuses into BCC or FCC

γ

iron. Interstitial atomsMatrix

atoms

Interstitial Diffusion mechanism

Steady State Diffusion

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• There is no change in concentration of solute atoms atdifferent planes in a system, over a period of time.

• No chemical reaction occurs. Only net flow of atoms.

C1

C2

Net flow of atoms

Per unit area per

Unit time = J

Solute atom flow

Diffusing

atoms

Unit

Area

Concentration

Of diffusing

atoms

Distance x

Steady State Diffusion

Fick’s First Law

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• The flux or flow of atoms is given by

• i.e. for steady state diffusion condition, the net flow ofatoms by atomic diffusion is equal to diffusion D times

the diffusion gradient dc/dx .

• Example: Diffusivity of FCC iron at 500oC is 5 x 10-15

m2 /s and at 1000oC is 3 x 10-11 m2 /s

dx

dc

D J −=

J = Flux or net flow of atoms.

D = Diffusion coefficient.

dx

dc= Concentration Gradient.

Fick s First Law

Diffusivity

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• Diffusivity depends upon

Type of diffusion : Whether the diffusion is

interstitial or substitutional.

Temperature: As the temperature increasesdiffusivity increases.

Type of crystal structure: BCC crystal has lower

APF than FCC and hence has higher diffusivity.

Type of crystal imperfection: More open

structures (grain boundaries) increases diffusion.

The concentration of diffusing species: Higher

concentrations of diffusing solute atoms will affectdiffusivity.

Diffusivity

Non-Steady State Diffusion

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• Concentration of solute atoms at any point in metalchanges with time in this case.

• Fick’s second law:- Rate of compositional change is

equal to diffusivity times the rate of change ofconcentration gradient.

⎟⎟ ⎠

⎞

⎜⎜⎝

⎛

= dx

dc

Ddx

d

dt

dC x x

Plane 1 Plane 2

Change of concentration of solute

Atoms with change in time in different planes

No Steady State us o

Fick’s Second Law

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• Cs = Surface concentration ofelement in gas diffusing

into the surface.

• C0 = Initial uniform concentrationof element in solid.

• Cx = Concentration of element at

distance x from surface at

time t1.

• x = distance from surface

• D = diffusivity of solute

• t = time.

Distance x

C0

Cx

Cs

Time = t2

Time= t1

Time = t0

x

⎟⎟ ⎠ ⎞⎜⎜

⎝ ⎛ =

−−

t s

xs

D xerf

C C C C

20

Phase Diagrams

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g

• Phase: A region in a material that differs in structureand function from other regions.

• Phase diagrams:

Represents phases present in metal at different conditions(Temperature, pressure and composition).

Indicates equilibrium solid solubility of one element in

another.

Indicates temperature range under which solidification

occurs.

Indicates temperature at which different phases start to

melt.

Phase Diagram of Pure Substances

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g

• Pure substance exist as solid, liquid and vapor.• Phases are separated by phase boundaries.

• Example : Water, Pure Iron.

• Different phases coexist at triple point.Ref: W. G. Moffatt, et al., “The Structure and Properties of Materials,” vol I: “Structure,” Wiley, 1965, p.151

Phase Rule

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• P+F = C+2

• For pure water, at triple point, 3 phases coexist.

• There is one component (water) in the system.

• Therefore 3 + F = 1 + 2 F = 0.• Degrees of freedom indicate number of variables that

can be changed without changing number of phases.

P = number of phases that coexist in a system

C = Number of components

F = Degrees of freedom

Phase Diagram from Cooling Curves

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g g

• Series of cooling curves at different metal compositionare first constructed.

• Points of change of slope of cooling curves (thermal

arrests) are noted and phase diagram is constructed.

• More the number of cooling curves, more accurate is

the phase diagram.

The Lever Rule

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• The Lever rule gives the weight % of phases in anytwo phase regions.

Wt fraction of solid phase

= Xs = w0 – w1

ws – w1

Wt fraction of liquid phase

= X1 = ws – w0

ws – w1

Iron Carbide Phase Diagram

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• Plain carbon steel: 0.03% to 1.2% C, 0.25 to 1% Mn andother impurities.• α

Ferrite: Very low solubility

of carbon. Max 0.02 % at 7230

Cand 0.005% at 00C.

• Austenite: Interstitial solid

solution of carbon inγ

iron. Solubility of C is

2.08% at 11480C and 0.8%

at 00C.

• Cementite: Intermetallic compound.

6.67% C and 93.3% Fe.

Binary Eutectic Alloy System

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• In some binary alloy systems, components have limited

solid solubility.

• Eutectic composition freezesat lower temperature than all

other compositions.

• This lowest temperature is

called eutectic temperature.

Liquid

solid solution +β

solid solution

Eutectic temperature

Cooling

Example : Pb-Sn alloy.

Intermediate Phases and Compounds

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• Terminal phases:Phases occur at the endof phase diagrams.

