MSE 102Lecture 9

8/20/2019 MSE 102Lecture 9

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Lecture

9Chapter 9: Phase Diagrams

8-1

8/20/2019 MSE 102Lecture 9


Chapter 10: Phase Diagrams

Chapter Outline:

Definitions and basic concepts

Phases and microstructure

Binary isomorphous systems (complete solid solubility)

Binary eutectic systems (limited solid solubility)Binary systems with intermediate phases/compounds

The iron-carbon system (steel and cast iron)

8/20/2019 MSE 102Lecture 9


Definitions: Components and Phases

• Component: chemically recognizable species (e and ! in carbon steel" #$% and &a!l

in salted water)' binary alloy contains two components" a ternary alloy three" etc'

• Phase: a portion of a system that has uniform physical and chemical characteristics' Two

distinct phases in a system ha*e distinct physical or chemical characteristics (e'g' water

and ice) and are separated from each other by definite phase boundaries' phase may

contain one or more components'

• single-phase system is called homogeneous" systems with two or more phases are

mixtures or heterogeneous systems'

8-2

α (darker

phase)

β (lighter

phase)

Aluminum-

Copper Alloy

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Phase Diagram

• graphical representation of the combinations of temperature! pressure! composition! or

other "ariables for #hich specific phases exist at e$uilibrium%

• &or '(O! a typical diagram sho#s the temperature and pressure at #hich ice )solid*!#ater

)li$uid* and steam )gas* exist%

Phase diagrams:

+epresents phases present in metal at

different conditions ),emperature! pressure

and composition* #ill help us to

understand and predict the microstructures%

ndicates e$uilibrium solid solubility of one

element in another%

ndicates temperature range under #hich

solidification occurs%

ndicates temperature at #hich different phases

start to melt%

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Definitions: .olubility Limit

• .ol"ent host or ma+or component in solution" solute - minor

component (!hapter ,)'

• .olubility Limit of a component in a phase is the maimum

amount of the component that can be dissol*ed in it (e'g' alcohol

has unlimited solubility in water" sugar has a limited solubility"

oil is insoluble)' The same concepts apply to solid phases. !uand &i are mutually soluble in any amount (unlimited solid

solubility)" while ! has a limited solubility in e'

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/ .olution solid! li$uid! or gas solutions! single phase

/ ixture more than one phase

Question: What is the

solubility limit for sugar in

water at 20°C? Answer: 6 wt! sugar "

At 20°C# if C $ 6 wt! sugar:

syrup

At 20°C# if C % 6 wt! sugar:

syrup & sugar

65

• olubility 0imit.

1aimum concentration for

which only a single phase

solution eists'

ugar/2ater Phase Diagram

. u g a r

, e m p e r a t u r e ) 2 C

*

0 (0 30 40 50 100

C 6 Composition )#t7 sugar*

L

)li$uid solution

i%e%! syrup*

.olubility

LimitL

)li$uid*

8

.

)solid

sugar*(0

30

40

50

10 0

9 a t e r

Phase $uilibrium: .olubility Limit

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'

$uilibrium

• system is at e3uilibrium if its free energy is at a minimum" gi*en a

specified combination of temperature" pressure and composition'

• The (macroscopic) characteristics of the system do not change with time 4

the system is stable' change in T" P or ! for the system will result in an

increase in the free energy and possible changes to another state whereby the

free energy is lowered'

• 53uilibrium is the state that is achie*ed gi*en sufficient time' But the time to

achie*e e3uilibrium may be *ery long (the 6inetics can be slow) that a state

along the path to the e3uilibrium may appear to be stable' This is called a

metastable state''

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Phase Diagram of Pure ubstances

• Pure substance exist as solid! li$uid and "apor%

• Phases are separated by phase boundaries%• xample : ater! Pure ron%

• Different phases coexist at triple point.

igure 7'8 igure 7'$

After W" (" )offatt# et al"# *+he ,truture an. /roperties of )aterials# 1ol : *,truture# Wiley# 346#8-3

8/20/2019 MSE 102Lecture 9


9ibbs Phase :ule

• P8& 6 C8(

• &or pure #ater! at triple point! ; phases coexist%

• ,here is one component )#ater* in the system%

• ,herefore ; 8 & 6 1 8 ( & 6 0%

• Degrees of freedom indicate number of "ariables that can be

changed #ithout changing number of phases%

P 6 number of phases that coexist in a system

C 6 <umber of components

& 6 Degrees of freedom

8-4

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!ooling !ur*es

• =sed to determine phase transition temperature%

• ,emperature and time data of cooling molten metal isrecorded and plotted%

• ,hermal arrest : a region of the cooling cur"e for apure metal #here temperature does not change #ithtime )heat lost 6 heat supplied by solidifying metal*representing the free>ing temperature%

