phases.pdf
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There are different ways in which the molecules associateTRANSCRIPT
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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?
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How do I predict?How do I predict?
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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.
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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?
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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!
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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
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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)
:
:
:
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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
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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)
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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
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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
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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
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Cu Ni
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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?
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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
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Phase Diagram DefinitionsPhase Diagram Definitions
Liquidus: Thesolubilitylimitb h habovewhichthereisonlyliquidpresent.
Solidus: TheLiquidus line Solidus line
L(Liquid) 1453C
+ L
solubilitylimitbelowwhichthereisonlysolidpresent.
1085C
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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
()
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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
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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
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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
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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:
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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:
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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.
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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:
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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.
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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.
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