Phase Diagrams: Lecture 2 (Manufacturing Technology)

1
Phase Diagrams
Lecture 2 (Manufacturing Technology)
CONTENTS
Basic definitions
Solubility Limits
Equilibrium
Interpretation of Phase Diagrams
Binary Isomorphous Systems (Cu-Ni)
Lever Rule
Gibbs Phase Rule
3
Importance of Phase Diagrams
There is a strong correlation between
microstructureandmechanical properties, and
the development of alloy microstructure is
related to the characteristics of its phase
diagram.
Phase diagrams provide valuable information
about melting, casting, crystallizationandother
phenomena.
4
Components:
The elements or compounds that are mixed initially (Al and Cu).
Phases:
A phase is a homogenous, physically distinct and mechanically separable
portion of the material with a given chemical composition and structure
(a and b).
a (darker
phase)
b (lighter
phase)
Basic Definitions
Aluminum-
Copper
Alloy
Solution solid, liquid, or gas solutions, single phase
Mixture more than one phase
Phase Equilibria: Solubility Limit
Question: What is the
solubility limit for salt in
water at 20C?
Answer: 65 wt% Salt.
At 20C, if C <65 wt% salt: salty water
At 20C, if C >65 wt% salt: salty water +salt
65
Solubility Limit:
Maximum concentration for
which only a single phase
solution exists.
Salt/Water Phase Diagram
S
a
l
t
T
e
m
p
e
r
a
t
u
r
e

(
C
)
0
20
40 60
80 100
C =Composition (wt% salt)
L
(liquid solution
i.e., salty water)
Solubility
Limit
L
(liquid)
+
S
(solid
salt) 20
40
60
80
100
W
a
t
e
r
6
7
Criteria for Solid Solubility
Crystal
Structure
electronega
tivity
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
Rotheryrules) suggestinghighmutual solubility.
Simple system(e.g., Ni-Cu solution)
Ni andCuaretotallysolubleinoneanother for all proportions.
8
Microstructure
In metal alloys, microstructure is characterized
by the number of phases, their proportions,
and the way they are arranged.
The microstructure depends on:
Alloying elements
Concentration
Heat treatment (temperature, time, rate of cooling)
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Equilibrium
A system is at equilibrium if its free energy is at a
minimum, given a specified combination of
temperature(T), pressure(P) andcomposition( C).
The (macroscopic) characteristics of the systemdo not
changewithtimethesystemisstable.
A change in T, P or C for the systemwill result in an
increase in the free energy and possible changes to
another statewherebythefreeenergyislowered.
One Component Phase Diagram
10
11
Binary Isomorphous Systems
Cu-Ni system:
The liquid L is a homogeneous liquid solution composed of
Cu and Ni.
The phase is a substitutional solid solution consisting of
Cu and Ni atoms with an FCC crystal structure.
At temperatures below 1080 C, Cu and Ni are mutually
soluble in each other in the solid state for all compositions.
The complete solubility is explained by their FCC structure,
nearly identical atomic radii and electro-negativities, and
similar valences.
The Cu-Ni system is termed isomorphousbecause of this
complete liquid and solid solubility of the 2 components.
12
Cu-Ni
phase
diagram
Isomorphous Binary Phase Diagram
Phase diagram:
Cu-Ni system.
System is:
-- binary
2 components:
Cu and Ni.
-- isomorphous
i.e., complete
solubility of one
component in
another; a phase
field extends from
0 to 100 wt% Ni.
wt% Ni
20 40 60 80 100 0
1000
1100
1200
1300
1400
1500
1600
T(C)
L (liquid)
a
(FCC solid
solution)
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Phase Diagrams
Indicate phases as a function of Temp, Comp and Pressure.
Focus on:
- binary systems: 2 components.
- independent variables: T and C (P =1 atm is almost always used).
Cu-Ni
system
2 phases:
L
(liquid)
a
(FCC solid solution)
3 different phase fields:
L
L +a
a
wt% Ni
20 40 60 80 100 0
1000
1100
1200
1300
1400
1500
1600
T(C)
L (liquid)
a
(FCC solid
solution)
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Effect of solid solution strengthening on:
--Tensile strength (TS) --Ductility (%EL,%AR)
--Peak as a function of C
o
--Min. as a function of C
o
Mechanical Properties: Cu-Ni System
E
l
o
n
g
a
t
i
o
n

(
%
E
L
)
Composition, wt%Ni
Cu
Ni
0 20 40 60 80 100
20
30
40
50
60
%EL for
pure Ni
%EL for pure Cu
T
e
n
s
i
l
e

