407 class notes

8/2/2019 407 Class Notes

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Classification of Materials

Most materials can be broadly classified into three main groups: metalsceramics and polymers. In addition, modern engineering materials includecomposites, semiconductors, and biomaterials.

Metals-- normally combinations of metallic elements (alloys), e.g. Cu/Zn and

Pb/Sn.-- optically opaque-- strong and ductile

-- good electrical and thermal conductors--

.

Ceramics-- compounds of metallic and non-metallic elements, e.g. oxides and

car es-- can be optically transparent-- hard and brittle-- heat and corrosion resistant-- structural and functional applications

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Polymers

-- or anic com ounds of carbon h dro en and other non-metallic

elements, e.g. polyethylene and polystyrene-- low density, flexible and formable-- resistant to chemical attack--

Composites-- composed of more than one material type, e.g. glass fiber in a polymer

ma r x.-- combines best characteristics of each of the component materials

-- high specific strength and fracture resistant-- mainl structural a lications

Semiconductors-- electrical properties intermediate between conductors and insulators

-- proper es ex reme y sens ve o m nu e races o mpur y e emen s, e.g.P and B in Si-- vapor processing of thin planar arrays of doped-Si forms the basis of the

integrated circuit industry

-- unc ona app ca ons

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oma er a s-- materials that are non-toxic when implanted in the human body

-- used for replacement of diseased or damaged body parts, e.g. hip

Current Materials Challenges

-- re uce energy use n ranspor a on sys ems y eve op ng owcost, high performance structural composites for weight reduction,

and (2) ceramic engines for increased operating efficiency.--

,as wind turbines and solar cells.

-- improve quality of the environment by (1) developing cleanermaterials refining and processing technologies, and (2) increasing

recycling efforts.-- develop nanostructured materials and technologies for the next

generation of miniaturized engineered systems.

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Atomic Bonding in Solids

A.Primary Bonds

Strong bonds (~100 kcal/mol) arising from transfer or sharing ofvalence electrons.

1. Ionic bond

-- transfer of valence electrons-- electron localization (ionic species)-- non-directional bonding

-- NaCl, ZnO, Li2O, etc.-- ex rem es o er o c a e

2. Covalent bond

---- partial electron delocalization (molecular unit)-- hybridization of electron orbitals-- highly directional bonding-- H2, H2O, CH4, graphite, diamond, fullerene, etc.

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3. Metallic bond

-- complete sharing of valence electrons (free electron gas)-- comp e e e ec ron e oca za on-- non-directional bonding-- no valency restrictions (alloying)-- Fe, Cu, Fe-Ni, Cu-Zn, etc.

B. Secondary BondsWeak bonds (~1 kcal/mol) arising from dipole interactions.

molecules

1. Permanent dipole-- arises when centers of ositive and ne ative char e in amolecule do not coincide

-- directional-- asymmetric polar molecules, such as H2O, H2S, NH3, CF2H2,

etc.

2. Induced dipole-- arises from permanent dipole in one molecular group inducing

a dipole in a neighboring group-- rec ona

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3. Fluctuating dipole

-- arises from fluctuating charge distribution (no permanent dipole)-- non-directional-- , , 4, 4,

C. Hydrogen BondIntermediate bond (~5 kcal/mol)

-- arises when H atom forms a bridge between two electronegativeatoms

-- highly directional-- n lon cellulose etc.

D. Addition (or Chain) PolymerizationPolymerization consists of joining a large number of molecules together

-- ro en ou e on g ves wo car on or a s or on ng-- directional-- chain-like structure that is called a polymer-- ol eth lene ol st rene etc.

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Schematics of Secondary Bonds

(a) Electrically symmetric atom(b) Induced atomic dipole

H dro en bondin in h dro enfluoride (HF)

Polar hydrogen chloride (HCl)molecule

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Ionic Bond

This is easiest to visualize:-- results from strong electrostatic attraction between

oppositely charged ions-- stable ionic aggregates due to ions with filled outer

shells-- non-directional bonding permits close packing-- combination of elements with low ionization energy

(e.g. Na) and high electron affinity (e.g. Cl)

Ionization Energy is the energy required to remove the least tightly bound

Electron affinity is the energy released when an electron is captured byan atom (forms negative ion).

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Figure 1 An example of an ionic bond showing electron transfer

rom a o o orm a ca on an-

an on pa r.

The ionization energy of Na Na+ is 5.14 eV, whereas the electronaffinit of Cl Cl- is 4.02 eV. Hence the net ener work re uiredto create a pair of isolated Na+ and Cl- ions is 1.12 eV.

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-

separation distance x0. Note the approximately linear slope of the total force

curve in the vicinity of x0. (b) The bond-energy curve for the ionic compound

NaCl showing the location of the equilibrium separation distance x0.

Interaction Energy

1 2

distance r.

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The interaction energy E is the sum of two terms: attractive energy EA and repulsive

energy ER

E = EA + ER(attractive) (repulsive)

= (1)

(negative) (positive)

no

21

rr4+

o is permittivity of vacuum, b and n are constants, which depend on iontype; n ~ 8-10.

0dE =dr

rr=

0nbQQ

dr

dE)1n(2

21 ==+

Rearranging terms

b1n

0 *)r(*r4n+=

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Now from (1)

(3)n

0

21

b*)r(

b

*r4E +

=

Substituting (2) in (3)

=

11

QQE 21b

Cohesive Ener

nr0

Figure 3A unit cell for the rock salt, or

sodium chloride (NaCl) crystal structure.


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Na+ ion has 6 first nearest neighbor Cl- ions at r*.

Na+ ion has 12 second nearest neighbor Na+ ions at 2 r*.etc.

By summing the contributions from all ions, it can be shown that theco es ve energy mo s

=

11

*

AQQNE 21

where N is Avogadros number, and A is the Madelung constant, which

depends on structure type.

0

For NaCl, one electronic charge is involved in transfer of valence electron;hence Q1 Q2 = (+e) (-e) = -e2

=n

11

*r4

ANeE

0

2

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Substance A r*() n Cohesive energy(kcal/mol)

*

a+ -

Zn++O--.

