2/26/2013

1

Chapter 10Chapter 10Phase Diagrams Phase Diagrams EquilibriumEquilibrium

Lecture #12

Learning Objectives:

What is a phase?

What is thermodynamic equilibrium?

What three components need to be used (established) to define the equilibrium?equilibrium?

How to determine the composition and fraction of a phase in a two-phase regime (Lever Rule).

1 Pages 359-387.Relevant Reading for this Lecture...

What am I?What am I?

AlSi

Al-Si alloy

AlSi

2What am I composed of?What am I composed of?

6

How do I predict?How do I predict?

2/26/2013

2

Phase BPhase A

Alloys and PhasesAlloys and Phases Components: The elements or compounds which are present

in the alloy (e.g., Ni and Cu; Al and Cu; etc.)

Al i

Phase BIntermetallic

Phase ASolid solution

Nickel atomCopper atom

Aluminum-CopperAlloy

(darker phase)

(lighter phase)

Adapted from chapter-opening photograph, Chapter 9, Callister, Materials Science & Engineering: An Introduction, 3e.

3

When we combine two (or more) elements...what is the resulting equilibrium state?

Questions to Address...Questions to Address...(components)

In particular, if we specify...-- the composition (e.g., wt% Cu - wt% Ni), and-- the temperature (T)

then...1) How many phases form?1) How many phases form?2) What is the composition of each phase?3) What is the amount of each phase?

4

2/26/2013

3

What is a Phase?What is a Phase?

Aphase isahomogeneousportion ofasystemthathas uniform physical and chemical characteristicshasuniformphysicalandchemicalcharacteristics

AphasedoesnotneedtobecontinuousTwo Phases of H2O1 Liquid (water)

You can have many phases present at the same time 1. Liquid (water)

2. Solid (ice)present at the same time

The phases can even be from the same components

ItsallH2O!

5

Solubility LimitsSolubility Limits

Insomesystems,twocomponentscanmixandmaintainasinglephase:example,sugar(SOLUTE)+tea(SOLVENT)=SYSTEM tea

Whenweaddasolutetoasolvent,inmostsystems,thesolventisabletodissolvethesolutewhilemaintainingasinglephase(SOLIDSOLUTION).

h l b d d

add some sugar

add lots of sugar

tea+sugar1 phase

Thesolventbecomessaturatedandcannolongerdissolveanysoluteatthesolubilitylimit.Addingsolutebeyondthesolubilitylimityieldstwodifferent phases.

f g

2 phases

6

2/26/2013

4

In atwophase region,thephases present inasystemwill havedifferent compositions thantheaveragecompositionofthemixture.

Composition of PhasesComposition of Phases

EXAMPLE:Assumethesolubilitylimitforaglassoficedteaat25oCis4packsofsugar,andyouadded5packs.Theconcentrationsofthealloy(tea+sugar),liquid,andsolidarethen:

C 5 1Alloy

CS = 1 p sugar, 0 p tea

CL = 4 p sugar, 1 p tea

Co = 5 p sugar, 1 p teaAlloy(tea + sugar)

Liquid(Saturated tea)

Solid(Precipitate)

:

:

:

7

Phase Equilibria: Solubility LimitPhase Equilibria: Solubility Limit

Solubility Limit:Maximum concentration for

Sugar/Water Phase Diagram

Solubility 100

Solution solid, liquid, or gas solutions; single phase Mixture more than one phase

RECALL:

Question: What is thesolubility limit for sugar in water at 20C?

A

which only a single phase solution exists.

Tem

pera

ture

(C

)

L(liquid solution

i.e., syrup)

Solubility Limit L

(liquid) + S

(solid sugar)20

40

60

80

Answer: 65 wt% sugar.At 20C, if C < 65 wt% sugar: syrupAt 20C, if C > 65 wt% sugar:

syrup + sugar

65

Suga

r

0 20 40 60 80 100C = Composition (wt% sugar)

Wat

er

Adapted from Fig. 10.1, Callister & Rethwisch 4e.

