Phase
Diagrams
Di
g
Why do cocktail ice served in expensive
restaurants are clear whereas the ice
formed in your refrigerator is cloudy?
What is a solder alloy?
What is the best composition for solder?
How is ultrpure Si for computer chips
produced?
d
d
Melting
M
ng point
p n of
f an
n alloy
y
Liquid,
Liquid L
1453ºC
L+
1085 C
1085ºC
Solid solution, 
Cu
Wt% Ni
Ni
E
ilib i
h
di
Equilibrium
phase
diagram
or
Equilibrium
diagram
E ilib i
di
or
Ph
Phase
diagram
di
A diagram
di
in
i th
the space of
f relevant
l
t
thermodynamic variables (e.g., T
and
d x)) iindicating
di ti phases
h
iin
equilibrium is called a phase
diagram.
di
Components
The independent chemical species (element or
compound) in terms of which the composition of
the system is described are called components.
components
S
System
components
phases
h
Water
H2O
liquid
Water +ice
H2O
Liquid+solid
shikanji
nimbu, chini and pani
liquid solution
Mild steel
Fe + C
 + Fe3C
A single component phase diagram:
Unary diagram
A two-component phase diagram:
y diagram
g
Binary
A three-component
three component phase diagram:
Ternary diagram
Cu-Ni binary
phase diagram
Any given point (x,T) on the
phase diagram represents
an alloy of composition x
held at equilibrium at
temperature T
Point A:
60 wt% Ni at 1100ºC

Point B:
35 wt% Ni at 1250ºC
Callister, Fig. 9.2
Phase Diagrams
D g m
For any given
g ven po
nt (x,
point
(x,T)) the phase
diagram can answer the following:
1 What
1.
Wh t phases
h
are present?
t?
2.. What ar
are the
th phase
phas compositions?
compos t ons?
3. What are the relative amounts of
th phases
the
h
(phase
( h
proportions
ti
or
phase fractions)?
Point A:
60 wt% Ni at 1100ºC
Q
Q: Phase p
present?
Ans: 
Q: Phase composition ?

Ans: 60 wt%Ni
Q: Phase amount ?
Ans: 100%
Point B:
35 wt% Ni at 1250ºC
Q
Q: Phases p
present?
Ans:  + L
Q: Phase compositions ?

Tie Line Rule
Q: Phase amounts ?
Lever Rule
Composition of phases in the two-phase region
Tie Line Rule

L
Tie Line

CL= 31
31.5
5 wt%
t% Ni
C= 42.5 wt% Ni
Amount of phases in the two-phase region

L
Tie-Line: A lever
Alloy composition C0: Fulcrum
fL: weight at liquidus point
f: weight at solidus point
fL
f
The lever is balanced
f L (C0  C L )  f (C  C0 )
f L  f  1
Tie Lever Rule
C  C0 opposite
pp
lever arm
fL 

C  C L
total lever arm
The Lever Rule: A Mass balance Proof

L
Prob. 7.6
Wt of alloy = W
Wt of  in alloy
= fW
Wt of L in alloy
= fLW
W of
Wt
f Ni in
i alloy
ll = W C0/100
Wt of Ni in 
= fWC/100
Wt of Ni in L
= fL WCL/100
Wt of Ni in alloy = Wt of Ni in  + Wt of Ni in L
C f + CL fL = C0
f + fL = 1
C  C0 opposite
arm
it lever
l
fL 

total lever arm
C  C L
Development of Microstructure during
lidifi ti
solidification
35  32 3
  0.273
43  32 11
f L  1  f  0.727
f 
Single phase
polycrystalline 
Solder alloy?
An alloy of Pb and Sn
What is best composition of the
solder alloy?
Requirements:
1. should melt easily
2 should
2.
h ld give
i a strong jjoint
i
Solder alloy
1-2-1 rule
327
183 
Eutectic diagram
L
L
L
Eutectic horizontal
Eutectic
temperature

Eutectic
point

Pb
232
62
Wt % Sn
Sn
Eutectic
composition
Pb: monatomic fcc
Sn: monatomic bct
:
Pb rich substitutional solid
solution of Pb and Sn
crystal structure: monatomic FCC
:

Sn
n rrich
ch substitutional
su st tut ona so
solid
solution of Pb and Sn
crystal
st l structure:
st
t
monatomic
t i BCT
Woods
metal
tea
W
m
party
Bi
B 50.0
50 0 wt%
%
Pb 25.0 wt%
Cd 12.5
12 5 wt%
%
Sn 12.5 wt%
An eutectic alloy with m
m.p.
p of 70ºC
70 C
100 g
US$ 181
Anti-Fire Sprinklers
Eutectic
ti
reaction
Invariant
reaction
L
62
wt%Sn
cooll
183ºC

18
wt%Sn
%
 
97
wt%Sn
%
Eutectic mixture
Callister Figs. 9.11, 12
375 X
L
(40 wt% Sn)

L
L

18 wt% Sn
L+

L (62 wt% Sn)
Eutectic mixture 
+
Primary 
18 wt%
t% Sn
Eutectic 
(18 wt % Sn)
Eutectic  (97 wt %
Sn)
Hypoeutectic alloy
Microstructure of hypoeutectic alloy
Eutectc mixture 
Proeutectic
or Primary 
18
62
97
f total   1  0.72  0.28
Amount of total  and total  at a temperature just below 183ºC
Tie lline just below
b l
1 º (red)
183ºC
( d)
f total 
97  40
57


 0 . 72
97  18
79
Eutectc mixture 
Proeutectic
or Primary 
18
62
97
f eut     1  0.5  0.5
Amount of proeutectic  at a temperature just below 183ºC
= Amount of  at a temperature just above 183ºC
Tie line just above 183ºC (green)
f pro