• lloys solidify o"er a range of temperature )nothermal arrest*

Pure etal

ron

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33

Phase Diagrams

• ;ndicate phases as a function of Temp" !omp and Pressure'

• ocus on. - binary systems. $ components'

- independent *ariables. T and ! (P < 8 atm is almost always used)'

Cu-5i

system

• 2 phases:

7li8ui.9α 7CC soli. solution9

• ; .ifferent phase fiel.s:

& αα

wt! 5i20 <0 60 =0 30003000

3300

3200

3;00

3<00

300

3600

+7°C9

7li8ui.9

α

7CC soli.

solution9

6

& α l i 8

u i . u s

s o l i . u s

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32

• !hanging T can change = of phases. path to B'

• !hanging !o can change = of phases. path B to D'

ffect of ,emperature ? Composition )Co*

wt> &i$? ,? @? 7? 8???8???

88??

8$??

8A??

8,??

8??

8@??

T(C!)

0 (li3uid)

α (!! solid solution)

0 D α l i 3

u i d u

s

s o l i d

u s

A

>

Cu

!u-&i

system

8/20/2019 MSE 102Lecture 9


Binary ;somorphous lloy ystems

• @inary alloy

• somorphous system: complete solid solubility of the t#o

components )both in the li$uid and solid phases*%

• xample: Cu-<i solution%

ixture of

t#o systems

,#o component

system

Composition at li$uid and solid

phases at any temperature

can be determined by dra#ing

a tie line%

igure 8?'A

A.apte. from *)etals @an.boo# 1ol" =# =th e."# Amerian soiety of )etals# 34';# p"8-5

,hree phase region can be identified on the phase diagram: Li$uid )L* ! solid 8 li$uid)A 8L*! solid )A *

• Li$uidus line: separates li3uid

from li3uid solid

• .olidus line: separates solid

from li3uid solid

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@inary somorphous .ystems

• ;n one-component system melting occurs at a well-defined melting temperature'

• ;n multi-component systems melting occurs o*er the range of temperatures"

between the solidus and li3uidus lines'

• olid and li3uid phases are in e3uilibrium in this temperature range'

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Phase Diagram from !ooling !ur*es

• .eries of cooling cur"es at different metal composition

are first constructed%

• Points of change of slope of cooling cur"es )thermal

arrests* are noted and phase diagram is constructed%

• ,he greater the number of cooling cur"es the more

accurate the phase diagram%

igure 7',

8-6

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36

• :ule 8. ;f we 6now T and !o" then we 6now.

--how many phases and which phases are present'

• Bamples:

wt% Ni20 40 60 80 10001000

1100

1200

1300

1400

1500

1600 T(°C)

L (liqid)

α (!CC s"lids"lti"#)

$(110060)

&

( 1 2 5 0

% 3 5 )

Cu-5i

phase

.iagram

$(1100 60)'

1 phase' α&(1250 35)'

2 phases' L α

Determination of phase)s* present

)elting points: Cu D

30=°C# 5i D 3<; °C

olidus - Temperature where alloy is completely solid' bo*e this line" li3uefaction begins'

0i3uidus - Temperature where alloy is completely li3uid' Below this line" solidification begins'

8/20/2019 MSE 102Lecture 9


3'

• :ule $. ;f we 6now T and !o" then we 6now.

--the composition of each phase'

• Bamples:

wt% Ni

20

1200

1300

T(°C)

L (liqid)

α

(s"lid)

30 40 50

T$$

T

T&&

tie li#e

433532C"CL Cα

C*Nis+ste,

Composition of Phases

At + A D 3;20°C:

Enly i8ui. 79 presentC D C0

7 D ; wt! 5i9

At +> D 320°C:

>othα

an. present

At + D 3340°C:

Enly ,oli. 7α9 present

Cα D C0 7 D ; wt! 5i9

C D C li8ui.us 7 D ;2 wt! 5i9

Cα D C soli.us 7 D <; wt! 5i9

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3=

• :ule A. ;f we 6now T and !o" then we 6now.

--the amount of each phase (gi*en in wt>)'

Cu-5i system

- ./a,ples'

$t T&' &"th α a#d L

$t T$' #l+ Liqid (L)

L 100wt% α 0

$t T' #l+ "lid (α)

L 0 α 100wt%

C" 35wt%Ni

wt% Ni

20

1200

1300

T(°C)

L (liqid)

α

(s"lid)30 40 50

T$$

T

T&&

tie li#e

433532C"CL Cα

eight &ractions of Phases

L = 43−35

43−32= 3wt%= Cα − C"

Cα − CL

D 2'wt !

=C" − CL

Cα

− CL

α

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nterpretation of Phase Diagrams

• or a gi*en temperature and composition we can use phase diagram to

determine.