1.64.

1.97 8 964

divalent ions.

Since Q1Q2 = (-2e) (+2e) = - 4e2 for ZnO, the cohesive energy/mol is at least fourmes a o a .

Coordination number is defined as number of nearest neighbors at the bond.

-- NaCl has CN = 6

-- other ionic crystals have different values, e.g. CsCl has CN = 8

-- determined by relative size of anion and cation

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Ionic Radius is defined as the radius of the hard sphere that represents the

ion.-- radius of anion is usually larger than that of the neutral

atom.

-- radius of cation is usuall smaller than that of the neutralatom.

Element Charge at Ionic radius Atomic

Sodium +1 0.98 1.86or ne

MagnesiumOxygen

-+2-2

.0.781.32

.1.590.60

CN = 6

Consider NaCl structure (see Table 1), where each Na+ cation is surrounded- .

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R = ionic radius of anion Cl-

RC = ionic radius of cation (Na+)

AACA R22R8)RR(2 ==+

[ ] 2A2

A2

CA )R2()R2()RR(2 +=+

AC R12R =

414.012RC ==A

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This is the smallest value of RC/RA for which all 6 anions touch the cation,

called the critical radius ratio.-- larger values allowed

-- smaller values not allowed

Figure 4 Stable and unstable anion-cation coordination

represent cations.

CN = 4

Consider ZnS structure (see Table 1), where each Zn2+ cation (0.83) issurrounded by four S2- anions (1.74) at the bond distance.

2RR CA =+2R2 A =

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Table 1. The critical (r/R) ratio foreach coordination number.

( )23 =

CR

== 0.2250.22516RC =2RA

Note that for crystals havingequal numbers of anions

,of 2, 3, 4, 6, 8 and 12 satisfysymmetry requirements.

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Crystal Structures

We have examined the forces responsible for aggregation of atoms ormolecules. Now we will consider how they are organized or distributed in

Periodic arrays crystalline materialsRandom arrays amorphous materials

Crystal lattice is defined as an array of points, infinite in extent, in whichevery po n as en ca surroun ngs.

Unit cell is the smallest re ion that com letel defines the cr stal lattice

-- vertices of unit cell are known as lattice points-- lengths of unit cell are known as lattice parameters

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Figure 5 Possible unit cells for a 2-D space lattice: (a)

square, (b) rectangle, and (c) parallelogram.

There are 14 possible arrangements for 3-D lattices, which areknown as Bravais lattices. These can be grouped into 7 crystalsystems, based on edge lengths of unit cell (unit vectors) and theangles between them.

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Figure 6 The 14 Bravais lattices grouped into the 7 crystal systems. Therestrictions on the lattice parameters a, b, and c and the angles between

the edges of the unit cell, , andare listed for each unit cell. 21


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Miller Indices

os common conven on use o eno e po n s, rec ons, an p anesin crystal lattices

PointsRight-hand Cartesian coordinate

points, e.g. 1,0,0.

Directions

Specific directions denoted bysquare brackets, e.g. [111].Families of directions denotedby angle brackets, e.g.

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Angle between directions [h1k1l1] and [h2k2l2] is given by:

)kh()kh(

)kkhh(cos

222222

212121

ll

ll

++++

++=

Planes

Defined as the reciprocals of the intercepts on coordinate axes

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, . . ., . . .

Families of planes denoted byFamilies of planes denoted by bracesbraces, e.g. {111}., e.g. {111}.24


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Structures of MetalsThree main types:

-- body centered cubic (bcc)

-- face centered cubic (fcc)

-- hexa onal close acked hc

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cc an cp s ruc ures orme y eren s ac ng sequences o c ose-pac eplanes.

ABABABA.hcp Both have

.

Figure 7 Close packed stacking sequence (ABCABCA) for fcc structure26


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Figure 8 Close packed stacking sequence (ABABABA) for

hc structure.

Density=

26.98; a = 4.04 x 10-8 cm; A0 = 6.02 x 1023 mol-1

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23

24cm/g72.2

10x94.65.

v===

c ua measure ens y s . g cm

Calculate packing factor (PF) for bcc, fcc and hcp structures.

(PF = volume of atoms/volume of unit cell)

bcc structure

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3

0

3

34

2a

r

PFbcc

=

3

Sinceao =3

r

0.68== 8

bcc

fcc structure

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3

3

fcca

r3

4

4PF

=

2

r4Since a0 =

=

=23

PF fcc 0.74

hc structure

Same as for fcc, since both structures are ideally close-packed, withCN = 12.

PF hcp = 0.74

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Interstitial Sites

The locations of the largest holes in bcc, fcc and hcp structures areknown as interstitial sites

fcc structure

Largest hole in an fcc structure is located at the center of the unit cell.-- known as an octahedral site, since the polyhedron connecting

nearest neighbor atoms has 8 sides-- there are 12 equivalent octahedral sites located at edge

centers of the unit cell-- each edge site is shared by four unit cells, hence there are 4 =

[(12 x ) + (1 x 1)] octahedral sites per unit cell-- if hole radius is k, then the radius ratio k/r = 0.414-- hence atoms about 40% of the size of the host atoms can fit

into octahedral sites

The fcc structure also contains tetrahedral sites, located at , , -type

-- there are 8 equivalent tetrahedral sites that lie completelywithin the unit cell

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-- the radius ratio, k/r, for a tetrahedral site is 0.225

-- ence, a oms a ou o e s ze o e os a oms can n otetrahedral sites

Thus, there are twice as many tetrahedral sites as octahedral sites, andeac e ra e ra s e s a ou one- a e ame er o an oc a e ra s e.

bcc structure

This structure also contains both octahedral and tetrahedral sites-- octahedral sites are located at face centers and edge centers of

the unit cell, giving a total of 6 sites per unit cell and k/r = 0.155.-- e ra e ra s es are oca e a , , ype pos ons, g v ng atotal of 12 tetrahedral sites per unit cell and k/r = 0.291.

