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1Chapter 7 Phase Equilibria and Phase Diagrams
The one-component phase diagram Gibbs Phase Rule
Phase equilibria in a two-component system The isomorphous
diagram The lever rule Equilibrium solidification and
microstructure of
isomorphous alloys Liquidius and solidus boundaries Deviations
from ideal behavior
Chapter 7 Phase Equilibria and Phase Diagrams, Continued
Phase equilibria in a two-component system The eutectic phase
diagram The peritectic phase diagram The monotectic phase diagram
Complex diagrams Phase equilibria involving solid-to-solid
reactions
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2Why important ?Some properties that might be difficult to
predict using a common sense without the knowledge of the phase
diagrams
example 1: Melting temperature of a mixture AB (solution) of two
components A and B could be either lower or higher than the melting
point of each component (!). This could be a failure mechanism in
electronic or mechanical components. But could also be used to your
advantage.
example 2: Upon cooling to a lower temperature a phase
transformation of a material could cause expansion, which could
cause internal stresses and failure (e.g. tin food cans will
crumble at low T)
example 3: No abrupt liquid-to-solid transformation when two
components are present (solid + liquid in a temperature range)
Example: Chip-Solder-Joint-Failure
Why important ?Some properties that might be difficult to
predict using a common sense without the knowledge of the phase
diagrams
example 4: Tmelt (Sn) = 232 C, Tmelt (Pb) = 327 C
but Tmelt(Sn0.62Pb0.38) = 183 C, so this is a common soldering
alloy
example 5: Tmelt (Au) = 1064 C, Tmelt (Si) = 2550 Cbut
Tmelt(Au0.97Si0.03) = 363 C, so thin layer of gold is used to
attach Si chip to a ceramic substrate (shock protection)
example 6: Mechanical properties (hardness and tensile strength)
of an alloy could be substantially higher than that of the
individual components (e.g. hardness (AgCu) about twice the harness
of Ag or Cu)
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3One-Component Phase Diagrams
F = C P + 2C- ComponentsP- Number of phasesF- Degrees of
freedomF = 2
F = 1
F = 0
# of state variables (e.g. two: P and T)
Gibbs Phase rule:
Two-Component Phase Diagrams
F = C P + 1
F = 2
F = 1T
In a two-phase field need to specify either the temperature or
the composition of one of the phases.
Xs Xl
Isomorphous system ( complete solubility over the composition
range)
If pressure is fixed (1 atm)
Hume-Rothery Rules for substitutional solution: The size <
~15%. The electronegativities and valance
similar The crystal structures of the two species
must be the same to form a continuous series of solid
solutions.
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4Two-Component Phase Diagrams
Composition, XB
Tem
pera
ture ( )
( )( )( )
1
11
l s
o l l s s
l s
o l s s s
o l l s s s
o l s s l
o ls
s l
f fX X f X ff fX X f X fX X X f X fX X f X X
X Xf
X X
+ == +
= = += + =
= ( )( )s ol s lX X
fX X
=
The Lever Rule in a Two-Component System
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5Two-Component Phase Diagrams
Two-Component Phase Diagrams
Tem
pera
ture
, C
Composition, XBTime Time
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6Two-Component Phase Diagrams
Deviation from ideal behavior
Congruent melting maximum
EAB > 0.5 (EAA + EBB)
Two-Component Phase Diagrams
Deviation from ideal behavior Congruent melting
minimum
EAB > 0.5 (EAA + EBB)
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7Eutectic Phase Diagrams
F = 1, must specify temperatureor the compositionof one of the
phases
F = 1
F = 1
F = 1
F = 0
F = 0, temperatureand compositionsof the phase arefixed.
Composition, XB
TATB
X1 XE X2A B
Tem
pera
ture
F = 2
F = 2
F = 2, mustspecify temperatureand composition
F = 2 X X
TXs
XlT
Xs
Xl
T X X
Solvus
Cooling Curves and Phase Boundaries
Tem
pera
ture
Composition, XB
Time
Alloy 1
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8Cooling Curves and Phase BoundariesTe
mpe
ratu
re
Composition, XB
Time
Alloy 2
Cooling Curves and Phase Boundaries
Tem
pera
ture
Composition, XB
Time
Alloy 3
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9Various physical properties and their relationship to a
eutectic phase diagram
Eutectic Phase Diagrams
Tem
pera
ture
Composition, in % B
1. For the alloy composition of 0.27 % B calculate the fraction
of solid and the fraction of liquid that forms under equilibrium
cooling at the eutectic T
2. Calculate the amount of and that will form from the liquid
just below the eutectic isotherm
3. Calculate the amount of in the alloy at temperature just
below the eutectic T
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10
Eutectic Phase Diagrams
This liquid becomes theeutectic mixture of and when the
temperature drops just below the eutectic temperature which is
composedof: 0.73 0.37
0.73 0.200.68
f
f
0.37 0.200.73 0.200.32
f
f
Just above the eutectic temperature the fractionof liquid and
solid are:
0.27 0.200.37 0.200.41
l
l
f
f
0.37 0.270.37 0.200.59
f
f
The first solid that formsis called primary Just below the
eutectic temperaturethe microstructure is composed ofprimary that
formed above the eutectic temperature and from the eutectic
mixture
total primary eutecticf f f = +
0.59 (0.41)(0.68) 0.87total
f = + =0.73 0.270.73 0.20
f= 0.87f =or
Tem
pera
ture
Composition, in % B
Microstructure Above and Below the Eutectic Temperature for an
Off-Eutectic Alloy
Just above TE Just below TE
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11
Microstructure Above and Below the Eutectic Temperature for
Off-Eutectic Alloys
Just below TE
Increasing primary Decreasing eutectic
Decreasing primary Increasing eutectic
Deviation from Hume-Rotherys Rules
Increasing deviation leads to decrease in the maximum solid
solubility of B in .