Solubility limit increases with T:e.g., if T = 100C, solubility limit = 80wt% sugar.8

4

2/26/2013

5

EquilibriumEquilibrium

Thermodynamicequilibriumisinlowest energy state atsomespecifiedcombinationoftemperature,pressure,andcomposition.p

Thecharacteristicofthesystemdoesnotchange withtime.Thesystemisstable.

Metastable:Notinthelowestenergystate,butkineticallyconstrained in a higher energy state which does not changeconstrainedinahigherenergystatewhichdoesnotchangeforlongperiodoftime(ex.Diamond,carbonwouldloweritsenergyifitweregraphite)

Variableswechangetoadjustequilibrium temperature,pressure,composition.Theseareourknobsasengineers9

Single Component (or Unary) SystemSingle Component (or Unary) SystemPhase Diagram for HPhase Diagram for H22OO

GasSTEAMSTEAM

100C

Tempe

rature

Gas

Solid

Liquid

ICEICE

WATERWATER

1 atm

100C

0CF1atm= 0

PhasediagramsshowuswhichphasesarepresentasafunctionofstatevariablesPressure (P) Temperature (T) Composition (x or c)

Pressure(logscale)

10

2/26/2013

6

Temperature

Multiple Component SystemMultiple Component SystemPP--TT--xx Phase Diagram for APhase Diagram for A--BB

L(Liquid)+L

+L

Pressure

Gas

Solid

Liquid+

Temperature

Composition

A

B

Gas

In condensed materials we usually fix P = 1 atm.11

Types of Phase DiagramTypes of Phase Diagram Multiplecomponentphasediagrams:

Binary =2components Ternary =3componentsQuaternary = 4 components

Ternary isotherm

Quaternary =4components Quinary =5components Etc.

Binary

+L

L

+L

mpe

ratu

re

Weusephasediagramsasmapstoguidedesignwithmaterials.

A B% B

+

Tem

12

2/26/2013

7

Effects of Temperature & Composition Effects of Temperature & Composition (C(Coo)) Altering T can change # of phases: path A to B.

Altering Co can change # of phases: path B to D.

B (100C,Co = 70)1 phase

Solubility limit

erat

ure

(C

)

L(liquid solution

i e syrup)

100

40

60

80 L (liquid)

+ S

(solid )

water-sugarsystem

D (100C,Co = 90)2 phases

1 phase

70 80 1006040200

Tem

pe

C = Composition (wt% sugar)

i.e., syrup)

20

0

sugar)

Adapted from Fig. 9.1, Callister & Rethwisch 8e.

A (20C,Co = 70)2 phases

13

2

RECALLRECALL

Criteria for Solid Solubility Criteria for Solid Solubility Simple system (e.g., Cu-Ni solution)

1600T(C)

CrystalStructure Electroneg r (nm) valence

Ni FCC 1.9 0.1246 +2

Cu FCC 1.8 0.1278 +2

20 40 60 80 10001000

1100

1200

1300

1400

1500

1600

L (liquid)

(FCC solid solution)

Both have the same crystal structure (FCC) and valence (+2), and have similar electronegativities and atomic radii (W. HumeRothery rules)suggesting high mutual solubility.

Ni and Cu are totally soluble in one another for all proportions.

wt% Ni20 40 60 80 1000

14

Cu Ni

2/26/2013

8

ReviewReview(up to this point)(up to this point)

Weusephasediagramstodeterminehi h/ h h t bl f tiwhich/wherephasesarestableasafunction

ofthestatevariables

Whatarevariablestochangephases?Intheprevious slides what variable have wepreviousslides,whatvariablehaveweassumedisconstant?

15

L

How to Read a Phase Diagram: CuHow to Read a Phase Diagram: Cu--NiNi

Allliquid,1phase

L(Liquid)

+

1453C

L

Liquid+solid,2phases,likeiceteasaturatedwithsugar.

1085CAllsolid,1solidsolution.

singlephase,

Whatareweassumingaboutoneofthestatevariables?16

1

2/26/2013

9

Phase Diagram DefinitionsPhase Diagram Definitions

Liquidus: Thesolubilitylimitb h habovewhichthereisonlyliquidpresent.

Solidus: TheLiquidus line Solidus line

L(Liquid) 1453C

+ L

solubilitylimitbelowwhichthereisonlysolidpresent.