• Intermediate phases:Phases occur in acomposition range insidephase diagram.

• Examples: Cu-Zndiagram has bothterminal andintermediate phases.

• Five invariant peritecticpoints and one eutecticpoint.

Intermediate Phases in Ceramics

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• In Al2O

2– SiO

2system, an intermediate phase called

Mullite is formed, which includes the compound

3Al2O3.2SiO2.

Ref: A. G. Guy, “Essentials of Materials Science, “McGraw-Hill, 1976

Ternary Phase Diagrams

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• Three components

• Constructed by using a equilateral triangle (等邊三角形)

as base.

• Pure components at eachend of triangle.

• Binary alloy composition

represented on edges.

Temperature can be

represented as uniform

throughout the

Whole Diagram -----

Isothermal section.

Ternary Phase Diagram

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• Example:- Iron-Chromium-Nickel phase diagrams.

•Isothermal reaction at 6500C

for this system

• Composition of any metal

at any point on the phase

diagram can be found by

drawing perpendicular

from pure metal corner to

opposite side and calculatingthe % length of line at that

point

Ref: “Metals Handbook,” vol. 8: American Society of Metals, 1973, p. 425.

Ceramics

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• Ceramics are inorganic and nonmetallic.• Bounded by ionic or covalent bonds.

• Good electrical and heat insulation property.

• Brittle, and lesser ductility and toughness than

metals.

• High chemical stability and high melting

temperature.

• Traditional Ceramics: Basic components (Clay and

Silica).

• Engineering Ceramics: Pure compounds (Al2O3,

SiC).

Zinc Blende (ZnS) Crystal Structure

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• Four zinc and four sulfur atoms.• One type (Zn or S) occupies lattice points and another

occupies interstitial sites of FCC unit cell.

• S Atoms (0,0,0) ( ½ ,½ ,0) ( ½ , 0, ½ ) (0, ½ , ½ )Zn Atoms ( ¾ ,¼ ,¼ ) ( ¼ ,¼ ,¾ )( ¼ ,¾,¼ ) ( ¾ ,¾ ,¾ )

• Tetrahedrally covalently bonded

• (87% covalent character) with

CN = 8.

• CdS, InAs, InSb and ZnSe have

similar structures.

ref: W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976.

Important Crystal Structures

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• Perovskite (CaTiO3) : Ca2+

and O

2-

ions form FCC unitcell.

Ca2+ Ions occupy corners

O2-

Ions occupy face centers. Ti4+ ions are at octahedral

sites.

• Graphite : Polymorphic formof compound.

• Layered structure with carbon

atoms in hexagonal arrays.

• Good lubricating properties.

Ref: W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976.

Silicate Structures

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• Silicate (SiO44-

) is building block of silicates.• 50% ionic and 50% covalent.

• Many different silicate structures

can be produced.• Island structure: Positive ions

bond with the oxygen of SiO44-

tetrahedron.

• Chain/ring structure: Two

corners of each SiO44- tetrahedron

bonds with corners of other

tetrahedron.

Ref: M. Eisenstadt, “Mechanical properties of Materials,” Macmillan, 1971, p.82.

Sheet Structures of Silicates

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• Sheet structure: Three corners of same planes of silicatetetrahedron bonded to the corners of three other silicatetetrahedra.

• Each tetrahedron has oneunbounded oxygen and hence

chains can bond with other

type of sheets.• If the bondings are weak,

sheets slide over each other

easily.

Ref: M. Eisenstadt, “Mechanical properties of Materials,” Macmillan, 1971, p.83.

Silicate Networks

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• Silica: All four corners of the SiO44-

tetrahedra shareoxygen atoms.

• Basic structures: Quartz, tridymite and cristobalite.

• Important compound of many ceramic and

glasses.

• Feldspars: Infinite 3D

networks.

• Some Al3+ Ions replace

Si4+ Ions Net negative charge.

• Alkaline and alkaline fit into interstitial sites.

Ref: W. D. Kingery, H. K. Bowen, D. R. Uhlmann, “ Introduction to Ceramics,”2nd ed., Wiley, 1976.

Traditional Ceramics

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• Made up of clay, silica and feldspar.• Clay: Provide workability and hardness.

• Silica: Provide better temperature resistance and MP.

• Potash Feldspar: Makes glass when ceramic is fired.

Source: F. Norton, Elements of Ceramics, 2nd ed., Addision-Wesley,1974, p.140.

Quartz

grain High-silica

glass

SEM of Porcelain

Engineering Ceramics

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• Alumina (Al2O3): Aluminum oxide is doped withmagnesium oxide, cold pressed and sintered. Uniform structure. Used for electric applications.

• Silicon Nitride (Si3 N4): Compact of silicon powder isnitrided in a flow of nitrogen gas.

Moderate strength and used for parts of advanced engines.

• Silicon Carbide (SiC): Very hard refractory carbide,sintered at 21000C.

Used as reinforcement in composite materials.

