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ENGI 5911: Chemistry and Physics of Materials II Chapter 9 Dr. Amy Hsiao Winter 2014
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ENGI 5911: Chemistry and Physics of Materials II
Chapter 9
Dr. Amy Hsiao Winter 2014
Chapter 9
Phase DiagramsEquilibrium Microstructural Development
Single-phase microstructure of commercially pure molybdenum, 200. Although there are many grains in this microstructure, each grain has the same uniform composition. (From ASM Handbook, Vol. 9: Metallography and Microstructures, ASM International,
Materials Park, OH, 2004.)
(a) Schematic representation of the one-component phase diagram for H2O. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with the familiar transformation temperatures for H2O (melting at 0C and boiling at
100C).
One Component Phase Diagram for H20
Pressure-temperature phase diagram for water. Point 2 corresponds to the
melting point at 1 atm, T = 0C, and Point 3 corresponds to the boiling
temperature, T = 100C.
(a) Schematic representation of the one-component phase diagram for pure iron. (b) A projection of the phase diagram information at 1 atm generates a temperature scale labeled with important transformation temperatures for iron. This projection
will become one end of important binary diagrams
Components: The elements or compounds which are mixed initially
(e.g., Ni and Cu)
Phases: The physically and chemically distinct material regions
that result (e.g., a and b).
COMPONENTS AND PHASES
Cu-Ni Alloy System
Components: The elements or compounds which are mixed initially
(e.g., Al and Cu)
Phases: The homogeneous portion of a system that has uniform physical and
chemical characteristics; distinct material regions result (e.g., a and b).
System:
Aluminum-
Copper
Alloy
COMPONENTS, PHASES, SYSTEMS
Phase Diagrams
Solubility Limit the maximum concentration of solute atoms that may dissolve in the solvent to form a solid solution for a given alloy system at a specific temperature
Effect of T & Composition (Co) Changing T can change # of phases:
D (100C,90) 2 phases
B (100C,70) 1 phase
path A to B.
Changing Co can change # of phases: path B to D.
A (20C,70) 2 phases
70 80 100 60 40 20 0
Tem
pera
ture
(C
)
Co =Composition (wt% sugar)
L
( liquid solution i.e., syrup)
20
100
40
60
80
0
L
(liquid) +
S
(solid sugar)
water-
sugar
system
Equilibrium
A system is at equilibrium if its free energy is at a minimum under a specified combination of temperature, pressure, and composition. The system is stable and does not change with time. A change in T, P, or C for a system in equilibrium will result in an increase in the free energy and possibly a spontaneous change to another state whereby the free energy is lowered.
Binary phase diagram showing complete solid solution. The liquid-phase field is labeled L, and the solid solution is designated SS. Note the two-phase region labeled L + SS.
Complete solid solution a binary system where the two components are completely soluble in each other in both the solid and the liquid states. The liquidus is the upper boundary of the two-phase region above which a single liquid phase is present and the solidus is the lower boundary of the two-phase region below which the system has completely solidified.
The compositions of the phases in a two-phase region of the phase diagram are determined by a tie line (the horizontal line connecting the phase compositions at the system temperature).
At a given temperature and composition (state point) within the two-phase region, an A-rich liquid coexists in equilibrium with a B-rich solid solution. The compositions of each is given by the intersection point with the liquidus (for liquid phase) and solidus (for solid phase). This tie line connects the two phase compositions.
Various microstructures characteristic of different regions in the complete solid-solution phase diagram.
CuNi phase diagram. (From Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, OH, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, ed., American Society for Metals,
Metals Park, OH, 1986.)
Binary Phase Diagram for a Complete Solid Solution
At a given temperature and composition (state point) within the two-phase
region, an A-rich liquid coexists in equilibrium with a B-rich solid solution.
The compositions of each is given by the intersection point with the liquidus
(for liquid phase) and solidus (for solid phase). This tie line connects the two
phase compositions.
Phase Equilibria
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.
Simple (complete) solid solution system (e.g., Ni-Cu solution)
Ni and Cu are totally miscible in all proportions.