1085C

17

Composition of PhasesComposition of Phases

Inasinglephaseregion,alloycomposition and

Co

compositionandphasecompositionarethesame.

Co =50%Ni CS,1100oC=50%NiC 1500 C 50% Ni

Single phase

(L)

Single CL,1500oC=50%Ni

WHATABOUTTHE2PHASEREGION?

gphase

()

18

1

2/26/2013

10

Binary Phase Diagram DefinitionsBinary Phase Diagram Definitions

Themeltingtemperatureofapure component is

Solidus line

L(Liquid) 1453C

C2

Liquidus line+ L

purecomponentisfixed.

Inalloysmeltingtemperaturesdependoncomposition

C1Melting complete

Melting starts

Melting complete

1085C

composition.

Completemeltingofalloys occursover arange oftemperatures.19

4

Melting starts

Materials SystemsMaterials Systems

Whatisthecompositionfortwophases?DifferentthanCo!

RECALL:Sweettea(i.e.,tea+sugar)isanalogoustoamaterials system! Compositionofthe

l d

Co

materialssystem!Compositionoftheliquid

solid

CS = 1 p sugar, 0 p tea

CL = 4 p sugar, 1 p tea

Co = 5 p sugar, 1 p tea

20

2/26/2013

11

Lever Rule:Lever Rule:Gives you the amounts of each phaseGives you the amounts of each phase

Compositionofh l d

ML M

Tieline connectsthephasesinequilibrium.Itissometimescalledanisotherm.

theliquid

Composition

R S

M x S ML x RA tie line is like a A tie line is like a

teeterteeter--tottertotter

Avg.Compositionofthealloy

ofthesolid

0 0 LLL L

C C C CS RW WR S C C R S C C

21

1

Tie Line and Quantitative CalculationsTie Line and Quantitative Calculations

WL W

The amount of any phase is the opposite side of the leverdivided by the total length of the lever.

W + WL = 1KEEP IN MIND:

22

2/26/2013

12

T(C)

For a 40 wt% Sn-60 wt% Pb alloy at 150C, determine:-- the phases present Pb-Sn

system

EX 1: Pb-Sn Eutectic System

Answer: + the phase compositions

L+L+

+

20018.3

300

100

L (liquid)

183C61.9 97.8

-- the phase compositions

-- the relative amountof each phase

150 SR

Answer: C = 11 wt% SnC = 99 wt% Sn

W= C - C0C - CS

R+S =

Answer:

23

C, wt% Sn20 60 80 1000 40C0

11C 99C

C C

= 99 - 4099 - 11 =5988 = 0.67

R S

W =C0 - CC - C

=RR+S

= 2988

= 0.33= 40 - 1199 - 11

Adapted from Fig. 10.8, Callister & Rethwisch 4e.

3

the phase compositionsT(C)

For a 40 wt% Sn-60 wt% Pb alloy at 220C, determine:-- the phases present: Pb-Sn

system

EX 2: Pb-Sn Eutectic System

Answer: + LAnswer: C = 17 wt% Sn-- the phase compositions

L+

+

200

300

100

L (liquid)

L+

183C

-- the relative amountof each phase

W =CL - C0 =

46 - 40

220 SRCL = 46 wt% Sn

Answer:

24

C, wt% Sn20 60 80 1000

W= CL - C = 46 - 17=

629 = 0.21

WL =C0 - CCL - C

=2329 = 0.79

40C046CL

17CAdapted from Fig. 10.8, Callister & Rethwisch 4e.

3

2/26/2013

13

SummarySummary

PhaseisahomogeneousportionofasystemthathasuniformphysicalandchemicalcharacteristicsAll iti C i h h f h t i l i i d Alloycomposition,Co,ishowmuchofeachmaterialismixedtogether.

Inasinglephaseregion,compositionofthephase=Co. Inatwophaseregion,thecompositionofeachphasedoes

notchangewithalloycompositionatfixedtemperature,andl h f h l h h l b lisequaltotheintersectionofthetielinewiththesolubility

limits.

Inatwophaseregion,theamountofeachphasecanbedeterminedbytheinverseleverrule,dividingtheoppositesideoftheleverbythelengthofthetieline.

25