• Zirconia (ZrO2): Polymorphic and is subject to cracking. Combined with 9% MgO to produce ceramic with high

fracture toughness.

Electrical Properties

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• Basic properties of dielectric: Dielectric constant:-

Q = CV

Q = Charge

V = Voltage

C = CapacitanceC =ε0A/d ε0 = permittivity of free space

= 8.854 x 10-12 F/m

• When the medium is not free spaceC = K ε0A/d Where K is dielectric constant of the

material between the plates

Dielectric Strength and Loss Factor

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• Dielectric strength is measure of ability of material to holdenergy at high voltage.

Defined as voltage gradient at which failure occurs.

Measured in volts/mil. 1 mil=(1/1000) in=25 μm• Dielectric loss factor: Current leads voltage by 90 degrees

when a loss free dielectric is between plates of capacitor.

• When real dielectric is used, current leads voltage by 900 –δ

whereδ is dielectric loss angle.

• Dielectric loss factor = K tanδ

measure of electric

energy lost.

Ceramic Materials for Capacitors

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• Ceramics are used as dielectric materials for capacitors.

• Example: Disk ceramic capacitors.

BaTiO3

+ additive

Very high dielectric

constant

Used in ceramic basedthick film hybrid

electronic circuit

Higher capacitance per unit area

Ceramic Semiconductors

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• Ceramics can be used as semiconducting materials.

• Thermistor: Thermally sensitive resistor.

• NTC thermistor: Conductivity raises with temperature.

• Solid solution oxides of Mn, Ni, Fe, Co and Cu are used to

obtain necessary property ranges.

• By combining low conducting metal oxide with lowconducting oxides intermediate properties are obtained.

• Example: Conductivity of Fe3O4 is reduced gradually by

adding increasing amounts in solid solution of MgCr 2

O4

Thermal Properties of Ceramics

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• Low thermal conductivity and high heatresistance.

• Many compounds are used as industrial

refractories.

• For insulating refractories, porosity is desirable.

• Dense refractories have low porosity and highresistance to corrosion and errosion.

• Aluminum oxide and MgO are expensive and

difficult to form and hence not used as refractories.

Insulation for Space Shuttle Orbital

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• About 70% of external surface is protected from heat by24000 ceramic tiles.

• Material: Silica fiber compound.

• Density is 4kg/ft3

and withstands temperature up to 12600

C.

Oxidation – Reduction Reactions

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• A metal (e.g. – Zn) placed in HCl undergoes corrosion.

Zn + 2HCl ZnCl2 + H2

or Zn + 2H+ Zn2+ + H2

also

Zn Zn 2+ + 2e- (oxidation half cell reaction)2H+ + 2e- H2 (Reduction half cell reaction)

• Oxidation reaction: Metals form ions at local anode.

• Reduction reaction: Metal is reduced in local charge atLocal cathode.

• Oxidation and reduction takes place at same rate.

Macroscopic Galvanic Cells with 1M Electrolyte

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•Two dissimilar metal electrodes immersed in

solution of their own ions.

• Electrode that has more

negative oxidation potential

will be oxidized.

Zn Zn2+, Cu2+ Cu

Half cell reactions are

Zn Zn 2+ + 2e- E0 = -0.763 V

Cu Cu2+ + 2e- E0 = + 0.337 V

Or Cu2+ + 2e- Cu E0 = -0.337 V (negative sign)

Adding two reactions,

Zn + Cu2+ Zn2+ + Cu E0

cell

= -1.1V

Galvanic Cells With Electrolytes not 1M

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• If the concentration of electrolyte surrounding anode isnot 1 molar, driving force for corrosion is greater.

• There will be more negative emf half cell reaction

M Mn+ + ne-

• Nernst Equation:

ionC n

E E log0592.00 +=

E = Net emf of half cellE0 = Standard emf of half cell

n = Number of electrons transferred

Cion = Molar concentration of ions.

Galvanic Cells With Acid or Alkaline Electrolytes

C id i d l d i idi l l

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• Consider iron and copper electrodes in acidic electrolyte.• Since standard electrode potential of Fe to oxidize is

–0.44 , compared to 0.337 of copper,

Fe Fe2+

+ 2e-

• Since there are no copper ions to reduce

2H+

+ 2e-

H2• If electrolyte contains oxidizing agent

O2 + 4H+ + 4e- 2H2O

• If electrolyte is neutral or basic,O2 + 2H2O + 4e

- 4OH-

Ref: J. Wulff et al., “ The Structure and Properties of Materials,” vol. II, Wiley, 1964, p.164.

Grain – Grain boundary Electrochemical cells

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• Grain boundaries are more anodic and hence get corroded by electrochemical attack.• Grain boundaries are at higher energy.

• Impurities migrate to grain boundaries.• Solute segregation might cause grain boundaries to

become more cathodic.

Cartridge Brass

GrainBoundary

Grain boundary

(anode)

Grain boundary

(cathode)

anode

Chap2 IBT

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