8' The phases that are present

$' !ompositions of the phases

A' The relati*e fractions of the phases

• &inding the composition in a t#o phase region:

8' 0ocate composition and temperature in diagram

$' ;n two phase region draw the tie line or isotherm

A' &ote intersection with phase boundaries' :ead compositions at the

intersections'

• The li3uid and solid phases ha*e these compositions'

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,he Le"er +ule

• &inding the amounts of phases in a t#o phase region:

8' 0ocate composition and temperature in diagram

$' ;n two phase region draw the tie line or isotherm

A' raction of a phase is determined by ta6ing the length of the tie line to the

phase boundary for the other phase" and di*iding by the total length of tie

line'

,' The le"er rule is a mechanical analogy to the mass balance calculation' The

tie line in the two-phase region is analogous to a le*er balanced on a fulcrum'

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The 0e*er :ule

• ,he Le"er rule gi"es the #eight 7 of phases in any t#o

phase regions%

t fraction of solid phase

6 Bs 6 #0 #1

#s #1

t fraction of li$uid phase

6 Bl 6 #s #0

#s #1

igure

8-7

2? is the weight percentage of the alloy'

2s is the weight percentage within the solid

phase

2l is the weight percentage in the li3uid

phase

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,he Le"er +ule

ass fractions: L6 . )+8.* 6 )Cα - Co* )Cα- CL*

α 6 + )+8.* 6 )Co - CL* )Cα- CL*

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De"elopment of microstructure in isomorphous alloys

$uilibrium )"ery slo#* cooling

olidification in the solid li3uid phase occurs gradually upon

cooling from the li3uidus line'

The composition of the solid and the li3uid change gradually

during cooling (as can be determined by the tie-line method')

&uclei of the solid phase form and they grow to consume all

the li3uid at the solidus line'

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2<

wt! 5i20

3200

3;00

;0 <0 0330 0

7li8ui.9

α

7soli.9

6 & α

6 & α

+7°C9

A

;C0

: ;wt!5i

Cu-5isystem

• Phase diagram. !u-&i system'

• !onsider

microstuctural

changes that

accompany the

cooling of a

!? < A wt> &i alloy

Ex: Equilibrium Cooling of a Cu-Ni Alloy

<6;

<;;2

α: <; wt! 5i

: ;2 wt! 5i

>α: <6 wt! 5i: ; wt! 5i

C

B: 2< wt! 5i

α: ;6 wt! 5i

2< ;6

8/20/2019 MSE 102Lecture 9


• De*elopment of

microstructure during the

non-e3uilibrium

solidification of a A wt

> &i-@ wt> !u alloy

outcome.

• egregation-non-uniform

distribution of elements

within grains'

• 2ea6er grain boundaries

if alloy is reheated'

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De"elopment of microstructure in isomorphous alloys

<on-e$uilibrium cooling

!ompositional changes re3uire diffusion in solid and li3uid phases

Diffusion in the solid state is *ery slow'

⇒

The new layers that solidify on topof the eisting grains ha*e the e3uilibrium composition at that temperature but

once they are solid their composition does not change' ⇒ ormation of layered

(cored) grains and the in*alidity of the tie-line method to determine the

composition of the solid phase'

The tie-line method still wor6s for the li3uid phase" where diffusion is fast'

*erage &i content of solid grains is higher' ⇒ pplication of the le*er rule

gi*es us a greater proportion of li3uid phase as compared to the one for

e3uilibrium cooling at the same T' ⇒ olidus line is shifted to the right (higher

&i contents)" solidification is complete at lower T" the outer part of the grains

are richer in the low-melting component (!u)'

Epon heating grain boundaries will melt first' This can lead to premature

mechanical failure'

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- Cα hanges as it soli.ifies"

- Cu-5i ase:

• ast rate of ooling: Core. struture

• ,low rate of ooling: B8uilibrium struture

irst α to soli.ify has Cα D <6wt!5i"

ast α to soli.ify has Cα D ;wt!5i"

!irst α t" s"lid+'

46wt%Ni

7#i"r, Cα'35wt%Ni

Last α t" s"lid+'

35wt%Ni

Cored "s $uilibrium Phases

• !oring can be eliminated by means of a homogenization heat treatment carried out at temperatures

below the alloyFs solidus' During the process" atomic diffusion produces grains that arecompositionally homogeneous'

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&on 53uilibrium olidification of lloys

• ery slo# cooling )e$uilibrium* gi"es rise to cored

structure as composition of melt continuously changes%

• +apid cooling delays solidification but also leads to

cored structure

%• 'omogeni>ation: Cast ingots heated

to ele"ated temperature to eliminate

cored structure%

• ,emperature of homogeni>ation

must be lo#er than lo#est melting

point of any of the alloy components'

igure igure

8-8

2?<A?> !u

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24

• 5ffect of solid solution strengthening on.