NiOMgO phase diagram. (After Phase Diagrams for Ceramists, Vol. 1, American Ceramic Society, Columbus, OH, 1964.)
Binary eutectic phase diagram showing no solid solution.
Eutectic Diagram with no solid solution A and B components are so dissimilar that their solubility in each other is negligible or non-existent. Characteristic features: at relatively low temperatures, there is a two-phase field for pure solids A and B (since they cant dissolve in each other). Second, the solidus is a horizontal line at the eutectic temperature. This means that only material with the eutectic composition is fully melted at the eutectic temperature. Any other composition than the eutectic will not melt immediately, but must be heated further through a two-phase region to the liquidus line.
Various microstructures characteristic of different regions in a binary eutectic phase diagram with no solid solution.
Eutectic Diagram with no solid solution Eutectic composition is fine-grained. Issues: limited time for diffusion and ordering of A and B atoms into layers, etc.
AlSi phase diagram. (After Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, Ed., American Society for Metals, Metals Park, OH, 1986.)
Binary eutectic phase diagram with limited solid solution. The only difference between this diagram and the one shown previously (no solid solution) is the presence of solid-solution regions and .
Eutectic Diagram with limited solid solution A and B components are
partially soluble in each other. It looks like an intermediate case of the solid
solution binary phase diagram and the no solid solution binary phase diagram.
The two solid-solution phases, a and b, are distinguishable and usually have different crystal structures. So the
crystal structure of a will be that of A, and A is the solvent which consists of B
atoms in solid solution. In the same way, the crystal structure of b will be
that of B, where atoms of A act as solutes in the B crystal lattice.
Various microstructures characteristic of different regions in the binary eutectic phase diagram with limited solid solution. This illustration is essentially equivalent to previous illustration, except that the solid phases are now solid solutions ( and ) rather
than pure components (A and B).
PbSn phase diagram. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, Ohio, 1973, and Binary Alloy Phase Diagrams, Vol. 2, T. B. Massalski, Ed., American Society for Metals,
Metals Park, OH, 1986.)
This eutectoid phase diagram contains both a eutectic reaction and its solid-state analog, a eutectoid reaction.
b coolingL )eutectic(
ba cooling)(eutectoid
Representative microstructures for the eutectoid diagram from the previous slide.
FeFe3C phase diagram. Note that the composition axis is given in weight percent carbon even though Fe3C, and not carbon, is a component. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, OH, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, Ed., American Society for Metals, Metals Park, OH,
1986.)
FeC phase diagram. The left side of this diagram is nearly identical to the left side of the FeFe3C diagram (Figure 9.19). In this case, however, the intermediate compound Fe3C does not exist. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, OH, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski,
Ed., American Society for Metals, Metals Park, OH, 1986.)
(a) A relatively complex binary phase diagram. (b) For an overall composition between AB2 and AB4, only that binary eutectic diagram is needed to analyze microstructure.
AlCu phase diagram. (After Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, Ed., American Society for Metals, Metals Park, OH, 1986.)
CuZn phase diagram. (After Metals Handbook, 8th ed., Vol. 8: Metallography, Structures, and Phase Diagrams, American Society for Metals, Metals Park, OH, 1973, and Binary Alloy Phase Diagrams, Vol. 1, T. B. Massalski, Ed., American Society for Metals,
Metals Park, OH, 1986.)
(left) Microstructural development for white cast iron (of composition 3.0 wt % C) shown with the aid of the FeFe3C phase diagram.
Microstructural development for eutectoid steel (of composition 0.77 wt % C).
Microstructural development for a slowly cooled hypereutectoid steel (of composition 1.13 wt % C).
Microstructural development for a slowly cooled hypoeutectoid steel (of composition 0.50 wt % C).
Microstructural development for gray cast iron (of composition 3.0 wt % C) shown on the FeC phase diagram. The resulting low-temperature sketch can be compared with the micrograph in Figure 11.1b. A dramatic difference is that, in the actual
microstructure, a substantial amount of metastable pearlite was formed at the eutectoid temperature. The small amount of silicon added to promote graphite precipitation is not shown in this two-component diagram.