Thus, there are twice as many tetrahedral sites as octahedral sites, and

each tetrahedral site is about twice the diameter of an octahedral site.

hcp structure

Similar to fcc, as indicated in Table 2.

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Table 2. The size and number of tetrahedral and octahedral interstitial

sites in the BCC, FCC, and HCP crystal structures. The sizes of the

interstitial sties are given in terms of the radius ratio (k/r) where k is the

radius of the largest atom that can fit into the interstitial position and ris the radius of the host atoms. The number of interstitial sites is given in

number of sites per host atom.

Structure

tetrahedralsites

octahedralsites

tetrahedral sitesper unit cell (perhost atom)

octahedral sitesper unit cell (perhost atom)

BCCFCCHCP

k/r = 0.291k/r = 0.225k/r = 0.225

k/r = 0.155k/r = 0.414k/r = 0.414

12 (6)8 (2)12 (2)

6 (3)4 (1)6 (1)

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Figure 9 The locations of the interstitial sites in the common crystal

octahedral sites in BCC, (d) tetrahedral sites in BCC, (e) octahedralsites in HCP, and (f) tetrahedral sites in HCP.

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St t f C i


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Structures of Ceramics

The structures of many ceramic crystals can be visualized in terms ofstacking of close-packed planes of anions, with interstitial sites occupiedby the cations.

Two types of interstitial sites:---- octahedral (CN=6)

Crystal structures determined by:-- stacking sequence (fcc vs. hcp)-- manner in which interstitial sites are occupied

Figure 10 -- The stacking of one

lane of close- acked s heres(anions) on top of another:

tetrahedral and octahedral

positions between the planes

,

respectively

Example NaCl structure-- fcc arra of close- acked anions of the 111 t e-- cations reside in octahedral sites, each with 6 nearest neighbor anions-- all octahedral sites are occupied

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crystal structure from which a corner

has been removed. The exposed plane

of anions (dark spheres inside the

triangle) is a {111}-type plane: the

cations (light spheres) occupy theinterstitial octahedral positions.Density

*Other ionic structures can be understood in similar manner.

( )Ac AAn +=

Density

Acn = number of formula units within unit cellAc = sum of at. wt. of cationsAA = sum of at. wt. of anionsVc = volume of unit cell

NA = Av. number 36


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Calculate the density of NaCl.n =4

C Na .AA = ACl = 35.45 g/moleVC = a3

+ += r2r2a

( )3ClNa

3c r2r2aV + +==

81.1rCl

=

.Na +

( )[ ] 23388 10023.61081.11002.12..

+=

3cm/.g14.2=

37The experimental value is 2.16 g/cm3


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AX-Type Crystal Structures

Equal numbers of cations and anions, known as AX compounds.

NaCl(CN = 6)

ZnS(CN = 4)

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AmXP-Type Crystal Structures

When charges on cations and anions are not the same, a compound with

the formula AmXP can exist, e.g. CaF2

RC/RA = 0.8, so that CN = 8

half of center positions only are occupiedby Ca2+ ions

A B X -Type Crystal Structures

Compounds that have more than one type of

BaTiO3 (perovskite structure).

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Silicate Ceramics


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Silicate Ceramics

The basic building block of all silicate ceramics (amorphous and crystalline)

is the tetrahedron.

-- each silicon atom is tetrahedrally bonded to four oxygen atoms

-- since each oxygen atom requires an extra electron to achieve a stable

electronic structure, a charge of 4 is associated with every tetrahedron.

Figure 12 A silicon-oxygen (SiO4)4-tetrahedron.

Si4+ = 0.39 Hence r Si (ion)/rO (ion) = 0.3

O2-

= 1.32 41

Thi l i ithi th t bilit 0 225 /R < 0 414 (T bl 3) f


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This value is within the stability range 0.225 r/R < 0.414 (Table 3) fortetrahedral coordination (CN=4). Since the Si-O bond is mixed ionic andcovalent about 50:50 the tetrahedron satisfies the bondinrequirements of both ionic radius ratio and covalent directionality.

Various silicate ceramics arise from the different ways in which the-

4 -, -, - .Because of the high charge on the Si4+ ion, the tetrahedral units areseldom joined edge to edge and never face to face, but almost alwaysshare corners, with no more than two tetrahedra sharing a corner.

Figure 13 Effect of corner edge, and face sharing on cation-cation

separa on. e s ances 1: 2: 3 are n e ra o : . : . ; a s,

cation-cation repulsion increases on going from left to right, which

tends to destabilize the structure. 42


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Silica


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Silicon dioxide or silica SiO has a three-dimensional structure such thatevery corner oxygen atom in each tetrahedron is shared by adjacenttetrahedra.

-- most common crystalline forms are quartz, cristobalite and tridymite.-- relatively open structures of low density

-- high melting points, due to strength of Si-O bonds

Figure 14Figure 14 22--D representations of (a) silica glass, (b) crystalline silica.D representations of (a) silica glass, (b) crystalline silica.44

Sili l


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Silica glass

Also known as vitreous silica, silica glass has a highly disorderedstructure, i.e. it lacks the long-range order characteristic of crystallinesilica, Fig. 14.

---- Oxides, such as BOxides, such as B22OO33 and GeOand GeO22, which readily form glassy, which readily form glassystructures, are referred asstructures, are referred as network formersnetwork formers. When added to a. When added to as ca g ass, ey su s u e or e s ca es ca g ass, ey su s u e or e s ca e e ra e rae ra e ra, so a e, so a elonglong--range order is retained.range order is retained.

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-- Oxides, such as Na2O and K2O, which are incapable of forming glassystructures, are referred as network modifiers. When added to a silica

glass, they break-up the tetrahedral network and create a moredisordered structure.

-- x es, suc as 2 an 2 3, n w c e ca ons su s u e or silicon and help to stabilize the network, are called intermediates.

viscosity of the glass, making it easier to form into useful shapes. Thus,glass containers and windows are made from low melting point soda-lime-

silica glasses, while furnace tubes are made from high melting point vitreoussilica.