--Tensile strength (T) --Ductility (>50">:)

--Pea6 as a function of !o --1in' as a function of !o

echanical Properties: Cu-<i .ystem

. l " # g a t i "

#

( %

. L )

C",p"siti"# wt%NiC Ni

0 20 40 60 80 10020

30

40

50

60

%.L "rpre Ni

%.L "r pre C

T e # s i l e

3 t r e # g

t h

( 9

: a )

C",p"siti"# wt%NiC Ni

0 20 40 60 80 100200

300

400

T "rpre Ni

T "r pre C

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;0

Binary ;somorphous ystems

Cu-<i system:

• The li3uid 0 is a homogeneous li3uid solution composed of !u and &i'

• The G phase is a substitutional solid solution consisting of !u and &i atoms with an

!! crystal structure'

• t temperatures below 8?7? !" !u and &i are mutually soluble in each other in thesolid state for all compositions'

• The complete solubility is eplained by their !! structure" nearly identical

atomic radii and electro-negati*ities" and similar *alences'

• The !u-&i system is termed isomorphous because of this complete li3uid and solid

solubility of the $ components'

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;3

utectic

• eutectic or eutectic mixture is a miture of two or more

phases at a composition that has the lowest melting point'

• ;t is where the phases simultaneously crystallize from molten

solution'

• The proper ratios of phases to obtain a eutectic is identified by

the eutectic point on a binary phase diagram'

• The term comes from the 9ree6 Heute6tosH" meaning Heasily

melted'I

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Binary 5utectic lloy ystem

• n some binary alloy systems! components ha"e limited

solid solubility%

• utectic composition free>es

at lo#er temperature than all

other compositions%• ,his lo#est temperature is

called eutectic temperature%

Li$uid A solid solution 8 E solid solutionutectic temperature

Cooling

xample : Pb-.n alloy%

igure 7'88

8-9

8/20/2019 MSE 102Lecture 9


;;

0 α

0β

α β

$??

T(C!)

87'A

!" wt> n

$? @? 7? 8???

A??

8??

0 (li3uid)

α 87AC! @8'J JK'7

β

• or a ,? wt> n-@? wt> Pb alloy at 8?C!" determine.

-- the phases present Pb-nsystem

)x 1* Pb-.n utectic .ystem

ns#er: α β-- the phase compositions

-- the relati*e amount of each phase

8?

,?

!?

88!α

JJ!β

ns#er: !α < 88 wt> n

!β < JJ wt> n

2α

<!β - !?

!β - !α

<JJ - ,?

JJ - 88<

J

77< ?'@K

2β

!? - !α

!β - !α

<

<

$J

77 < ?'AA<

,? - 88

JJ - 88

ns#er:

8/20/2019 MSE 102Lecture 9


.lo# Cooling of 407 Pb 307 .n alloy

• Li$uid at ;000C%

• t about (3F0C first

solid forms proeutectic

solid%

• .lightly abo"e 15;0C

composition of alphafollo#s solidus and

composition of sn "aries

from 307 to 41%97%

• t eutectic temperature!all the remaining li$uid

solidifies%

• &urther cooling lo#ers alpha .n content and beta Pb%

•),hey try to mo"e to e$uilibrium*

igure 7'8A

igure 7'8$

rom F" 5utting an. G" (" >aer# *)irostruture of )etals# nstitute of )etals# on.on#8-10

8/20/2019 MSE 102Lecture 9


;

• or alloys where

!? L $ wt> n

• :esult at room temperature is a polycrystalline with grains of α

phase ha*ing composition !?

icrostructural De"elopments

in utectic .ystems -

?

0 α$??

T(C!)

! " wt> n8?

$

$?

!?

A??

8??

0

α

A?

α β

,??

(room T solubility limit)

T5

α0

0. !? wt> n

α. !? wt> n

:;*#s+ste,

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;6

$ wt> n L !? L 87'A wt> n

• :esults in polycrystalline

microstructure with α grains and

small β-phase particles at lower

temperatures'

icrostructural De"elopments in utectic .ystems -

0 α

$??

T(C!)

! " wt> n8?

87'A

$??!?

A??

8??

0

α

A?

α β

,??