S
t
r
e
n
g
t
h

(
M
P
a
)
Composition, wt%Ni
Cu Ni
0 20 40 60 80 100
200
300
400
TS for
pure Ni
TS for pure Cu
15
Rule 1: If we know T and C
o
, then we know:
--how many phases and which phases are present.
Examples:
wt% Ni 20 40 60 80 100 0
1000
1100
1200
1300
1400
1500
1600
T(C)
L (liquid)
a
(FCC solid
solution)
L

+

a
l
i
q
u
i
d
u
s
s
o
l
i
d
u
s
A(1100,60)
B
(
1
2
5
0
,
3
5
)
Cu-Ni
phase
diagram
A(1100, 60):
1 phase: a
B(1250, 35):
2 phases: L +a
Determination of phase(s) present
Melting points: Cu =
1085C, Ni =1453 C
Solidus- Temperature where alloy is completely solid. Above this line, liquefaction begins.
Liquidus- Temperature where alloy is completely liquid. Below this line, solidification begins.
16
o
, then we know:
--the composition of each phase.
Examples:
wt% Ni
20
1200
1300
T(C)
L (liquid)
a
(solid)
L

+

a
l
i
q
u
i
d
u
s
s
o
l
i
d
u
s
30 40 50
T
A
A
D
T
D
T
B
B
tie line
L

+

a
43 35 32
C
o
C
L
C
a
Cu-Ni
system
Phase Diagrams: compositionof phases
At T
A
=1320C:
Only Liquid (L) present
C
L
=C
0
( =35 wt% Ni)
At T
B
=1250C:
Both
a
and L present
At T
D
=1190C:
Only Solid (a) present
C
a
=C
0
( =35 wt% Ni)
C
L
=C
liquidus
( =32 wt% Ni)
C
a
=C
solidus
( =43 wt% Ni)
17
o
, then we know:
--the amount of each phase (given in wt%).
Cu-Ni system
Examples:
At T
B
: Both a and L
At T
A
: Only Liquid (L)
W
L
=100wt%, W
a
=0
At T
D
: Only Solid (a)
W
L
=0, W
a
=100wt%
C
o
=35wt%Ni
wt% Ni
20
1200
1300
T(C)
L (liquid)
a
(solid)
L

+

a
l
i
q
u
i
d
u
s
s
o
l
i
d
u
s
30 40 50
T
A
A
D
T
D
T
B
B
tie line
L

+

a
43 35 32
C
o
C
L
C
a
R S
Phase Diagrams: weight fractionsof phases
W
L

43 35
43 32
73wt %

C
a

C
o
C
a

C
L
=27wt %
C
o
C
L
C
a
C
L
Wa
Sum of weight fractions:
18
Conservation of mass (Ni):
Combine above equations:

W
L
W
a
1

C
o
W
L
C
L
W
a
C
a
R
R
S

W
a

C
o
C
L
C
a
C
L
S
R
S
W
L

C
a

C
o
C
a

C
L
A geometric interpretation:
C
o
R
S
W
a
W
L
C
L
C
a
moment equilibrium:

1 W
a
solving gives Lever Rule

W
L
R W
a
S
THE LEVER RULE: A PROOF
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wt% Ni
20
1200
1300
30 40 50
1100
L (liquid)
a
(solid)
T(C)
A
35
C
0
L: 35wt%Ni
Cu-Ni
system
Phase diagram:
Cu-Ni system.
Consider
microstuctural
changes that
accompany the
cooling of a
C
0
=35 wt% Ni alloy
Ex: Equilibrium Cooling of a Cu-Ni
Alloy
46
35
43
32
a: 43 wt%Ni
L: 32 wt%Ni
B
a: 46 wt%Ni
L: 35 wt%Ni
C
E
L: 24 wt%Ni
a: 36 wt%Ni
24
36
D
Development of
microstructure during
the non-equilibrium
solidification of a 35 wt%
Ni-65 wt% Cu alloy
outcome:
Segregation-nonuniform
distribution of elements
within grains.
Weaker grain boundaries
if alloy is reheated.
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Gibbs Phase Rule
Phase diagrams and phase equilibria are subject to the laws of thermodynamics.
Gibbs phase rule is a criterion that determines how many phases can coexist within a
system at equilibrium.
P + F = C + N
P: # of phases present
F: degrees of freedom (temperature, pressure, composition)
C: components or compounds
N: noncompositional variables
For the Cu-Ag system @ 1 atm for a single phase P:
N=1 (temperature), C = 2 (Cu-Ag), P= 1 (a, b, L)
F = 2 + 1 1= 2
This means that to characterize the alloy within a single phase
field, 2 parameters must be given: temperature and composition.
If 2 phases coexist, for example, aL , bL, ab, then according to GPR, we have 1
degree of freedom: F = 2 + 1 2= 1. So, if we have Temp or composition, then we can
completely define the system.
If 3 phases exist (for a binary system), there are 0 degrees of freedom. This means the
composition and Temp are fixed. This condition is met for a eutectic system by the
eutectic isotherm.

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