Pyrex, a glass composition containing the network formers SiO2 and B2O3,an e ne wor mo ers a2 an a , as proper es n erme a e

between those of soda-lime-silicate glass and vitreous silica, e.g. it has aboutthree times the thermal shock resistance of silica glass, but does not requirethe hi h rocessin tem erature of vitreous silica.

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Layered silicates


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y

-a planar array of tetrahedra.

-- formula unit is (Si2O5)2-

-- a negative charge is associated with the unbonded oxygen

atoms projecting out of the plane.

Figure 15Figure 15 SchematicSchematic

representation of the tworepresentation of the two--

structure having a repeat unitstructure having a repeat unit

formula of (Siformula of (Si22OO55))22--..

Such a negatively charged sheet can bond with an equivalent positivelySuch a negatively charged sheet can bond with an equivalent positivelychar ed sheet to form an electricall neutral structure.char ed sheet to form an electricall neutral structure.

---- sheet or layered silicate structures are characteristic of clayssheet or layered silicate structures are characteristic of clays

and other mineralsand other minerals 47


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-- bonding within a two-layered sheet is strong (ionic-covalent),

der Waals).

Clays

Aluminosilicates that contain chemically bound water.

-- crystal structures are relatively complicated

,hydroplasticity

-- can be fired at relatively low temperature to form a dense and

strong ceramic

Kaolinite

Compound is formed by bonding between Al2(OH)42+ and (Si2O5)2- layers.

-- formula unit is Al2(OH)4 Si2O5-- crystalline kaolinite is composed of many such double layers,

stacked one upon the other

-- additive to paper products

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Figure 16 The structure ofkaolinite clay.

Compound comprises 1 sheet of MgCompound comprises 1 sheet of Mg33(OH)(OH)224+4+ + 2 sheets of (Si+ 2 sheets of (Si22OO55))22--

---- formula unit is Mgformula unit is Mg33(OH)(OH)22 (Si(Si22OO55))22---- slips easily, like graphiteslips easily, like graphite

---- absorbs waterabsorbs water49


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Glass Properties

Glass transition temperature

For an amorphous or non-crystalline material, the glass transitiontem erature T is the critical tem erature that se arates lassbehavior from rubbery behavior, in the time scale of the experiment.

-- most easil detected via measurements of chan es inspecific volume (1/ = v/unit mass) associated with heatingor cooling a material

-- upon heating, the material undergoes a transition fromthe glassy state to the supercooled liquid state, and thento the fully liquid state.

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Figure 17 Specific volume as a function of temperature for a series of

. .

discontinuous change in volume occurs at the melting temperature Tm. (b)The liquid-to-glass transformation (the liquid-to-crystal curve is shown for

reference). The temperature range in which the slope of the liquid-glass

curve changes is the glass transition temperature Tg. (c) Specific volume

versus temperature for a semicrystalline material. The discontinuous

change in volume occurs at Tm, and a change in slope occurs at Tg. 51


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Viscosity-temperature behavior

The temperature dependence of the viscosity of a glassy material is thekey to proper selection of processing parameters.

-- melting point (viscosity 100 P) is the temperature where the glass isfluid enough to be considered a liquid.

-- working point (viscosity 104 P) is the temperature where the glass iseasily deformed.

-- softening point (viscosity 4 x 107

P) is the maximum temperaturew ere g ass can e an e w ou s or on.

-- annealing point (viscosity 1013 P) is the temperature were anyresidual stress in the glass can be eliminated.

-- strain point (viscosity 3 x 1014 P) is the temperature where fractureoccurs before plastic deformation.

Most glass-forming operations are carried out in the working range,which is between the working and softening temperature.

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Figure 18 Logarithm of viscosity versus temperature for fused

silica and several silica glasses. 53

Structures of Polymers


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y

Hydrocarbon moleculesMost polymers are derived from hydrocarbon precursors. It is instructive,therefore, to consider the structures of some typical hydrocarbonmolecules.

All four valence electrons in carbon participate in bonding. Moreover,hybridization of s and p orbitals of the valence electrons gives directionalbonding.

-- 4 equivalent sp3 orbitals, as in methane and ethane-- 3 equivalent sp2 orbitals, as in ethylene-- 2 equivalent sp1 orbitals, as in acetylene

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single bond -- formed by overlapping sp3 orbitals with the orbitals of

double bond -- formed by overlapping sp2 orbitals with the orbitals of twodifferent carbon atoms

triple bond -- formed by overlapping sp1 orbitals with the orbitals of two

Saturated hydrocarbons

sp3 orbitals of both CH4 and C2H6 directed towards the corners of a

regular tetrahedron 55

U t t d h d b


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Unsaturated hydrocarbons

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Polymer molecules


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Polymer molecules

-- Activator (catalyst) is needed to start process of polymerization. For

Directional nature of covalent bonds enables carbon atoms to form long-chainmolecules.

example, ethylene gas can be transformed into polyethylene solid byheating under pressure in the presence of a catalyst.

-- Polymerization process begins when an active mer is formed byreaction of an ethylene gas molecule with a catalyst species (R).Polymer chain is then formed by the sequential addition ofpolyethylene monomer units. In so doing, the active site is

transferred to each end-unit monomer as it is linked to the growingchain.

57

Activator (catalyst) is needed to start process of polymerization. Forexample, ethylene gas can be transformed into polyethylene solid byh ti d i th f t l t


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p , y g p y y yheating under pressure in the presence of a catalyst.

The polymerization process begins when an active mer is formed byreaction of an ethylene gas molecule with a catalyst species (R). Thepolymer chain is then formed by the sequential addition of polyethylenemonomer units. In so doing, the active site is transferred to each end-

.

, ,is a long chain polyethylene molecule. Carbon atoms form a zig-zagbackbone in the molecule, with an angle of 109 between the bonds; theC-C bond length is 0.154 nm. 58


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Figure 19 For polyethylene, (a) a schematic representation of mer and

chain structures, and (b) a perspective of the molecule, indicating thezigzag backbone structure.