Figure 11.1 (right) Typical microstructures of (a) white iron (400 ), eutectic carbide (light constituent) plus pearlite (dark constituent);
(b) gray iron (100 ), graphite flakes in a matrix of 20% free ferrite (light constituent) and 80% pearlite (dark constituent).
Figure 11.1 (continued) (c) ductile iron (100 ), graphite nodules (spherulites) encased in envelopes of free ferrite, all in a matrix of pearlite; and (d) malleable iron (100 ), graphite nodules in a matrix of ferrite. (From Metals Handbook, 9th ed., Vol. 1, American Society for Metals,
Metals Park, OH, 1978.)
A more quantitative treatment of the tie line introduced earlier allows the amount of each phase (L and SS) to be calculated by means of a mass balance.
Microstructural development during the slow cooling of a eutectic composition.
Microstructural Development During Slow Cooling
Microstructural Development During Slow Cooling
Co < 2 wt% Sn Result:
--at extreme ends --polycrystal of a grains
i.e., only one solid phase.
Microstructures in Eutectic Systems: I
0
L + a 200
T(C)
Co , wt% Sn 10
2
20 Co
300
100
L
a
30
a + b
400
(room T solubility limit)
TE (Pb-Sn System)
a L
L: Co wt% Sn
a: Co wt% Sn
Microstructural Development of Hypoeutectic Composition During
Slow Cooling
2 wt% Sn < Co < 18.3 wt% Sn Result:
Initially liquid + a
then a alone
finally two phases
a polycrystal fine b-phase inclusions
Microstructures in Eutectic Systems: II
Pb-Sn
system
L + a
200
T(C)
Co , wt% Sn 10
18.3
20 0 Co
300
100
L
a
30
a + b
400
(sol. limit at TE)
TE
2 (sol. limit at T room )
L
a
L: Co wt% Sn
a b
a: Co wt% Sn
Microstructural Development During Slow Cooling
The Lever Rule
The relative amounts of the two phases in a microstructure can be calculated from a mass balance.
ab
a
ba
b
ab
b
ba
a
babbaa
cc
cc
mm
m
cc
cc
mm
m
mmcmcmc
0
0
0 )(
Where ca and cb are the
compositions of the two phases, c0
is the overall composition, and ma
is the mass of a and mb is the
mass of b.
The Lever Rule
ab
a
ba
b
ab
b
ba
a
xx
xx
ww
w
xx
xx
ww
w
0
0
Given a solid solution binary phase diagram of an 50:50 A-B alloy weighing 1
kg, calculate the amount in each phase when
the temperature of the alloy is lowered until
the liquid solution composition is 18 wt% B
and the solid-solution composition is 66
wt%B.
The alloy is reheated to a temperature at
which the liquid composition is 48 wt% B
and the s-s composition is 90 wt % B.
Calculate the amount in each phase.
Microstructural Development During Slow Cooling
Co = CE
Result: Eutectic microstructure (lamellar structure)
--alternating layers (lamellae) of a and b crystals.
Microstructures in Eutectic Systems: III
160 m
Micrograph of Pb-Sn eutectic microstructure
Pb-Sn
system
L b
a b
200
T(C)
C, wt% Sn
20 60 80 100 0
300
100
L
a b
L + a
183C
40
TE
18.3
a: 18.3 wt%Sn
97.8
b: 97.8 wt% Sn
CE 61.9
L: Co wt% Sn
HYPOEUTECTIC & HYPEREUTECTIC
: Min. melting TE
2 components has a special composition
with a min. melting T.
Recap: Binary-Eutectic Systems
Eutectic transition L(CE) a(CaE) + b(CbE)
3 single phase regions (L, a, b )
Limited solubility: a : mostly Cu
b : mostly Ag
TE : No liquid below TE
CE
composition
Ex.: Cu-Ag system
Cu-Ag
system
L (liquid)
a L + a L + b b
a b
Co , wt% Ag 20 40 60 80 100 0
200
1200
T(C)
400
600
800
1000
CE
TE 8.0 71.9 91.2 779C
Lamellar Eutectic Structure
54
Intermetallic Compounds
Mg2Pb
Note: intermetallic compound forms a line - not an area - because
stoichiometry (i.e. composition) is exact.
