Transcript Chapter 9

Phase Diagrams
Binary Eutectoid Systems
Iron-Iron-Carbide Phase Diagram
Steels and Cast Iron
1
What is Phase?
• The term ‘phase’ refers to a separate and identifiable
state of matter in which a given substance may exist.
• Applicable to both crystalline and non-crystalline
materials
• An important refractory oxide silica is able to exist as
three crystalline phases, quartz, tridymite and
cristobalite, as well as a non-crystalline phase, silica
glass, and as molten silica
• Every pure material is considered to be a phase, so
also is every solid, liquid, and gaseous solution
• For example, the sugar–water syrup solution is one
phase, and solid sugar is another
2
Introduction to Phase Diagram
• There is a strong correlation between
microstructure and mechanical properties,
and the development of microstructure of an
alloy is related to the characteristics of its
phase diagram
• It is a type of chart used to show conditions at
which thermodynamically distinct phases can
occur at equilibrium
• Provides valuable information about melting,
casting, crystallization, and other phenomena
3
ISSUES TO ADDRESS...
• When we combine two elements...
what equilibrium state do we get?
• In particular, if we specify...
--a composition (e.g., wt% Cu - wt% Ni), and
--a temperature (T )
then...
How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
Phase B
Phase A
Nickel atom
Copper atom
4
Solubility Limit
• At some specific temperature, there is a
maximum concentration of solute atoms that
may dissolve in the solvent to form a solid
solution, which is called as Solubility Limit
• The addition of solute in excess of this solubility
limit results in the formation of another
compound that has a distinctly different
composition
• This solubility limit depends on the temperature
5
Solubility Limit Sugar-Water
6
Microstructure
• the structure of a prepared surface of material as
revealed by a microscope above 25× magnification
• The microstructure of a material can strongly
influence properties such as strength, toughness,
ductility, hardness, corrosion resistance, high/low
temperature behavior, wear resistance, etc
7
Components and Phases
• Components:
The elements or compounds which are present in the mixture
(e.g., Al and Cu)
• Phases:
The physically and chemically distinct material regions
that result (e.g., a and b).
AluminumCopper
Alloy
b (lighter
phase)
a (darker
phase)
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Effect of T & Composition (Co)
• Changing T can change # of phases: path A to B.
• Changing Co can change # of phases: path B to D.
B (100°C,70) D (100°C,90)
1 phase
watersugar
system
Temperature (°C)
100
2 phases
L
80
(liquid)
60
L
+
S
i.e., syrup)
(solid
sugar)
(liquid solution
40
A (20°C,70)
20
2 phases
0
0
20
40
60 70 80
100
Co =Composition (wt% sugar)
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PHASE EQUILIBRIA
• Free Energy -> a function of the internal energy of a
system, and also the disorder of the atoms or
molecules (or entropy)
• A system is at equilibrium if its free energy is at a
minimum under some specified combination of
temperature, pressure, and composition
• A change in temperature, pressure, and/or
composition for a system in equilibrium will result in
an increase in the free energy
• And in a possible spontaneous change to another
state whereby the free energy is lowered
10
Unary Phase Diagram
• Three externally controllable parameters that
will affect phase structure: temperature,
pressure, and composition
• The simplest type of phase diagram to
understand is that for a one-component
system, in which composition is held constant
• Pure water exists in three phases: solid, liquid
and vapor
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Pressure-Temperature Diagram (Water)
• Each of the phases will exist under equilibrium conditions
over the temperature–pressure ranges of its corresponding
area
• The three curves (aO, bO, and cO) are phase boundaries; at
any point on one of these curves, the two phases on either
side of the curve are in equilibrium with one another
• Point on a P–T phase diagram where three phases are in
equilibrium, is called a triple point
12
Binary Phase Diagrams
• A phase diagram in which temperature and
composition are variable parameters, and
pressure is held constant—normally 1atm
• Binary phase diagrams are maps that
represent the relationships between
temperature and the compositions and
quantities of phases at equilibrium, which
influence the microstructure of an alloy.
• Many microstructures develop from phase
transformations, the changes that occur when
the temperature is altered
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Phase Equilibria
Simple solution system (e.g., Ni-Cu solution)
Crystal
Structure
electroneg
r (nm)
Ni
FCC
1.9
0.1246
Cu
FCC
1.8
0.1278
• Both have the same crystal structure (FCC) and have
similar electronegativities and atomic radii (W. Hume –
Rothery rules) suggesting high mutual solubility.
• Ni and Cu are totally miscible in all proportions.
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Phase Diagrams
• Indicate phases as function of T, Compos, and Press.