Hence, the formula unit for a polyethylene molecule may be

HH ||

represen e as o ows, w ere n s e num er o e y ene mo ecu esw ere n s e num er o e y ene mo ecu es

(monomers) that bond together to form the long chain molecule.(monomers) that bond together to form the long chain molecule.

n

HH

CC

||

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The molecular structures of PTFE, PVC and PP are shown in Figure 21. In

PTFE, all the hydrogen atoms in polyethylene have been replaced byfluorine atoms, whereas in PVC and PP every fourth hydrogen atom alongthe chain has been replaced by Cl or CH3 (methyl group).

Figure 20 Mer and chain structures for

a po y e ra- uoroe y ene, po yv ny

chloride, and (c) polypropylene.

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Molecular shape


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p

Long chain molecules are capable of rotation and bending in threedimensions. This is because any carbon atom in a chain can lie at anypoint on the cone of revolution (109 angle) with the bond of thepreceding carbon atom, Figure 22. Thus, a long chain molecule typicallyhas a very complex shape, involving many bends, twists and kinks.

Figure 21 Schematic representations of how polymer chain shape is

influenced by the positioning of backbone carbon atoms (solid circles).For (a), the rightmost atom may lie anywhere on the dashed circle and

Straight and twisted chain segments are shown in (b) and (c),

respectively.

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Polymer crystallinity


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The crystalline state of a polymer is more complex than that of ametal or ceramic, because of the difficulty of aligning the long chainmolecules in a regular close-packed structure. However, it does occurreadily in molecules, such as PE and PTFE, where the atoms are arrangedsymme r ca y a ong e car on ac one. o ye y ene can ecrystallized with the orthorhombic structure, Figure 23, which represents

the closest packing of the long chain molecules.

Figure 22 Arrangement of

molecular chains in a unit

.

63

-- degree of crystallinity may range from completely amorphous up toabout 95% crystalline


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--counterpart because of the closer packing of molecules in thecrystalline state

-- degree of crystallinity achieved by a polymer depends on the coolingra e rom e qu s a e

-- many bulk polymers that are crystallized from the melt formspherulites, Fig. 24, which are considered to be the polymer

Figure 23 A transmission photo-

micrograph (using cross-polarized

light) showing the spherulite

structure of ol eth lene. Linear

boundaries form between adjacentspherulites, and within each

spherulite appears a Maltese

cross. .

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Polymer characteristics


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1. Side groups-- clusters of atoms that are attached to the carbon backbone

2. Degree of polymerization

-- defines average chain size of a polymer

3. Cross linking

-- joining of two chains together by an atom, group of atoms or another

chain

4. Elastomers

-- polyisoprene experiences large elongations under load, and returns to itsoriginal shape upon unloading

-- trans-poly on opposite sides (rigid solid)

-- cis- ol on same side steric hindrance causes kinkin i.e. chains tocoil.

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5.Vulcanization-- cross-linking process in elastomers; non-reversible reaction at


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cross linking process in elastomers; non reversible reaction at

-- automobile tires have 3-5% S and are elastic-- battery cells have more S and are more rigid

6.Stereoisomerism

-- same composition but different structureisotactic all on one side

atactic randomly on opposite sides

7.Thermo lastic ol mer-- softens when heated and hardens when cooled (reversible process),as in polyethylene

-- due to breaking and reforming of weak secondary bonds between

8.Thermosetting resin-- decom ose before the soften because of extensive cross linkin , as

in epoxy resin

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9. Conformation-- this refers to the outline or shape of the long chain molecule


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--

10. Configuration-- this refers to the arrangement of atoms positions along the chain-- can be altered only by breaking and reforming primary bonds

Melting and crystallization

Carbon backbone of a long chain polymer is strong, since it is composed ofa c a n o - pr mary on s. n e crys a ze s a e, e c ose-pac esegments of the long chain molecules are held together by weak secondarybonds

It follows that when a cr stalline ol mer is heated thermal ener caneasily disrupt the regular periodicity of the crystalline domains, therebyforming a disordered network of long chain molecules. As in ceramics,melting and solidification occurs over a temperature range, T = Tm Tg.

.state, leading to a glassy solid (fast), semi-crystalline solid (intermediate),and crystalline solid (slow)

67


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Figure 24 Specific volume

versus temperature, upon

,

totally amorphous (curve A),

semicrystalline (curve B), andcrystalline (curve C) polymers

Polyethylene readily crystallizes by slow cooling from the melt, whereaspolystyrene does not, due to the presence of bulky side groups (benzenerings)

-- abrupt changes in elastic stiffness, heat capacity and thermal expansiocoefficient occur at Tg

--temperature range T = Tm Tg, where the material is in its softened,rubber-like state.

68


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In addition, graphite has high resistance to thermal shock, high absorptionof gases, and good machinability. Applications include heating elements,rocket nozzles electrical contacts batter electrodes and air urification


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rocket nozzles electrical contacts batter electrodes and air urification

devices.

Diamond

A metastable form of carbon, diamond is composed entirely of strongcovalently-bonded carbon atoms, with tetrahedral coordination. The

properties of diamond are exceptional in many respects.-- hardest known material

-- very low electrical conductivity

-- unusually high thermal conductivity

-- optically transparent in the visible and infrared

-- high index of refraction

Synthetic diamonds are produced commercially by a high pressure-high

temperature process. Industrial grade diamond grits are used for grindingand cutting operations, and polycrystalline diamond compacts are used forrock drill bits and machine tools.

ThinThin filmsfilms of of diamonddiamond areare alsoalso manufacturedmanufactured byby aa ChemicalChemical VaporVaporDepositionDeposition (CVD)(CVD) processprocess.. SuchSuch filmsfilms areare usedused asas wearwear resistantresistant coatingscoatings

onon drills,drills, bearings,bearings, dies,dies, andand lenseslenses.. 70

Fullerenes


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Discovered in 1985, C60 fullerene is a molecular form of carbon thatconsists of a hollow spherical cluster of sixty carbon atoms.

-- same symmetry as that of a soccer ball

-- composed of 20 hexagons and 12 pentagons, such that no two

pentagons share a common side,

each C60 molecule is a molecular analogue of such a dome.