(sol' limit at T5)

T5

$(sol' limit at T room )

0

α

0. !? wt> n

αβ

α. !? wt> n

:;*#s+ste,

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icrostructures in utectic .ystems -

:;*#

s+ste,

- !o < !5

- :esults in a

eutecticmicrostructure

with alternating

layers of α and β crystals'

n)wt>K'7J(n)wt>'A7(8 n)wt>J'@8( β α + L

ooling

heating

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;=

Lamellar utectic .tructure

$-phase microstructure resulting

from the solidification of a li3uid

ha*ing the eutectic composition where

the phases eist as a lamellae that

alternate with one another'

ormation of eutectic layered

microstructure in the Pb-n system

during solidification at the eutectic

composition' !ompositions of G and M

phases are *ery different' olidification

in*ol*es redistribution of Pb and n

atoms by atomic diffusion'

Pb-rich

Sn-rich

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;4

Pb-.n icrostructures

The dar6 layers are Pb-rich G phase" the lightlayers are the n-rich M phase'

8/20/2019 MSE 102Lecture 9


<0

• or alloys with87'A wt> n L !? L @8'J wt> n• :esult. α phase particles and a eutectic micro-constituent

icrostructures in utectic .ystems -

87'A @8'J JK'7

eutectic αeutectic β

20 < (8- 2 α ) < ?'?

!α < 87'A wt> n

!0 < @8'J wt> n

2α < < ?'?

• Nust abo*e T5 .

• Nust below T5 .

!α

< 87'A wt> n

!β < JK'7 wt> n

2

α < < ?'K$K

2β < ?'$KA wt> n

Pb-.n system:

0β

$??

T(C!)

!" wt> n

$? @? 7? 8???

A??

8??

0

αβ

0α

,?

α

β

T5

0. !?wt> n 0

α0

α!0 - !?

!0 - !α

!< - !?

!< - !α

Primary =

8/20/2019 MSE 102Lecture 9


Oarious 5utectic tructures

• .tructure depends on factors liGe minimi>ation of free

energy at A E interface%• anner in #hich t#o phases nucleate and gro# also

affects structures%

igure 7'8,

After W" C" Winegar.# *An ntro.ution to the ,oli.ifiation of )etals# nstitute of )etals# on.on# 346<"8-11

8/20/2019 MSE 102Lecture 9


Binary Peritectic lloy ystem

• Peritectic reaction: Li$uid phase reacts #ith a solid

phase to form a ne# and different solid phase%Li$uid 8 A E

cooling

• Peritectic reaction occurs

#hen a slo#ly cooled alloy

of &e-3%; #t7 <i passes

through Peritectic

temperature of 1F1HC%

• Peritectic point is in"ariant%

Li$uid)F%3 #t7 <i* 8 I )3%0 #t7 <i* J 3%; #t 7 <icooling

igure 7'8@

8-12

8/20/2019 MSE 102Lecture 9


Peritectic lloy ystem

• t 3(%3 7 g ? 13000C

Phases present Li$uid lpha

Composition FF7 g H7gmount of Phases 3(%3 H FF-3(%3

FF H FF - H

6 H37 6 (47

• t 3(%37 g and 11540C K,

Phase Present @eta only

Composition 3(%37 g

mount of Phase 1007

• t 3(%37 g and 11540C 8 K,

Phases present Li$uid lpha

Composition 44%;7 g 10%F7g

mount of Phases 3(%3 10%F 44%;-3(%3

44%; 10%F 44%;10%F

6 FH7 63;7

igure 7'8K

igure 7'87

8-13

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:apid olidification in Peritectic ystem

• .urrounding or ncasement: During peritectic

reaction! L8 A E ! the beta phase created surroundsprimary alpha%

• @eta creates diffusion barrier resulting in coring%

igure 7'$?

igure 7'8J

After Ghines# * /hase iagrams in )etallurgy#)(raw- @ill# 346# p"8-14

8/20/2019 MSE 102Lecture 9


Binary 1onotectic ystems

• onotectic +eaction: Li$uid phase transforms into

solid phase and another li$uid% L1 A 8 L(

Cooling

• ,#o li$uids are immiscible%

• xample:- Copper Lead

system at 9FF0C and ;47 Pb'

5utectic

5utectoid

Peritectic

Peritectoid

1onotectic

igure 7'$A

Table 7'8

)etals @an.boo# 1ol" =: *)etallography ,trutures an. /hase iagrams# =th e."# Amerian ,oiety of )etals# 34';# p" 246"8-15

ntermetallic Compounds

8/20/2019 MSE 102Lecture 9


<6

ntermetallic Compounds

g(Pb

&ote. intermetallic compounds eist as a line on the diagram - not a phase

region' The composition of a compound has a distinct chemical formula'

8J wt> 1g-78 wt> Pb

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Cu-n .ystem )@rass*

Cartri.ge brass:

'0 wt! Cu

t t id ? P it ti

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<=

utectoid ? Peritectic

!u-n Phase diagram

utectoid transformation γ 8 ε

Peritectic transformation γ 8 L

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<4

• 5utectoid one solid phase transforms to two other solid phases

olid8 > olid$ olidA

γ α eA! (or e-!" K$K°!" ?'K@ wt> !)

utectic! utectoid! ? Peritectic

• 5utectic - li3uid transforms to two solid phases0 α β (or Pb-n" 87A°!" @8'J wt> n)ool

heat

• Peritectic - li3uid and one solid phase transform to a $nd solid phase olid8 0i3uid > olid$

