PHASE DIAGRAMS

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PHASE DIAGRAMS

• THEORY AND APPLICATIONS

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Some basic concepts

• Phase
• A homogeneous region with distinct structure and
  physical properties
• In principle, can be isolated
• Can be solid, liquid or gas
• Phase Diagram
• Representation of phases present under a set of
  conditions (P, T, Composition etc.)

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Concepts...

• Phase transformation
• Change from one phase to another
• E.g. L S, S S etc.
• Occurs because energy change is negative/goes
  from high to low energy state
• Phase boundary
• Boundary between phases in a phase diagram

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A simple phase diagram
System H2O
Liquid
Phase boundary
Pressure
Solid
Triple point (Invariant point)
Vapor
Temperature
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Gibbs Phase Rule
P F C 2
Pnumber of phases Cnumber of components Fnumber
of degrees of freedom (number of independent
variables)
F C - P 2
Modified Gibbs Phase Rule (for incompressible
systems)
P F C 1
F C - P 1
Pressure is a constant variable
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Application of the phase rule
At triple point, P3, C1, F0 i.e. this is an
invariant point
At phase boundary, P2, C1, F1
In each phase, P1, C1, F2
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Solidification(cooling) curves
Pure metal
Alloy
L
Soldification begins
L
TL
L S
L
S
Tm
TS
Solidification complete
S
S
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Construction of a simple phase diagram

• Conduct an experiment
• Take 10 metal samples(pure Cu, Cu-10Ni,
  Cu-20Ni, Cu-30Ni, pure Ni)
• Melt each sample and then let it solidify
• Record the cooling curves
• Note temperatures at which phase transformations
  occur

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Results
L
T
L
S
L
L
TL
TL
L
TNi
L S
L S
L
S
Pure Ni
TS
S
S
TS
TCu
S
Cu-20Ni
Pure Cu
Cu-10Ni
t
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Binary isomorphous phase diagram
L
Temp
TNi
x
x
x
x
x
x
x
x
x
x
LS
x
x
x
x
x
x
x
x
TCu
x
x
Cu
S
Ni
0
100
10
60
70
80
90
30
40
50
20
Cu
Ni
Ni
Composition
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Microstructural changes during solidification
Pure metal
L
T
L
S
L
S
Tm
S
S
t
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Microstructural changes during solidification
L
Alloy
T
L
TL
L S
TS
S
S
t
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Binary isomorphous phase diagram
L
T
L
L
T1
T2
LS
T3
L
T4
S
S
CL
C0
CS
0
100
10
60
70
80
90
30
40
50
20
A
B
B
Composition
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Notes

• This is an equilibrium phase diagram (slow
  cooling)
• The phase boundary which separates the L from the
  LS region is called LIQUIDUS
• The phase boundary which separates the S from the
  LS region is called SOLIDUS
• The horizontal (isothermal) line drawn at a
  specific temperature is called the TIE LINE
• The tie line can be meaningfully drawn only in a
  two-phase region
• The average composition of the alloy is CO

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Notes..

• The intersection of the tie line with the
  liquidus gives the composition of the liquid, CL
• The intersection of the tie line with the solidus
  gives the composition of the solid, CS
• By simple mass balance,
• CO fS CS fL CL
• and fS fL 1
• CO fS CS (1- fS) CL

Lever Rule
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Some calculations

• In our diagram at T3, CO A-40B,
• CSA-90B and CLA-11B
• Therefore, fS29/79 or 37 and
• fL50/79 or 63
• If we take an initial amount of alloy 100 g,
• amt. of solid37 g (3.7 g of A and 33.4 g of B)
  and amt. of liquid63 g (56.07 g of A and 6.93 g
  of B)

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The Eutectic Phase Diagram
Liquidus
L
a b (TE, CLCE)
Solidus
Solvus
T
L
bL
aL
TE
b
a
E
ab
CE
A
B
WtB
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Pure A or B
L
T
L
S
L
CE
L
bL
aL
TE
b
ab
L
a
ab
E
Other alloys between A and B
ab
CE
L
A
B
La
WtB
L
ab
ab
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Solidification for alloy of eutectic composition
T
L
L
bL
aL
TE
b
a
E
ab
S
ab
CE
A
B
WtB
ab
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Eutectic microstructure
Lamellar structure
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L
T
L
bL
aL
b
TE
a
Proeutectic a
ab
CE
ab
A
B
WtB
ab
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T
L
L
bL
L
aL
b
TE
a
ab
a
CE
A
B
WtB
b particles
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The Eutectoid Phase Diagram
a b (TE, CgCE)
g
T
g
b g
a g
TE
b
a
E
ab
CE
A
B
WtB
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Cooling of an alloy of eutectoid composition
T
g
g
b g
g
a g
TE
b
a
E
ab
S
ab
CE
A
B
WtB
ab
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Cooling of an alloy of hypoeutectoid composition
g
T
g
g
b g
a g
TE
b
Pro-eutectiod a
a
g
E
ab
Pro-eutectiod a
ab
S
A
B
WtB
ab
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The Peritectic Phase Diagram
b (at TP)
a L
Note a and L will react only in a certain
proportion NPPM
L
L
T
b
L
a L
TP
a
N
b L
P
M
ab
b
CP
b
A
B
WtB
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b ( at TP)
a L
Note a and L will react only in a certain
proportion NPPM
NPPM12
T
L
L
a
L
a L
TP
a
N
b L
P
a
M
L
ab
CP
b
b
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85
60
10
A
B
WtB
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b (at TP)
a L
Note a and L will react only in a certain
proportion NPPM
L
L
T
a
L
a L
TP
a
b
N
b L
P
M
L
ab
CP
b
b
A
B
WtB
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