-- other molecular forms with larger numbers of carbon atoms

have been found-- properties of these fullerene molecules are being investigated

Recently, methods have been found to produce nanoscale tubular andpo y e ra s ruc ures. ar on nano u es sp ay very g spec c

strengths.Many structural applications for this new class of superstrong carbon

.

71


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72

Polymer characteristics


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.-- clusters of atoms that are attached to the carbon backbone

2. Degree of polymerization--

3. Cross linking-- joining of two chains together by an atom, group of atoms or another

4. Elastomers-- polyisoprene experiences large elongations under load, and returns to its

-- trans-poly on opposite sides (rigid solid)-- cis-poly on same side (steric hindrance) causes kinking, i.e. chains to

coil.

5. Vulcanization-- cross-linking process in elastomers; non-reversible reaction at

elevated temperatures using sulfur compounds-- automobile tires have 3-5% S and are elastic-- battery cells have more S and are more rigid

1

ElastomersPolyisoprene experiences large elongations under load, and returns toits ori inal sha e u on unloadin


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its ori inal sha e u on unloadin

trans-poly on opposite sides(rigid solid)

cis-poly on same side (sterichindrance) causes kinking, i.e.

Vulcanization

- -temperatures using sulfur compounds

2

6.Stereoisomerism-- same com osition but different structure


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isotactic all on one sidesyndiotactic alternating side groupsatactic randomly on opposite sides

7.Thermoplastic polymer

-- softens when heated and hardens when cooled (reversible process),as in polyethylene

--chains

8.Thermosetting resin

-- ,in epoxy resin

9. Conformation--

-- can be modified by a simple bond rotation10. Configuration

---- can be altered only by breaking and reforming primary bonds

3

Stereoisomerism


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ame compos on u eren a om c arrangemen :

Isotactic R groups all on oneside

alternating on opposite sides

Atactic R groups randomly onopposite sides

4

Binary Phase Diagrams

Relevant terms


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-- component is a pure element (e.g. Fe, Si, or B) or stoichiometriccompound (e.g. NaCl, Al2O3, or Si3N4), i.e. a component is achemically distinct substance.

-- system is the volume occupied by a substance or series ofalloys (e.g. Fe-C, Al2O3-Cr2O3, or ice-water).

-- phase is a chemically and structurally homogeneous regionof a material.

-- homogeneous region is a region (or volume) in which theproperties of a system are uniform.

-- phase diagram is a map of the regions in which the different

phases exist when the system is in equilibrium.

-- solid solution describes the substitution of solute in solventwithout a phase change.

Examples

-- pure fcc-Cu is a single component (Cu) single phase (fcc) system


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pure fcc Cu is a single component (Cu), single phase (fcc) system.

-- a mixture of ice and water is a single component (H2O) systemcomposed of two phases.

-- a mixture of bcc-Fe (ferrite) and fcc-Fe (austenite) is a singlecomponent system composed of two phases.

-- solid solution of Cu-Ni (or NiO-MgO) is a two-component, single-phase system.

One-component system

Simplified case, where phase relationships may be represented on apressure-temperature diagram.


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Fig. 25 - The equilibrium

temperature-pressure diagramfor iron.

Fig. 26 Pressure-temperature

phase diagram for SiO2.

Phase equilibria can be described by the Gibbs phase rule

F = C P + 2

which relates number of degrees of freedom, F, at equilibrium to numberof components, C, in the system, number of phases in equilibrium, P, andthe two state variables temperature and pressure.

In a one-component system, such as Fe or SiO2

- if 3 phases are in equilibrium, then F = 1 3 + 2 = 0. This meansthat there is no freedom in specifying variables, so that the 3phases can exist only at a point - triple point.


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p y p p p

-- if 2 phases are in equilibrium, then F = 1 2 + 2 = 1. Thismeans that if one variable is changed (T) then the other isautomatically fixed (P), so that the 2 phases can exist along aline - phase boundary line.

Two-component systemMost practical materials are composed of two components, and, since

pressure is usually fixed at 1 atmosphere, the important variables aretemperature and composition. In such cases, the appropriate expressionfor the phase rule is

F = C P + 1

When pressure is eliminated as a variable, a two-dimensional phasediagram can be constructed, showing the regions of composition andtemperature where the different phases are in equilibrium.

Specifying composition

In many practical situations, compositions are specified as weightpercentages (wt.%) or weight fractions of components. Alternatively,compositions may be specified in terms of atomic percentages (at.%)or atomic fractions.


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100

B.wt.at

B.%wt

A.wt.at

A.%wt

A.wt.at

A.%wt

A.%at

+

=

Similarly

100

B.wt.at

B.%at

A.wt.at

A.%at

A.wt.at

A.%at

A.%wt

+

=

Example

Calculate the atomic percentage of C in Fe for a two-component alloycontaining 0.8 wt.% C.

80


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100

85.55

2.99

12

8.0

12

8.0

C.%at

+

=

= 3.63 at.% C

In ceramic systems, compositions are usually expressed as molefractions. If mole fraction of component A is NA, then

)nn(nN

BA

AA

+=

where nA and nB are the numbers of moles of components A and B,respectively.

Isomorphous systemThis is the simplest two-component phase diagram.

-- displays complete solubility in both liquid andsolid states over the entire composition range.

-- for any mixture of the two components,


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solidification occurs over a temperature range,rather than at a specific temperature, as is thecase for a pure component.

-- liquidus curve separates single-phase liquidregion from two-phase (solid + liquid) region.

--solidus curve separates two-phase (solid +

liquid) region from single-phase solid region.

Fig. 27 - An idealized binary(A-B) phase diagram withassociated definitions.

Hume-Rothery rulesIn order to form a substitutional solid solution over a wide range of

compositions, the following conditions must be met:

-- crystal structures of the two components (A and B) must be the same

-- size difference between components must not differ by more than ~


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15%.

-- valences of the two components must be similar

-- electronegativities of the two components must be comparable

These conditions are satisfied for

many metallic and ceramicsystems, e.g. Cu-Ni, Ag-Au, NiO-MgO, Al2O3-Cr2O3.