δ 0 ? (or !u-n" J7C!" K7'@ wt> n)

ool

heat

ool

heat

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0

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;ntermediate Phases and !ompounds

• ,erminal phases: Phases

occur at the end of phasediagrams%

• ntermediate phases: Phases occur in a composition range inside

phase diagram%

• xamples: Cu-ndiagram has bothterminal and

intermediate phases%• &i"e in"ariant peritectic

points and one eutecticpoint%

igure 7'$

*)etals @an.boo# 1ol" =: *)etallography ,trutures an. /hase iagrams# =th e."# Amerian ,oiety of )etals# 34';# p"8-16

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;ntermediate Phases in !eramics

• n l(O( .iO( system! an intermediate phase called

ullite is formed! #hich includes the compound;l(O;%(.iO(%

igure 7'$@

After A" (" (uy# *Bssentials of )aterials ,iene# *)(raw-@ill# 34'6 8-17

;ntermediate !ompounds

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;ntermediate !ompounds

• n some phase diagrams! intermediate compound are formed

.toichiometric )fixed ratio of in"ol"ed atoms*

•Possess a mixture of metallic-onic or metallic-Co"alent bond depends onthe difference in the electro-negati"ities of the elements in"ol"ed%

• xample:- g-<i phase diagram contains

g<i( : Congruently melting compound)it maintains its composition right

up to the melting point* %

g(<i : ncongruently melting compound )since! upon heating! itundergoes peritectic decomposition at H41oC into li$uid and g<i(phases*

igure 7'$K

)etals @an.boo# 1ol" =: Amerian ,oiety of )etals# 34';# p" ;3<" 8-18

Mibbs Phase +ule

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<

Mibbs Phase +ule

• Phase diagrams and phase e3uilibria are sub+ect to the laws of thermodynamics'

• 9ibbs phase rule is a criterion that determines how many phases can coeistwithin a system at e3uilibrium'

P < ! &

P. = of phases present

. degrees of freedom (temperature" pressure" composition)

!. components or compounds

&. noncompositional *ariables

or the !u-g system Q 8 atm for a single phase P. &<8 (temperature)" ! < $ (!u-g)" P< 8 (a" b" 0)

< $ 8 8< $

This means that to characterize the alloy within a single phase

field" $ parameters must be gi*en. temperature and composition';f $ phases coeist" for eample" a0 " b0" ab" then according to 9P:" we ha*e

8 degree of freedom. < $ 8 $< 8' o" if we ha*e Temp or composition"then we can completely define the system'

;f A phases eist (for a binary system)" there are ? degrees of freedom' This meansthe composition and Temp are fied' This condition is met for a eutectic system

by the eutectic isotherm'

8/20/2019 MSE 102Lecture 9


Chapter 9 )part (*

• ,he ron-ron Carbide Phase Diagram

• De"elopment of icrostructures in ron-Carbon lloys

• 'ypoeutectoid lloys

• 'ypereutectoid lloys

• nfluence of Other lloying lements

ron-Carbon .ystem

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6

ron-Carbon .ystem

• Pure iron when heated eperiences $ changes in

crystal structure before it melts'

• t room temperature the stable form" ferrite (α

iron) has a B!! crystal structure'

• errite eperiences a polymorphic transformation

to !! austenite (γ iron) at J8$ R! (8@K, R)'

• t 8AJ,R! ($,8R) austenite re*erts bac6 to B!!

phase δ ferrite and melts at 8A7 R! ($7?? R)'

• ;ron carbide (cementite or eA!) an intermediate

compound is formed at @'K wt> !'

• Typically" all steels and cast irons ha*e carbon

contents less than @'K wt> !'

• !arbon is an interstitial impurity in iron and forms

a solid solution with the α, γ, δ phases.

ron Carbon .ystem

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ron-Carbon .ystem

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lthough carbon is present in relati*ely low concentrations" it significantly

influences the mechanical properties of ferrite. (a) G ferrite" (b) austenite'

3 . lid Ph

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3 .olid Phases

ron carbide )Cementite or &e C*

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ron carbide )Cementite or &e;C*

• orms when the solubility limit of carbon in α ferrite is eceeded

at temperatures below K$K R!'

• 1echanically" cementite is *ery hard and brittle'

• or ferrous alloys there are A basic types" based on carboncontent.

;ron (ferrite phase). L?'??7 wt> ! room temp

teel (α eA! phase). ?'??7 to $'8, wt> !

!ast iron. $'8, to @'K? wt> !

60

C b )& C* Ph Di

8/20/2019 MSE 102Lecture 9


63

ron-Carbon )&e-C* Phase Diagram

• $ important points

- utectoid )@*:

γ α eA!