62  40
22


 0 .5
44
62  18
EXPERIMENT 5
Eutectc mixture 
Proeutectic
or Primary 
18
62
C0  51 wt % Sn
Let the fraction of proeutectic  in micrograph fpro = 0.25
Let the composition (wt% Sn) of the alloy be C0
Tie line just above 183ºC (green)
f pro

62  C 0

 0 . 25
62  18
97
Optimum composition for solders
F electronic
l t
i application
li ti
For
Eutectic solder
62 wt% Sn
18
62
97
Mi i
Minimum
h
heating
i
For general application
Hypoeutectic solder
Cheaper
Allows adjustment
j
of jjoint during
g
solidification in the L range
Modern Trend
Lead-free solders
Phase diagrams
g m can help
p in
identification of such solders
Sn-Ag-Cu
Please collect your Minor I
answer books from Lab in the
afternoon
Those who can, do. Those
who
h can’t
’t teach
t
h
G B Sh
G.B.
Shaw
Gibbs Phase Rule
Thermodynamic variables:
P,
P T,
T Phase Compositions
(overall composition is not considered)
If there are C components then C-1 compositions
have to be specified for each phase
Therefore total number of composition variables:
P (C-1)
(C 1)
With Pressure and Temperature
Temperature, total number of
variables = P (C-1) + 2
Gibbs phase
rule
p
u states that one
n
cannot specify all of the above
p
y in
P ((C-1)) + 2 variables independently
a system at equilibrium
Degrees of Freedom F:
No. of thermodynamic variables
that can be specified independently
Gibbs Phase Rule
F = Degrees of freedom
C = No. of components in the system
P = No.
No of phases in equlibrium
F=C–P+2
If pressure and temp both are variables
F=C–P+1
If pressure is held constant
F=C–P+1
C=2
F=3-P
F =2
At eutectic
u
reaction P=3
(L, , )
F =1
F=0
Invariant
reaction
The Iron-carbon system
Bicycle frame
Ship hull
Car
C body
b d
1410
Medium C steel
0.4-0.7 wt% C
1150
910
steel
Cast iron
725
0.8
0 02
0.02
Mild steel
0-0.3 wt% C
Rail wheel
rail axle
rails
High C steel
0.8-1.4 wt% C
Razor bl
R
blades
d
scissors, knives
Phases in Fe-C system
Phase Symbol
Description
Liquid
L
Liquid solution of Fe and C
-Ferrite

Interstitial solid solution of C in
-Fe
Fe (high temperature bcc phase)
Austenite

Interstitial solid solution of C in
-Fe ((FCC p
phase of Fe))
Ferrite

Interstitial solid solution of C in
-Fe (room temperature bcc phase)
Soft and Ductile
Cementite Fe3C
Intermetallic compound of Fe and C
( th h bi system)
(orthorhombic
t )
Hard and Brittle
Ferrite
Austenite
Invariant Reactions in Fe-C system
i
t l li
l
iindicates
di t an iinvariant
i t reaction
ti
Ah
horizontal
line always
in binary phase diagrams
Peritectic Reaction
 (0.1 wt % C )  L (0.5 wt % C )   (0.18 wt % C )
1493o C
Eutectic Reaction
L (4.3 wt % C )   (2.1 wt % C )  Fe3C (6.67 wt % C )
1150 o C
Eutectoid Reaction
 (0.8 wt % C )   (0.02 wt % C )  Fe3C (6.67 wt % C )
725o C
E t t id Reaction
R
ti
Eutectoid
      Fe 3 C
0.8
725 o C
cool
0.02
6.67
Pearlite
Eutectoid Reaction
      Fe
F 3C
0.8
725 o C
cool
0.02
6.67
Pearlite
Ammount of Fe3C in Pearlite
Red Tie Line below eutectoid temp
f
pearlite
F3C
0.8  0.02 0.78


 0.117
6.67  0.02 6.65
Development of
Microstructure
in a
hypoeutectoid
st l
steel
Proeutectoid
Ferrite
EXPERIMENT 5
Pearlite
Microsructure of a hypoeutectoid steel, 0.38 wt% C
f pearlite 
0.8  0.38 0.42

 0.54
0.8  0.02 0.78
fpearlite below TE = faustenite above TE
Tie-Line above the eutectoid temperature TE
f pearlite
0.8  0.38 0.42

 0.54

0.8  0.2 0.78
Development of
Microstructure
in a
hypereutectoid
steel
Pearlite
Proeutectoid
cementite on
prior
austenite
grain
boundaries
Microsructure of a hypereutectoid steel, 1.4 wt% C
Fproeutectoid cementite=fcementite above TE
f proeutectoid cementite
1.4  0.8
0.6


 0.10
6.67  0.8 5.87
Phase vs. microconstituents
fp
Ap
phase or a mixture of
phases which has a distinct
identity in a microstructure is called a
microconstituent
Pearlite is not a phase.
It is microconstituent which is a mixture of
two phases  and Fe3C.
Eutectoid
steell
Hypoutectoid
steell
Hypereutectoid
steell
+Fe3C
+Fe3C
+Fe3C
Pearlite
Pearlite +
proeutectoid ferrite
Pearlite +
proeutectoid
cementite
T
Principle of Zone Refining
L
TmA
C < CL
T
+L
L

A
C
C0 CL
Wt % B
SemiconductorTransistor was invented by
Bardeen, Brattain and Shockley
At AT&T Bell Labs
One needs ultrapure Si (impurity level few ppm)
Zone Refining was invented by Pfann at Bell Labs
as a process to obtain ultrapure Si
B i for
Basis
f modern
d
Sii technology
h l