• For this course:
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
T(°C)
• Phase
Diagram
for Cu-Ni
system
• 2 phases:
1600
1500
L (liquid)
a (FCC solid solution)
L (liquid)
1400
1300
a
(FCC solid
solution)
1200
1100
1000
0
20
40
60
80
• 3 phase fields:
L
L+a
a
100
wt% Ni
15
Phase Diagrams:
# and types of phases
• Rule 1: If we know T and Co, then we know:
--the number and types of phases present.
A(1100°C, 60):
1 phase: a
B(1250°C, 35):
2 phases: L + a
1600
L (liquid)
B (1250°C,35)
• Examples:
T(°C)
1500
1400
1300
1200
1100
1000
Cu-Ni
phase
diagram
a
(FCC solid
solution)
A(1100°C,60)
0
20
40
60
80
100
wt% Ni
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Phase Diagrams:
composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
• Examples:
T(°C)
Cu-Ni
system
A
TA
Co = 35 wt% Ni
1300 L (liquid)
At T A = 1320°C:
Only Liquid (L)
B
TB
CL = Co ( = 35 wt% Ni)
At T D = 1190°C:
1200
D
Only Solid ( a)
TD
Ca = Co ( = 35 wt% Ni)
20
3032 35
At T B = 1250°C:
CLCo
Both a and L
CL = C liquidus ( = 32 wt% Ni here)
Ca = C solidus ( = 43 wt% Ni here)
tie line
a
(solid)
4043
50
Ca wt% Ni
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Phase Diagrams:
weight fractions of phases
• Rule 3: If we know T and Co, then we know:
--the amount of each phase (given in wt%).
• Examples:
Co = 35 wt% Ni
At T A : Only Liquid (L)
W L = 100 wt%, W a = 0
At T D: Only Solid ( a)
W L = 0, Wa = 100 wt%
At T B : Both a and L
WL 
S  43  35  73 wt %
R + S 43  32
Wa 
R
= 27 wt%
R +S
Cu-Ni
system
T(°C)
A
TA
1300
TB
1200
TD
20
tie line
L (liquid)
B
R S
D
3032 35
CLCo
a
(solid)
40 43
50
Ca wt% Ni
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The Lever Rule
• Tie line – connects the phases in equilibrium with
each other - essentially an isotherm
T(°C)
How much of each phase?
Think of it as a lever (teeter-totter)
tie line
1300
L (liquid)
B
TB
a
(solid)
1200
R
20
Ma
ML
S
30C C
40 C
a
L o
R
50
S
M a S  M L R
wt% Ni
WL 
C  C0
ML
S

 a
ML  M a R  S Ca  CL
Wa 
C  CL
R
 0
R  S Ca  CL
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Ex: Cooling in a Cu-Ni Binary
• Phase diagram:
Cu-Ni system.
• System is:
--binary
i.e., 2 components:
Cu and Ni.
T(°C) L (liquid)
1300
L: 35 wt% Ni
a: 46 wt% Ni
• Consider
Co = 35 wt%Ni.
Cu-Ni
system
A
35
32
--isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100 wt% Ni.
L: 35wt%Ni
B
C
46
43
D
24
L: 32 wt% Ni
36
120 0
a: 43 wt% Ni
E
L: 24 wt% Ni
a: 36 wt% Ni
a
(solid)
110 0
20
30
35
Co
40
50
wt% Ni
20
Cored vs Equilibrium Phases
• Ca changes as we solidify.
• Cu-Ni case: First a to solidify has Ca = 46 wt% Ni.
Last a to solidify has Ca = 35 wt% Ni.
• Fast rate of cooling:
Cored structure
• Slow rate of cooling:
Equilibrium structure
First a to solidify:
46 wt% Ni
Last a to solidify:
< 35 wt% Ni
Uniform C a:
35 wt% Ni
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Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Ductility (%EL,%AR)
400
TS for
pure Ni
300
TS for pure Cu
200
0 20 40
Cu
60 80 100
Ni
Composition, wt% Ni
--Peak as a function of Co
Elongation (%EL)
Tensile Strength (MPa)
--Tensile strength (TS)
60
%EL for pure Cu
%EL for
pure Ni
50
40
30
20
0 20
Cu
40
60
80 100
Ni
Composition, wt% Ni
--Min. as a function of Co
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Eutectic System
A eutectic system is a mixture of chemical
compounds or elements that has a single
chemical composition that solidifies at a
lower temperature than any other
composition
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Binary-Eutectic Systems
has a special composition
with a min. melting T.