- utectic )*:

0 > γ eA!

e A

! ( c e m e n t i

t e )

8@??

8,??

8$??

8???

7??

@??

,??? 8 $ A , @ @'K

0

γ

(austenite)

γ 0

γ eA!

αeA!

α D γ

δ

(e) !" wt> !

88,7C!

T(C!)

α K$KC! < T eutectoid

,'A?

:esult. Pearlite <alternating layers ofα and eA! phases"

not a separate phase'

8$? µm?'K@

@

γ γ γ γ

0eA!

eA! (cementite-hard)

α (ferrite-soft)

>

Pearliteutectoid reaction:

8/20/2019 MSE 102Lecture 9


Pearliteutectoid reaction:

γ > α eA!

ustenite 0%H4 #t7 C

&errite - 0%0(( #t7 C

Cementite - 4%H0 #t7 C

:edistribution of carbon by diffusion

'ypoeutectoid .teel

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e A

! ( c e m

e n t i t e )

8@??

8,??

8$??

8???

7??

@??

,??? 8 $ A , @ @'K

0

γ

(austenite)

γ 0

γ eA!

α eA!

0eA!

δ

(e) !" wt> !

88,7C!

T(C!)

αK$KC!

!?

0 % H 4

'ypoeutectoid .teel

γ

γ γ

γ α

αα

2α <

2γ <(8 - 2α)

α

pearlite

pearlite < α eA!

2αF <

2 < (8 2αF)pearlite

1icrostructures for iron-iron carbide alloys that are below the

eutectoid with compositions between ?'?$$ and ?'K@ wt>

!arbon are hypoeutectoid'

!γ - !?

!γ - !α

CeA! - C0

!eA! - !α

'ypoeutectoid .teel

8/20/2019 MSE 102Lecture 9


6<

e A

! ( c e m

e n t i t e )

8@??

8,??

8$??

8???

7??

@??

,??? 8 $ A , @ @'K

0

γ

(austenite)

γ 0

γ eA!

α eA!

0eA!

δ

(e) !" wt> !

88,7C!

T(C!)

αK$KC!

!?

? ' K @

'ypoeutectoid .teel

α

pearlite

γ

γ γ

γ α

αα

γ γ γ γ

γ γ γ γ

Proeutectoid

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6

Proeutectoid

• ormed before the eutectoid

• errite that is present in the pearlite is called eutectoid ferrite'• The ferrite that is formed abo*e the Teutectoid (K$KC!) is proeutectoid'

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66

'ypereutectoid .teel

8/20/2019 MSE 102Lecture 9


e A

! ( c e m

e n t i t e )

8@??

8,??

8$??

8???

7??

@??

,??? 8 $ A , @ @'K

0

γ

(austenite)

γ 0

γ eA!

α eA!

0eA!

δ

(e) !" wt>!

88,7C!

T(C!)

α


? ' K @ C0

pearlite

eA!

γ γ

γ γ

*

O S

2 pearlite < 2γ

2α < S/(O S)

2 <(8 - 2α)e;CH

2 <(8-2γ )2γ </(* )

e;C

1icrostructures for iron-iron carbide alloys that ha*e

compositions between ?'K@ and $'8, wt> carbon are

hyper eutectoid (more than eutectoid)'


8/20/2019 MSE 102Lecture 9


6=


e A

! ( c e m

e n t i t e )

8@??

8,??

8$??

8???

7??

@??

,??? 8 $ A , @ @'K

0

γ

(austenite)

γ 0

γ eA!

α eA!

0eA!

δ

(e) !" wt>!

88,7C!

T(C!)

α

? ' K @ C0

eA!

γ γ

γ γ

γ γ γ γ

γ γ γ γ

pearlite

'ypereutectoid .teel )1 ( #t7 C*

8/20/2019 MSE 102Lecture 9


'ypereutectoid .teel )1%( #t7 C*

Proeutectoid. formed abo*e the Teutectoid (K$KC!)

pearlite

'ypoeutectic ? 'ypereutectic

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'0

0α0β

α β

$??

!" wt> n$? @? 7? 8???

A??

8??

0

α β

+B

,?

(Pb-n

ystem)

'ypoeutectic ? 'ypereutectic

8@? µm

eutectic micro-constituent

hypereutectic. (illustration only)

β

βββ

β

β

8K µm

α

α

α

ααα

hypoeutectic. !? < ? wt> n

T(C!)

@8'J

eutectic

eutectic. !? < @8'J wt> n

8/20/2019 MSE 102Lecture 9


'3

5ample Problem

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'2

5ample Problem

or a JJ'@ wt> e-?',? wt> ! steel at

a temperature +ust below theeutectoid" determine the

following.

a) The compositions of eA! and

ferrite (α)'

b) The amount of cementite (ingrams) that forms in 8?? g of

steel'

.olution to xample Problem

8/20/2019 MSE 102Lecture 9


';

.olution to xample Problem

W :e;C

= R

R +S = C 0 −C α

C :e;C

−C α

= 0"<0−0"022

6"'0−0"022 = 0"0'

b9 Ising the le1er rule with

the tie line shown

a) Esing the : tie line +ust below the eutectoid

!α < ?'?$$ wt> !