Fig. 28 Binary isomorphoussystems Cu-Ni and NiO-MgO

Lever ruleThe relative amounts of two phases in the semi-solid (solid + liquid) region

can be determined by the lever rule.

Amount of liquid of comp.

( )osL

CCpC

==


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Amount of solid of comp.

( )Ls CC()qp( +

( )( )Ls

Los

CC(

CC

)qp(

qC

=

+=

where Co is the composition of the mixture.

A CL C0 CS B

wt.% B

T

Cooling curvesExperimentally, liquidus and solidus curves can be determined by

taking cooling curves at different compositions.

-- for pure components, there is a sharp break in the coolingcurve (thermal arrest) due to heat of transformation


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(crystallization).-- for two-component mixtures, heat is released over a range of

temperaturesT = (TL TS), so that there is a change in slopeof the cooling curve.

Fig. 29 (a) A binary isomorphous phase diagram showing cooling

curves for (b) pure component A, and (c) alloy 1.

Solidification and microstructure

Under equilibrium conditions, all

i i i i h


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compositions in an isomorphoussystem solidify in a similar manner.

Figure 30 Equilibrium solidification ofalloy 1 (composition 0.6 B); (a) thecooling path and sketches showing thedevelopment of the microstructure, and(b) an expanded section of part (a)showing the compositions of the

liquidus and solidus boundaries in therange of 1010C to 1060C.

-- at T1 the alloy begins to solidify, and the first solid crystallites toform have a composition given by the intersection of the horizontal

T1 isotherm (tie line) with the solidus curve (xB = 0.70).

-- when the temperature is reduced to T2, the compositions of bothliquid and solid phases are given by the intersection of the tie line

ith th li id d lid ( 0 68 0 57)


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with the liquidus and solidus curves (xS = 0.68; xL = 0.57).

-- similarly for T3, T4, and T5, until at T5 solidification is complete.-- the final result of solidification is a polycrystalline (many-grained)

material.

-- at all temperatures, the amounts of liquid and solid phases are given

by the Lever rule.

Example

What are the mass fractions of solid and liquid phases in equilibrium at T2?

( )( )

73.057.068.060.068.0

)qp(pCL =

=

+=

( )( )

27.057.068.0

57.060.0

)qp(

q)C1(C Ls =

=

+==


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Eutectic system


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Figure 31 A binary eutectic phase diagram and the associatedterms used to describe regions of a eutectic system.

As in the isomorphous system, the boundaries separating the liquid andsolid phase fields and the two-phase fields are called liquidus and solidusboundaries, respectively.

-- the two liquidus curves converge at an eutectic point, E, which is

the lowest melting point in the system


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the lowest melting point in the system

-- at the eutectic point, the temperature and compositions of the twosolid phases ( and ) are fixed. The invariant reaction may berepresented as

L + where and are the terminal solid solutions of B in A (x1) and Ain B (x2) at the eutectic temperature.

Not present in an isomorphous system, solvus boundaries appear atboth ends of the eutectic phase diagram, representing the temperaturedependence of the solid solubility of each component.

Solidification and microstructure

1. Eutectic composition


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Fig. 32Schematic of theequilibrium microstructures

for a Pb-Sn alloy of eutecticcomposition C3above andbelow the eutectictemperature.


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Fig. 33 - Photomicrographshowing the microstructure ofa Pb-Sn alloy of eutectic

composition. 375 x.

Fig. 34 - Schematic representationof the formation of the eutecticmicrostructure in the Pb-Sn system.

Eutectic microstructure consists of alternating layers (lamellae) of (dark) and (light) phases, where and are solid solutions ofSn in Pb and Pb in Sn, respectively

-- microstructure is formed by counter-diffusion of Sn and Pbatoms just ahead of the advancing solid-liquid interfaceduring solidification.

-- scale of the eutectic microstructure decreases withincreasing cooling rate from the liquid state.

The weight fractions of andphases at the eutectic point are given bythe Lever rule.

45.0)3.188.97(

)9.618.97(

)qp(

pC =

=

+=

55.0)C1(C ==


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55.0)C1(C

2. Off-eutectic composition

Fig. 35 Schematic representations of the equilibriummicrostructures for a Pb-Sn alloy of composition C4as it iscooled from the liquid-phase region.


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Cooling curves

Cooling curves can be used to determine the locations of eutecticpoint, liquidus curve, and solidus curve


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Fig.37 The use of

cooling curves toestablish the liquidusand solidus in a binaryeutectic alloy underequilibrium conditions.

Alloy 3 (eutectic composition) experiences a sharp break in the coolingcurve, due to isothermal transformation of the liquid phase into two

solid phases (+).


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p ( )

Alloys 2 and 4 experience heat release over a range of temperatures T= (TL - TS), prior to isothermal solidification at the eutectic temperature,TE.

Alloys 1 and 5 behave like regular solid solution alloys, in that there is achange in slope of the cooling curve at TL and TS.

Complex systems

Most practical phase diagrams are more complex than the relatively

simple isomorphous and eutectic systems considered so far. Figure 38shows a binary phase diagram that comprises:


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shows a binary phase diagram that comprises:

-- two eutectic reactions (L + ; L + ), a peritecticreaction (L + ), and an intermediate phase reaction (L).

-- phase melts congruently, i.e. the compositions of liquid andsolid phases are the same.

-- phase melts incongruently, i.e. it decomposes into twophases (L + ), such that composition of the liquid phase isdifferent from that of the solid phase.


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Fig. 38 (a) Complex phase diagram containing a peritectic and two

eutectic reactions, and (b) invariant reactions in (a) emphasizedalong with their symbolic representations.

Eutectoid system

An eutectoid reaction is a solid-state reaction, involving the decompositionof a single solid phase () into two solid phases ( + ) having differentcompositions.

-- decomposition occurs by solute redistribution in the phase just


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p y p jin front of the two phase ( + ) region.

-- solid-state reaction is slower than liquid-state reaction, due tomuch slower diffusion rate in the solid state.