2 components
Cu-Ag
system
T(°C)
Ex.: Cu-Ag system
1200
• 3 single phase regions
L (liquid)
1000
(L, a, b)
a L + a 779°C
• Limited solubility:
L+b b
800
T
a: mostly Cu
8.0
71.9 91.2
E
b: mostly Ag
600
• TE : No liquid below TE
ab
400
• CE : Min. melting TE
composition
200
• Eutectic transition
L(CE)
0
a(CaE) + b(CbE)
20
40
60 CE 80
100
Co , wt% Ag
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EX: Pb-Sn Eutectic System (1)
• For a 40 wt% Sn - 60 wt% Pb alloy at 150°C, find...
--the phases present: a + b
T(°C)
--compositions of phases:
CO = 40 wt% Sn
Ca = 11 wt% Sn
Cb = 99 wt% Sn
--the relative amount
of each phase:
Wa =
C - CO
S
= b
R+S
Cb - C a
Pb-Sn
system
300
200
L (liquid)
a
L+ a
18.3
150
100
99 - 40
59
=
= 67 wt%
99 - 11
88
C - Ca
Wb = R = O
Cb - C a
R+S
L+b b
183°C
61.9
R
97.8
S
a+b
=
=
40 - 11
29
=
= 33 wt%
99 - 11
88
0 11 20
Ca
40
Co
60
80
C, wt% Sn
99100
Cb
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EX: Pb-Sn Eutectic System (2)
• For a 40 wt% Sn - 60 wt% Pb alloy at 220°C, find...
--the phases present: a + L
T(°C)
--compositions of phases:
CO = 40 wt% Sn
Ca = 17 wt% Sn
CL = 46 wt% Sn
--the relative amount
of each phase:
CL - CO
46 - 40
=
Wa =
CL - Ca
46 - 17
6
=
= 21 wt%
29
Pb-Sn
system
300
a
220
200
L+ a
R
L (liquid)
L+b b
S
183°C
100
CO - Ca
23
=
WL =
= 79 wt%
CL - Ca
29
a+b
0
17 20
Ca
40 46 60
Co CL
100
80
C, wt% Sn
26
Microstructures
in Eutectic Systems: I
• Co < 2 wt% Sn
• Result:
--at extreme ends
--polycrystal of a grains
i.e., only one solid phase.
T(°C)
L: Co wt% Sn
400
L
a
L
300
a
200
L+ a
(Pb-Sn
System)
a: Co wt% Sn
TE
a+ b
100
0
Co
10
20
30
Co, wt% Sn
2
(room T solubility limit)
27
Microstructures
in Eutectic Systems: II
L: Co wt% Sn
• 2 wt% Sn < Co < 18.3 wt% Sn 400T(°C)
• Result:
 Initially liquid + a
 then a alone
 finally two phases
 a polycrystal
 fine b-phase inclusions
L
L
a
300
L+a
a
200
TE
a: Co wt% Sn
a
b
100
a+ b
0
10
20
Pb-Sn
system
30
Co
Co , wt%
2
(sol. limit at T room )
18.3
(sol. limit at TE)
Sn
28
Microstructures
in Eutectic Systems: III
• Co = CE
• Result: Eutectic microstructure (lamellar structure)
--alternating layers (lamellae) of a and b crystals.
T(°C)
L: Co wt% Sn
300
Micrograph of Pb-Sn
eutectic
microstructure
L
Pb-Sn
system
a
200
L+a
Lb b
183°C
TE
100
ab
0
20
18.3
40
b: 97.8 wt% Sn
a: 18.3 wt%Sn
60
CE
61.9
80
160 m
100
97.8
C, wt% Sn
29
Lamellar Eutectic Structure
30
Microstructures
in Eutectic Systems (Pb-Sn): IV
• 18.3 wt% Sn < Co < 61.9 wt% Sn
• Result: a crystals and a eutectic microstructure
L: Co wt% Sn
T(°C)
300
L
a
L
Pb-Sn
system
a
200
a L
L+a
R
TE
L+b b
S
S
R
primary a
eutectic a
eutectic b
0
20
18.3
40
60
61.9
Ca = 18.3 wt% Sn
CL = 61.9 wt% Sn
Wa = S = 50 wt%
R+S
WL = (1- Wa) = 50 wt%
• Just below TE :
a+b
100
• Just above TE :
80
Co, wt% Sn
100
97.8
Ca = 18.3 wt% Sn
Cb = 97.8 wt% Sn
Wa = S = 73 wt%
R+S
Wb = 27 wt%
31
Hypoeutectic & Hypereutectic
300
L
T(°C)
a
200
L+ a
L+b b
TE
a+b
(Pb-Sn
System)
100
0
20
40
hypoeutectic: Co = 50 wt% Sn
a
a
a
60
80
eutectic
61.9
Co, wt% Sn
hypereutectic: (illustration only)
eutectic: Co = 61.9 wt% Sn
b
a a
b
a
175 m
100
b
b b
b
160 m
eutectic micro-constituent
32