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Materials Science Chapter 9 1
Chapter 9 Phase Diagram
• Basic Concepts• Isomorphous System • Detail in Isomorphous Phase Diagram• Microstructure Development in Isomorphous Phase
Diagram• Binary Eutectic System• More Complicated System• The Iron-Carbon System
Materials Science Chapter 9 2
Basic Concepts• Solubility limit
– Maximum concentration of solute atoms that may dissolve in the solvent to form a solution
– Dependence on temperature, pressure…
• Phase– A homogeneous portion of a system that has uniform physical
and chemical characteristics.
• Microstructure– Direct microscopic observation– Number of phases, proportions,
and distributions
• Phase equilibria– Free energy is at its minimum– Stable system with multiple phases– Metastable state
• Phase diagram (equilibrium)– The relationships between temperature,
compositions and quantities of phases at equilibrium.
Materials Science Chapter 9 3
Binary Isomorphous Systems (Cu-Ni System)• Phase diagram
– Liquid phase (homogeneous)
– α phase: substitutional solid solution
– Complete liquid and solid solubility (isomorphous)
– Liquidus line and solidus line
– Pure copper and pure nickel
– Cooling curve
Materials Science Chapter 9 4
What Can Be Known From Phase Diagram • Phases present
• Phase compositions– Single phase region
– Two-phase region
• Phase amounts (fraction)– Single phase region
– Two-phase region• Lever rule
0
0
0
1
32.05.315.42
5.3135
68.05.315.42
355.42
CCWCWWW
CCCC
SRRW
CCCC
SRSW
LL
L
L
L
LL
=+=+
=−−
=−−
=+
=
=−−
=−−
=+
=
αα
α
αα
α
α
Materials Science Chapter 9 5
Microstructure Development in Isomorphous
• Equilibrium cooling– Very slow cooling
– Maintain phase equilibrium
Materials Science Chapter 9 6
Microstructure Development in Isomorphous
• Nonequilibrium cooling– Diffusion process can not
be complete within limited time.
Materials Science Chapter 9 7
Mechanical Properties of Isomorphous Alloys
Materials Science Chapter 9 8
Binary Eutectic Phase Diagram• Three single-phase
regions– α, β, L
• Three two-phase regions
• Solubility limit• Solvus line, liquidus
line, and solidus line• Eutectic isotherm
(horizontal solidus line)
• Eutectic invariant point
• Eutectic reaction
)()()( EEE CCCL βα βα +↔)%2.91()%0.8()%9.71( AgwtAgwtAgwtL βα +↔
Materials Science Chapter 9 9
Eutectic Reaction
• Proceeds to completion at a constant temperature
• Generates two solid phases
• Different from the phase transformation of a pure component
• Three phases are in equilibrium only at the points along the eutectic isotherm.
Materials Science Chapter 9 10
Information From Phase Diagram • Phases present
• Phase compositions
• Phase amounts (fraction)
Materials Science Chapter 9 11
Microstructure Development in Eutectic Reaction
Materials Science Chapter 9 12
Microstructure Development in Eutectic Alloys
Materials Science Chapter 9 13
Microstructure Development in Eutectic Alloys
Materials Science Chapter 9 14
Relative Amount of Primary α and Eutectic α
RQPPW
RQPRQW
QPQW
QPPWW Le
++=
+++
=
+=
+==
β
α
α '
Materials Science Chapter 9 15
Materials Science Chapter 9 16
Systems with Intermediate Phases
Materials Science Chapter 9 17
System with Intermetallic Compounds
Materials Science Chapter 9 18
Eutectoid and Peritectic Reactions
• Eutectoid reaction
• Peritectic reaction
εγδ +⇔
εδ ⇔+ L
Materials Science Chapter 9 19
Congruent and Incongruent Phase Transformations
• Congruent– No change in
composition
• Incongruent– Involve changes in
composition (at least on one of the phases)
• Congruent melting point
Materials Science Chapter 9 20
The Gibbs Phase Rule
• The number of phases coexisting within a system follows
P + F = C + N– P: the number of phases present
– F: the number of degrees of freedom
– C: the number of components in the system
– N: the number of non-compositional variables
• One phase region
F = 3 – P = 3 – 1 = 2
• Two phase region F = 1
• Three phase region F = 0
Materials Science Chapter 9 21
The Gibbs Phase Rule
• The number of phases coexisting within a system follows
P + F = C + N– P: the number of phases present
– F: the number of degrees of freedom
– C: the number of components in the system
– N: the number of non-compositional variables
• One phase region
F = 3 – P = 3 – 1 = 2
• Two phase region F = 1
• Three phase region F = 0
Materials Science Chapter 9 22
Iron-Iron Carbide (Fe-Fe3C) Phase Diagram• Phases
– α phase: ferrite, BCC, magnetic
– γ phase: austenite, FCC, non-magnetic
– δ phase: δ ferrite, BCC– Intermediate compound:
cementite, Fe3C, very hard and brittle, metastable
– Not a true equilibrium phase diagram
• Solubility limit of C– Interstitial impurity– Influence mechanical
properties
Iron-Iron Carbide (Fe-Fe3C) Phase Diagram
• Characteristics• One eutectic reaction
• One eutectoid reaction
• Classification of ferrous alloys
– Iron: < 0.008wt%C, ferrite– Steel: 0.008 ~ 2.14wt%C– Cast iron: 2.14 ~ 6.7wt%C
)%7.6()%14.2()%3.4( 3 CwtCFeCwtCwtL +⇔ γ
)%7.6()%022.0()%76.0( 3 CwtCFeCwtCwt +⇔αγ
)%7.6()%14.2()%3.4( 3 CwtCFeCwtCwtL +⇔ γ
)%7.6()%022.0()%76.0( 3 CwtCFeCwtCwt +⇔αγ
Materials Science Chapter 9 23
Materials Science Chapter 9 24
Microstructure Development: Eutectoid Phase
Pearlite
Materials Science Chapter 9 25
Microstructure Development: Hypoutectoid
Materials Science Chapter 9 26
Microstructure Development: Hypereutectoid
Materials Science Chapter 9 27
Relative Amount Calculation
UTUW
UTTWP
+=
+=
'αXV
VW
XVXW
CFe
P
+=
+=
'3
