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IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
UniversityofVirginia,Dept.ofMaterialsScienceandEngineering
13
TheLeverRule
Massfractions:W
L=S/(R+S)=(C
-
Co
)/(C
-C
L)
W
=R/(R+S)=(C
o-
CL
)/(C
-C
L)
IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
UniversityofVirginia,Dept.ofMaterialsScienceandEngineering
14
Derivationoftheleverrule
WL=(C
-C
o)/(C
-C
L)
1)Allmaterialmustbeinonephaseortheother:
W
+W
L
=1
2)Massofacomponentthatispresentinbothphases
equalto
themassofthecomponentinonephase+
massof
thecomponentinthesecondphase:
W
C
+W
LC
L
=C
o
3)SolutionoftheseequationsgivesustheLeverrule.
W
=(C
o-C
L)/(C
-C
L)
IntroductiontoMaterials
Science,Chapter9,PhaseDiagrams
UniversityofVirginia,Dept.ofMaterialsScienceandEngineering
15
Phasecompositionsa
ndamounts.Anexample.
Massfractions:W
L=(C
-C
o)/(C
-C
L)=0.68
W
=(C
o-C
L)/(C
-C
L)=0.32
Co
=35wt.%,
CL=3
1.5wt.%,
C
=42.5wt.%
IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
Developmentofmicrostructureinisomorphousalloys
Equilibrium(veryslow)cooling
IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
Developm
entofmicrostructureinisomorphousalloys
Equilibrium(veryslow)cooling
Solidific
ation
in
thesolid
+
liquid
phaseoccurs
graduallyuponcoolingfromtheliquidusline.
Thecom
positionofthesolidandtheliquidchange
graduallyduringcooling(ascanbedeterminedbythe
tie-linem
ethod.)
Nucleiofthesolidphaseform
andtheygrowto
consume
alltheliquidatthesolidusline.
IntroductiontoMaterials
Science,Chapter9,PhaseDiagrams
Developmentofmicrost
ructureinisomorphousalloys
Non-equi
libriumcooling
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IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
UniversityofVirginia,Dept.ofMaterialsScienceandEngineering
43
Eutecticandeutectoidreactionsin
FeFe3C
Eutectoid:0.76wt%C,7
27
C
(0.76wt%C)(0.022wt%C)+Fe3C
Eutectic:4.30wt%C,
1147
C
L+Fe3CEutecticandeutectoidreactionsarevery
importantin
heattreatmentofsteels
IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
UniversityofVirginia,Dept.ofMaterialsScienceandEngineering
44
Developm
entofMicrostructureinIron-Carbonalloys
Microstructure
depends
on
composition
(carbon
content)andheattreatment.Inthediscussionbelowwe
considerslowcoolinginwhichequilibriumismaintained.
Microstructureofeutectoidsteel(I)
IntroductiontoMaterials
Science,Chapter9,PhaseDiagrams
UniversityofVirginia,Dept.ofMaterialsScienceandEngineering
45
Whenalloyofeutectoid
composition(0.7
6wt%
C)is
cooledslowlyitforms
perlite,alamellarorlayered
structureoftwophases:
-ferriteandcementite(Fe3C)
Thelayersofalternatingp
hasesinpearliteareformedfor
thesamereasonaslayeredstructureofeutecticstructures:
redistributionCatomsbetweenferrite(0.0
22wt%)and
cementite(6.7wt%)byato
micdiffusion.
Mechanically,pearlitehas
propertiesintermediatetosoft,
ductileferriteandhard,br
ittlecementite.
Microstructure
ofeutectoidsteel(II)
In
themicrograph,thedarkareasare
Fe3Clayers,
thelightphaseis-
fe
rrite
IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
Compositionstotheleftofeutectoid(0.022
-0.7
6wt%C)
hypoeutectoid(lessthaneutectoid-Greek)
alloys.
++Fe3CMicrostructureofhypoeutectoidsteel(I)
IntroductiontoMaterialsScience,Chapter9,PhaseDiagrams
Hypoeutectoidalloyscontainproeutectoidferrite(formed
abovetheeutectoidtemperature)plustheeutectoidperlite
thatcontain
eutectoidferriteandcementite.
Micr
ostructureofhypoeutectoidsteel(II)
IntroductiontoMaterials
Science,Chapter9,PhaseDiagrams
Compositionstotherightofeutectoid(0.7
6-2.1
4wt%C)
hypereutectoid(morethaneutectoid-Greek)alloys.
+Fe3C+Fe3C
Microstructureof
hypereutectoidsteel(I)
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