PHASE DIAGRAMS

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PHASE DIAGRAMS

• Phase Rule
• Types of Phase diagrams
• Lever Rule

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• Casting
• Metal Forming
• Welding
• Powder Processing
• Machining

Thermo-mechanical Treatments
Crystal
Atom
Structure
Microstructure
Component
Electro- magnetic
Phases
Defects

• Vacancies
• Dislocations
• Twins
• Stacking Faults
• Grain Boundaries
• Voids
• Cracks

Residual Stress

Processing determines shape and microstructure of
a component
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DEFINITIONS
Components of a system
Independent chemical species which comprise the
system Elements, Ions,Compounds E.g. Au-Cu
system Components ? Au, Cu Ice-water system
Component ? H2O Al2O3 Cr2O3 system
Components ? Al2O3, Cr2O3
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Phase
Physically distinct, chemically homogenous and
mechanically separable region of a system (e.g.
gas, crystal, amorphous...).

• Gaseous state always a single phase ? mixed at
  atomic or molecular level
• ?Liquid solution is a single phase ? e.g. NaCl
  in H2O
• ? Liquid mixture consists of two or more
  phases ? e.g. Oil in water (no mixing at the
  atomic/molecular level)
• Solids ? In general due to several
  compositions and crystals structures many
  phases are possible ? For the same
  composition different crystal structures
  represent different phases. E.g. Fe (BCC) and
  Fe (FCC) are different phases ? For the same
  crystal structure different compositions
  represent different phases. E.g. in Au-Cu alloy
  70Au-30Cu and 30Au-70Cu are different
  phases

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Phase transformation
Phase Transformation is the change of one phase
into another. E.g. ? Water ? Ice ? ?- Fe (BCC)
? ?- Fe (FCC)
Grain
The single crystalline part of polycrystalline
metal separated by similar entities by a grain
boundary
Microstructure
Structures requiring magnifications in the region
of 100 to 1000 times OR The distribution of
phases and defects in a material
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Phase diagram
Map demarcating regions of stability of various
phases. or Map that gives relationship between
phases in equilibrium in a system as a function
of T, P and composition (from textbook)
Variables / Axis of phase diagrams

• The axis are thermodynamic (T, P, V), kinetic
  (t) or composition variables (C, x)
• In single component systems the usual variables
  are T P
• In phase diagrams used in materials science the
  usual variables are T x
• In the study of phase transformation kinetics
  Time Temperature Transformation (TTT)
  diagrams or Continuous Cooling Transformation
  (CCT) diagrams are also used where the axis are T
  t

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The GIBBS PHASE RULE
F C ? P 2
For a system in equilibrium
F Degrees of FreedomC Number of ComponentsP
Number of Phases
or
F ? C P 2
The geometrically equivalent Eulers formula for
convex polyhedra
V0 V ? VerticesV1 E ? EdgesV2 F ? Faces
V0 ? V1 V2 2
V ? E F 2
or
Vertices degrees of Freedom
Faces Phases
Edges Components
8 12 6 2
8
F
C 2
P
?

Degrees of Freedom
What you can control
What the system controls
?

Can control the no. of components added and P T
System decided how many phases to produce given
the conditions
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Variables

• C No. of Components
• P No. of Phases
• F No. of degrees of Freedom
• Variables in the system Composition
  variables Thermodynamic variables
• Composition of a phase specified by (C 1)
  variables
• No. of variables required to specify the
  composition of all Phases P(C 1)
• Thermodynamic variables P T (usually
  considered) 2
• Total no. of variables in the system P(C 1)
  2
• F lt no. of variables ? F lt P(C 1) 2 i.e.
  C P 2 lt P(C 1) 2
• In a single phase system F no. of variables
• P ? ? F ?

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C 2
C 3
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Single component phase diagrams (Unary)
F C P 2
Gas
Single phase regionsF 1 1 2 2
Liquid
? (BCC)
Two phase coexistenceF 1 2 2 1
Temperature (ºC) ?
1535
1410
? (FCC)
Triple points 3 phase coexistenceF 1 3 2
0
? (HCP)
? (BCC)
Pressure (GPa) ?
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Binary Phase Diagrams

• Pressure changes often have little effect on the
  equilibrium of solid phases
• Binary phase diagrams are usually drawn at 1
  atmosphere pressure
• Variables are reduced to T composition

F C ? P 1
Phase rule for condensed phases
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F C P 1
System with complete solid solubility
M.P. of A
M.P. of B
C 1 P 2 F 0
C 2 P 2 F 1
T ?
A
B
B ?
The two component region expands withone degree
of freedom i.e. we can chose one Variable say
the T
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C 2 P 1 F 2
Variables ? T, CLB ?? 2
M.P. of A
C 1 P 2 F 0
Variables ? T, CLB, CSB ?? 3
C 2 P 2 F 1
M.P. of B
C 2 P 1 F 2
T ?
Variables ? T, CSB ?? 2
B
A
2 P
2 P
3 P
B ?
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• Complete liquid and solid solubility ?
  ISOMORPHOUS PHASE DIG.

