Phase Diagrams

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Phase Diagrams
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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?
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Melting point of an alloy
Liquid, L
1453ºC
Liquidus
L ?
solidus
1085ºC
Solid solution, ?
Cu
Ni
Wt Ni
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Equilibrium phase diagramorEquilibrium
diagramorPhase diagram
A diagram in the space of relevant thermodynamic
variables (e.g., T and x) indicating phases in
equilibrium is called a phase diagram.
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Components
The independent chemical species (element or
compound) in terms of which the composition of
the system is described are called components.
components
phases
System
H2O
Water
liquid
Water ice
H2O
Liquidsolid
liquid solution
nimbu, chini and pani
shikanji
? Fe3C
Fe C
Mild steel
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A single component phase diagram Unary diagram
A two-component phase diagram Binary diagram
A three-component phase diagram Ternary diagram
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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
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Phase Diagrams

• For any given point (x,T) the phase diagram can
  answer the following
• What phases are present?
• What are the phase compositions?
• What are the relative amounts of the phases
  (phase proportions or phase fractions)?

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Point A 60 wt Ni at 1100ºC
Q Phase present?
Ans ?
Q Phase composition ?
Ans 60 wtNi
Q Phase amount ?
Ans 100
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Point B 35 wt Ni at 1250ºC
Q Phases present?
Ans ? L
Q Phase compositions ?
Tie Line Rule
Q Phase amounts ?
Lever Rule
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Composition of phases in the two-phase region
Tie Line Rule
Tie Line
CL 31.5 wt Ni C? 42.5 wt Ni
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Amount of phases in the two-phase region
Tie-Line A lever
Alloy composition C0 Fulcrum
fL weight at liquidus point
f? weight at solidus point
The lever is balanced
Tie Lever Rule
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The Lever Rule A Mass balance Proof Prob. 7.6
Wt of alloy W
Wt of ? in alloy f?W
Wt of L in alloy fLW
Wt of Ni in alloy 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
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Development of Microstructure during
solidification
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Solder alloy?
An alloy of Pb and Sn
What is best composition of the solder alloy?
Requirements 1. should melt easily 2. should
give a strong joint
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Solder alloy
1-2-1 rule
Eutectic diagram
327
L
Liquidus
solidus
Liquidus
232
??L
solidus
L??
?
183
?
Eutectic horizontal
solvus
solvus
???
Pb
Sn
Wt Sn
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Pb monatomic fcc Sn monatomic bct
? Pb rich substitutional solid solution of Pb
and Sn crystal structure monatomic FCC
? Sn rich substitutional solid solution of Pb
and Sn crystal structure monatomic BCT
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Woods metal tea party
Bi 50.0 wt Pb 25.0 wt Cd 12.5 wt Sn 12.5 wt
An eutectic alloy with m.p. of 70ºC
100 g US 181
Anti-Fire Sprinklers
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Eutectic reaction
Invariant reaction
Callister Figs. 9.11, 12
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Microstructure of hypoeutectic alloy
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Eutectc mixture ???
Proeutectic or Primary ?
Amount of total ? and total ? at a temperature
just below 183ºC
Tie line just below 183ºC (red)
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Eutectc mixture ???
Proeutectic or Primary ?
Amount of proeutectic ? at a temperature just
below 183ºC
Amount of ? at a temperature just above 183ºC
Tie line just above 183ºC (green)
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EXPERIMENT 5
Eutectc mixture ???
Proeutectic or Primary ?
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)
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Optimum composition for solders
For electronic application
Eutectic solder 62 wt Sn
Minimum heating
For general application
Hypoeutectic solder
Cheaper
Allows adjustment of joint during solidification
in the ??L range
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Modern Trend
Lead-free solders
Phase diagrams can help in identification of such
solders
Sn-Ag-Cu
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Please collect your Minor I answer books from Lab
in the afternoon
Those who can, do. Those who cant teach G.B. Shaw
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Gibbs Phase Rule
Thermodynamic variables P, 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)
With Pressure and Temperature, total number of
variables P (C-1) 2
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Gibbs phase rule states that one cannot specify
all of the above P (C-1) 2 variables
independently in a system at equilibrium
Degrees of Freedom FNo. of thermodynamic
variables that can be specified independently
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Gibbs Phase Rule
F Degrees of freedom C No. of components in
the system P 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
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F C P 1
C2
F3-P
F 2
At eutectic reaction P3 (L, ?, ?)
F 1
F0
Invariant reaction
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Mild steel 0-0.3 wt C
The Iron-carbon system
Bicycle frameShip hullCar body
Medium C steel0.4-0.7 wt C
steel
Cast iron
Rail wheelrail axlerails
High C steel0.8-1.4 wt C
Razor bladesscissors, knives
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Phases in Fe-C system
Phase Symbol Description Liquid L Liquid
solution of Fe and C ?-Ferrite ?
Interstitial solid solution of C in ?-Fe
(high temperature bcc phase) Austenite
? Interstitial solid solution of C in ?-Fe
(FCC 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
(orthorhombic system) Hard and Brittle
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Ferrite
Austenite
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Invariant Reactions in Fe-C system
A horizontal line always indicates an invariant
reaction in binary phase diagrams
Peritectic Reaction
Eutectic Reaction
Eutectoid Reaction
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Eutectoid Reaction
Pearlite
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Ammount of Fe3C in Pearlite
Red Tie Line below eutectoid temp
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Development of Microstructure in a hypoeutectoid
steel
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ProeutectoidFerrite
EXPERIMENT 5
Pearlite
Microsructure of a hypoeutectoid steel, 0.38 wt C
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fpearlite below TE faustenite above TE
Tie-Line above the eutectoid temperature TE
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Development of Microstructure in a hypereutectoid
steel
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Pearlite
Proeutectoid cementite on prior austenite grain
boundaries
Microsructure of a hypereutectoid steel, 1.4 wt C
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Fproeutectoid cementitefcementite above TE
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Phase vs. microconstituents
A 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.
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Eutectoidsteel ?Fe3C Pearlite
Hypoutectoidsteel ?Fe3C Pearlite
proeutectoid ferrite
Hypereutectoidsteel ?Fe3C Pearlite
proeutectoidcementite
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T
Principle of Zone Refining
L
TmA
C? lt CL
T
?L
?
A
Wt B
C0
C?
CL
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SemiconductorTransistor was invented by
Bardeen, Brattain and Shockley
At ATT 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
Basis for modern Si technology
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