Tem
pera
ture
Composition, XBA
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12
Eutectic Phase Diagram, No Solid Solubility
Tem
pera
ture
Composition, XB
Eutectic Phase DiagramsAl-Si System
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13
Methods for Determining a Phase Diagram
Primary -aluminum
aluminum / silicon eutectic
Microstructure of an Aluminum-Silicon Alloy
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14
Phase Diagrams Containing Two Eutectics
Possible to have several solid solution regions: e.g. 2 eutectic
reactions and 3 solid solutions (, , and )
Note that upon cooling from T max at the alloy composition X
there is a phase change but no composition change (CONGRUENT
melting)
Line compound
Peritectic Phase Diagrams
l + =
if both the L and S phases have a tendency to cluster, the
liquidustemperature increase and the solidus temperature
decreases
In addition, a miscibility gap(region of non-mixing) appears
A progressive increase in the clustering tendency leads to the
PERITECTIC phase diagram
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15
The Use of Cooling Curves for Determining a Peritectic Phase
Diagram
Tem
pera
ture
Composition, XB TimeXP X2X2
TA
TL
TP
l + =
Analysis of a Peritectic Phase Diagram
Tem
pera
ture
Composition
Alloy 1 Alloy 2 Alloy 3
Alloy 3 at T20.88 0.600.88 0.30.48
l
l
f
f
= =
Alloy 3 at T5
0.90 0.600.90 0.340.54
f
f
= =
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16
Monotectic Phase Diagrams
A region of immiscibility (non-mixing) develops in the L
phase
example: oil and water
Liquid1 = Liquid2 + (solid)
L1 L2
XM
L2
L2
Review of Invariant Binary ReactionsEutectic Type
l
l2l1
Eutectic
Eutectoid
Monotectic
Monotectoid
l +
+
l1 + l2
1 2
2 1 +
Al-Si, Fe-C
Fe-C
Cu-Pb
Al-Zn, Ti-V
On cooling one phase going to two phases
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Review of Invariant Binary ReactionsPeritectic Type
ll +
+
Peritectic
Peritectoid
Fe-C
Cu-Al
On cooling two phases going to one phase
HW Questions
1. When a solid melts congruently, the liquid and solid have
different / the same composition(s).
2. At constant temperature the fraction of the phases in a
two-phase field changes / remains the same when the overall
composition of the alloy is
changed, but remains in the two-phase field.
3. Why would alloys close to the eutectic composition be
suitable for castings rather than alloy compositions far from the
eutectic composition?
4. On cooling when a two-phase liquid plus solid transforms to a
solid phase the transformation is eutectic / peritectic in
nature.
5. On cooling the peritectoid reaction written symbolically has
one phase going to two / two phases going to one.
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18
HW Questions
At what T an alloy containing 88% B will start melting?
At what T it will completely transform into liquid?
What is the composition of phase for this alloy @ T8?
What is the maximum solid solubility of B in a and A in b? Whose
rules apply here?
For an alloy containing 88% B, calculate the fraction of the
liquid and solid phases and their compositions at temperature T3,
T4, and T5
At a temperature just below the eutectic temperature, how much
is primary , what is the total fraction of , and what is the
fraction in the eutectic. (Alloy composition is 88% B)
Tem
pera
ture
Composition, XB
TA
TB
A B
1. Label all phase fields.
2. Identify all invariant reactions.
Labeling Complex Phase Diagrams
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Labeling Complex Phase Diagrams
Eutectic
Eutectic
PeritecticPeritectic
Eutectic
Eutectic l = +
l + =
l = +
Labeling Complex Phase Diagrams
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20
Summary One-component phase diagrams with
temperature and pressure as the experimental variables that
affect equilibrium.
Introduction to the Gibbs Phase Rule and its application to
one-component systems.
Two-component systems and the rules that govern the composition
of the phases, the number of phases and the amount of each phase at
equilibrium.
The applications of these rules to complex, two-component
systems illustrated that regardless of how complex the phase
diagram appeared, the rules that were developed could be easily
applied.