• A and B must satisfy Hume-Rothery rules
• E.g. Cu-Ni, Ag-Au, Ge-Si, Al2O3-Cr2O3

L
2200
Liquidus
L S
2100
T (ºC) ?
S
2000
Solidus
50
70
90
Al2O3
Cr2O3
10
30
Sn ?
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Tie line and Lever Rule

• Say the composition C0 is cooled slowly
  (equilibrium)
• At T0 there is L S equilibrium
• Solid (crystal) of composition C1 coexists with
  liquid of composition C2

Cooling
L

• At T0
• The fraction of liquid (fl) is ? (C0 ? C1)
• The fraction of solid (fs) is ? (C2 ? C0)

Tie line
T0
L S
T ?
S
C0
C2
C1
A
B
B ?
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Variations to the isomorphous phase diagram

• A?B bonds stronger than A?A and B?B bonds
• Solid stabilized ? Ordered solid formation

• A?A and B?B bonds stronger than A?B bonds
• Liquid stabilized ? Phase separation in the
  solid state

L ?
L
L
L ?
?
E.g. Au-Ni
?
?
?1
?2
? ?
?1 ?2
?1 ?2 are different only in lattice parameter
Ordered solid
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Congruently melting alloys
Variables ? T, CLB, CSB ?? 3
C 2 P 2 F 1

• Congruently melting alloys- just like a pure
  metal
• But in requiring that CLB CSB we have
  exhausted the degree of freedom. Hence T is
  automatically fixed

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Congruent transformations

• Melting point minimum
• Melting point maximum
• Order disorder transformation
• Formation of an intermediate phase

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Eutectic reactionL ? ? ?
Liquidus
327?C
L
300
232?C
Solidus
L ?
200
? L
?
T (ºC) ?
183?C
?
100
? ?
Solvus
62
97
18
50
70
90
Pb
Sn
10
30
Sn ?
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Eutectic reactionL ? ? ?
L
300
L ?
200
? L
?
T (ºC) ?
?
C 2 P 3 F 0
? ?
100
Increasing solubility of B in A with ?T
50
70
90
A
B
10
30
B ?
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Isomorphous to Eutectic

• A?A and B?B bonds stronger than A?B bonds
• Liquid stabilized

L
L ?
?
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Liquid (melt)
Cooling
L
Hypereutectic composition
300
? L
L ?
200
?
?
?
100
? ?
50
70
90
Pb
Sn
10
30
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Peritectic Phase Diagram
Peritectic reactionL ? ? ?
1700
L
1500
L ?
1300
T (ºC) ?
Melting points of the components vastly different
1100
?
? ?
900
?
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Isomorphous to Peritectic
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Fe-Cementite diagram
EutecticL ? ? Fe3C
Peritectic L ? ? ?
L
1493ºC
?
L ?
1147ºC
2.06
?
Eutectoid ? ? ? Fe3C
? Fe3C
723ºC
?
0.025
T ?
Fe3C
Fe
6.7
0.8
4.3
RT0.008
0.16
C ?
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• Cementite is metastable (more readily nucleates
  as compared to graphite the stable phase)
• Cementite can decompose into graphite- but
  usually does not- practically an equilibrium
  phase
• Austenite (?) ? FCC, Ferrite (?) ? BCC,
  Cementite (Fe3C) ? Orthorhombic

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?
? Fe3C

• ?

?
? Fe3C
Eutectoid ? ? ? Fe3C
T ?
Fe
0.02
0.8
C ?
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Cooling
?
C1
C2
C3
? Fe3C

• ?

?
? Fe3C
Eutectoid ? ? ? Fe3C
T ?
Fe
0.02
0.8
C ?
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C1
Pearlite a microconstituent
C2
C3
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Please read section 7.7 on Zone refining
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