-- most important commercial system that exhibits an eutectoidreaction is the Fe-Fe3C system

Fe-Fe3C system

Upon heating, pure Fe experiences two solid state reactions:

912C 1394C-ferrite -austenite -ferrite(bcc) (fcc) (bcc


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Fig. 39 The Fe-C phase diagram.

With the addition of C, these polymorphic transformations are drasticallymodified

-- the solubility of C in -austenite is large; maximum of 2.14 wt.% at 1147C.-- the solubility of C in -ferrite is small; maximum of 0.022 wt.% at 727C.-- when the solubility of C in and phases is exceeded, an intermediate

phase Fe3C, known as cementite, makes its appearance.

Upon cooling from the fully austenitic state, an alloy of composition 0.76wt.%C, the following eutectoid reaction occurs:

+ Fe3C


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(austenite) (ferrite) (cementite)

pearlite

Pearlite is the product of -austenite decomposition, and consists ofalternating layers (lamellae) of -ferrite and Fe3C-cementite.

-- pearlite is nucleated at the prior austenite grain boundaries, andpropagates by a diffusion controlled mechanism

-- C atoms diffuse away from the -ferrite regions into the adjacentFe3C cementite regions.


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Fig. 40 Schematics ofmicrostructures for an Fe-C alloy

of eutectoid composition (0.76wt.% C) above and below theeutectoid temperature.

Fig. 41 Photomicrograph of aneutectoid steel showing the

pearlite microstructure, whichconsists of alternating layers of-ferrite (light phase) and Fe3C-cementite (dark phase). 500x


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Fig. 42 Schematic representation of the formation ofpearlite from austenite; direction of carbon diffusionindicated by arrows.

The wt. fractions of the constituent and Fe3C phases in pearlitecan be determined using the Lever rule.

89.0)022.07.6(

)76.07.6(fraction.wt =

=

wt. fraction Fe3C = 0.11

Off-eutectoid composition

Alloy compositions to the left and right of the eutectoid (0.76 wt.% C) aretermed hypoeutectoid and hypereutectoid, respectively.

-- cooling a hypoeutectoid alloy from the fully austenitic region gives


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g yp y y g grise first to pro-eutectoid -ferrite (along the prior austenite grainboundaries) and then pearlite.

-- similarly for hypereutectoid alloys, except that the pro-eutectoid

phase is cementite.

-- the weight fractions of pro-eutectoid ferrite and total ferrite (pro-eutectoid + eutectoid ferrite) can be determined using the Lever rule.

Hypoeutectoid alloys comprise most of the commercially important steels,

since they combine high strength (due to pearlite) and good fracture toughness(due to pro-eutectoid ferrite).


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Fig. 43 Schematic of themicrostructures for an Fe-Calloy of hypoeutectoidcomposition C0(< 0.76 wt.%

C), as it is cooled fromwithin the austenite phaseregion to below theeutectoid temperature.

Fig. 44 - Photomicrographof a 0.38 wt.% C steelhaving a microstructureconsisting of pearlite and

pro-eutectoid ferrite. 635x.

Effect of cooling rate

Slow cooling from the fully austenitic region gives pearlite (diffusion-controlled transformation).

(fcc) (bcc) + Fe3C (orthorhombic)(austenite) (ferrite) (cementite)


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-- composed of alternating layers of ferrite () and cementite (Fe3C),Fig. 41.

-- formed by redistribution of C in the phase just ahead of theadvancing two-phase ( + Fe3C) interface, Fig. 42.

-- pearlite is strong and tough.

Fast cooling from the fully austenitic region gives martensite (diffusion-

less transformation).

(fcc) (bct)(austenite) (martensite)

-- martensite has a needle-like morphology and is hard and brittle.

pearlite


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When heated, Fe3C begins to form as fine precipitates within the martensiteneedles.

-- this has the effect of reducing hardness and increasing toughness,called tempering.

When heated just below the eutectoid temperature for a long time (~10 hours),a relatively uniform distribution of coarse Fe3C particles is formed in an -ferrite matrix.

-- such a microstructure, called spheroidite, possesses moderatestrength and good ductility.

Fig. 45 Progress of athermal martensitic transformation in an Fe-1.8wt.% C alloy after cooling to (a) 24C, (b) -60C, and (c) -100C.


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Fig. 46 Microstructure of a tempered martensite (spheroidite)in a steel with 0.7 wt.% C.

Isothermal transformation diagram

The pearlite transformation is both temperature and time dependent,whereas the martensite transformation depends solely on temperature,not time. This difference in behavior can be represented convenientlyon an isothermal transformation (IT) diagram.


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Fig. 47 Schematic of an isothermal transformation(IT) diagram for a eutectoid steel.

Curve A slow cooling gives 100% pearlite

Curve B fast cooling (quenching) gives 100% martensite

Curve C slow cooling to point X, followed by quenching, gives50% pearlite + 50% martensite

MartemperingThis is a commercially important quench-and-temper process:

-- quench to a temperature just above Ms and hold to minimizethermal gradients that can lead to surface cracking

-- quench again to ambient temperature to form 100% martensite

-- reheat to tempering temperature to develop fine-scale Fe3Cparticles


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particles

-- resulting tempered martensite has high strength and moderateductility

Fig. 48 Schematic showing thecooling curve superimposed onIT diagram for martempering, or

indirect quench process (with atemper step).


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Fig. 47 Schematic of an isothermal transformation(IT) diagram for a eutectoid steel.

Indicates microstructural consequences of changing cooling ratefrom the fully austenitic region

-- s ow coo ng orms pear te

-- fast cooling forms martensite


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Incubation period is characteristic of pearlitic transformation, since it

occurs via a diffusion-controlled mechanism

--

boundaries

Martempering

This is a commercially important quench-and-temper process:

-- quench to a temperature just above Ms and hold to minimizethermal gradients that can lead to surface cracking


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-- quench again to ambient temperature to form 100% martensite

-- reheat to tempering temperature to develop fine-scale Fe3Cparticles

-- ductility

Fig. 48 Schematic showing thecooling curve superimposed on

IT diagram for martempering, or

indirect quench process (with atemper step).

407 class notes

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