!&e;C < @'K? wt> !

e A

! ( c e m e n t i t e )

8@??

8,??

8$??

8???

7??

@??

,??? 8 $ A , @ @'K

0

γ(austenite)

γ 0

γ eA!

α eA!

0eA!

δ

! " wt> !

88,7C!

T(C!)

K$KC!

C0

:

CFe C

3C

mount of eA! in 8?? g

< (8?? g)2eA!

< (8?? g)(?'?K) < 'K g

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'<

lloying steel with other elements changes the 5utectoid Temperature"

Position of phase boundaries and relati*e mounts of each phase

.ummary

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'

• Phase diagrams are useful tools to determine.

-- the number and types of phases present"

-- the composition of each phase"

-- and the weight fraction of each phaseor a gi*en temperature and composition of the system'

• The microstructure of an alloy depends on

-- its composition" and

-- rate of cooling e3uilibrium

.ummary

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'6

+e"ie#

• #eating a copper-nic6el alloy of composition K? wt> &i-A? wt> !u from 8A??C!' twhat temperature does the first li3uid phase form

8/20/2019 MSE 102Lecture 9


''

what temperature does the first li3uid phase form

• olidus - Temperature where alloy is completely solid' bo*e this line" li3uefaction begins'

• nswer. The first li3uid forms at the temperature where a *ertical line at this composition

intersects the G-(G L) phase boundary--i'e'" about 8A?C!U

-

-

20 40 60 80 1000

1000

1100

1200

1300

1400

1500

1600 T(°C)

L (liqid)

α

(!CC s"lids"lti"#)

Wt% Ni

• (b) 2hat is the composition of this li3uid phase

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'=

(b) 2hat is the composition of this li3uid phase

• nswer . The composition of this li3uid phase corresponds to the intersection

with the (G L)- L phase boundary" of a tie line constructed across the G L

phase region at 8A?C!" J wt> &iU

Wt% Ni

-

-

20 40 60 80 10001000

1100

1200

1300

1400

1500

1600 T(°C)

L (liqid)

α

(!CC s"lids"lti"#)

• (c) t what temperature does complete melting of the alloy occur

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'4

( ) p p g y

• 0i3uidus - Temperature where alloy is completely li3uid' Below this line"

solidification begins'

• nswer. !omplete melting of the alloy occurs at the intersection of this same *ertical

line at K? wt> &i with the (G L)- L phase boundary--i'e'" about 8A7?C!U

20 40 60 80 10001000

1100

1200

1300

1400

1500

1600 T(°C)

L (liqid)


Wt% Ni

• (d) 2hat is the composition of the last solid remaining prior to complete melting

8/20/2019 MSE 102Lecture 9


=0

( ) p g p p g

• nswer. The composition of the last solid remaining prior to complete melting

corresponds to the intersection with G-(G L) phase boundary" of the tie line

constructed across the G L phase region at 8A7?C!--i'e'" about K7 wt> &i'

20 40 60 80 10001000

1100

1200

1300

1400

1500

1600 T(°C)

L (liqid)


Wt% Ni

,' L+ +=L: P+OO&

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- , " weight raAti"#s'

B

- C"#serati"# " ,ass (Ni)'

- C",;i#e a;"e eqati"#s'

L + α = 1

C" = LCL + αCα

=

+

α =C" − CL

Cα − CL

=

+

L= Cα − C"

Cα − CL

- $ ge",etriA i#terpretati"#'

C"

αL

CL Cα,",e#t eqili;ri,'

1− α

s"li#g gies Leer le

L

=

α

8/20/2019 MSE 102Lecture 9


,hanGs &or Nour ttention%%Q

+e"ie# for+e"ie# for

&inal xam&inal xam

Dr. Khalil Alhatab

Ternary Phase Diagrams

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y g

• ,hree components

• Constructed by using a e$uilateral triangle as base%

• Pure components at each

end of triangle%

• @inary alloy composition

represented on edges%

,emperature can be represented as uniform throughout the

hole Diagram sothermal section%

igure 7'$7

8-19

Ternary Phase Diagram (!ont'')

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y g ( )

• xample:- ron-Chromium-<icGel phase diagrams%

•sothermal reaction at 4F00C

for this system

• Composition of any metal

at any point on the phase

diagram can be found by

dra#ing perpendicular

from pure metal corner to

apposite side and calculating

the 7 length of line at that

point

MSE 102Lecture 9

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Transcript of MSE 102Lecture 9