To Recap: Phase Diagrams Indicate phases as function of T, Co, and P.
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
Phase
Diagram
for Cu-Ni
system
2 phases:
L (liquid) a (FCC solid solution)
3 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)
wt% Ni 20 40 60 80 100 0 1000
1100
1200
1300
1400
1500
1600
T(C)
L (liquid)
a
(FCC solid solution)
Cu-Ni
phase
diagram
Phase Diagrams: # and types of phases
Rule 1: If we know T and Co, then we know: --the # and types of phases present.
Examples:
A(1100C, 60): 1 phase: a
B (1250C, 35): 2 phases: L + a
B (
1250C
,35)
A(1100C,60)
wt% Ni
20
1200
1300
T(C)
L (liquid)
a
(solid)
30 40 50
Cu-Ni
system
Phase Diagrams: composition of phases
Rule 2: If we know T and Co, then we know: --the composition of each phase.
Examples:
T A A
35 C o
32 C L
At T A = 1320C:
Only Liquid (L) C L = C o ( = 35 wt% Ni)
At T B = 1250C:
Both a and L
C L = C liquidus ( = 32 wt% Ni here)
C a = C solidus ( = 43 wt% Ni here)
At T D = 1190C:
Only Solid ( a )
C a = C o ( = 35 wt% Ni )
C o = 35 wt% Ni
B T B
D T D
tie line
4 C a 3
Rule 3: If we know T and Co, then we know: --the amount of each phase (given in wt%).
Examples:
At T A : Only Liquid (L)
W L = 100 wt%, W a = 0
At T D : Only Solid ( a )
W L = 0, W a = 100 wt%
C o = 35 wt% Ni
Phase Diagrams: weight fractions of phases
wt% Ni
20
1200
1300
T(C)
L (liquid)
a
(solid)
3 0 4 0 5 0
Cu-Ni
system
T A A
35 C o
32 C L
B T B
D T D
tie line
4 C a 3
R S
At T B : Both a and L
% 733243
3543wt
= 27 wt%
WL S
R + S
Wa R
R + S
59
Tie line connects the phases in equilibrium with each other
The Lever Rule
How much of each phase?
Think of it as a lever (teeter-totter)
ML Ma
R S
RMSM L a
L
L
LL
LL
CC
CC
SR
RW
CC
CC
SR
S
MM
MW
a
a
a
a
a
00
wt% Ni
20
1200
1300
T(C)
L (liquid)
a
(solid)
3 0 4 0 5 0
B T B
tie line
C o C L C a
S R
wt% Ni 20
120 0
130 0
3 0 4 0 5 0 110 0
L (liquid)
a
(solid)
T(C)
A
35 C o
L: 35wt%Ni
Cu-Ni
system
Phase diagram:
Cu-Ni system.
System is:
--binary i.e., 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.
Consider
Co = 35 wt%Ni.
Ex: Cooling in a Cu-Ni Binary
46 35
43 32
a : 43 wt% Ni
L: 32 wt% Ni
L: 24 wt% Ni
a : 36 wt% Ni
B a: 46 wt% Ni L: 35 wt% Ni
C
D
E
24 36
Ca changes as we solidify. Cu-Ni case:
Fast rate of cooling:
Cored structure Slow rate of cooling:
Equilibrium structure
First a to solidify has Ca = 46 wt% Ni.
Last a to solidify has Ca = 35 wt% Ni.
Cored vs Equilibrium Phases
First a to solidify:
46 wt% Ni
Uniform C a :
35 wt% Ni
Last a to solidify:
< 35 wt% Ni
: Min. melting TE
2 components has a special composition
with a min. melting T.
Recap: Binary-Eutectic Systems
Eutectic transition L(CE) a(CaE) + b(CbE)
3 single phase regions (L, a, b )
Limited solubility: a : mostly Cu
b : mostly Ag
TE : No liquid below TE
CE
composition
Ex.: Cu-Ag system
Cu-Ag
system
L (liquid)
a L + a L + b b
a b
Co , wt% Ag 20 40 60 80 100 0
200
1200
T(C)
400
600
800
1000
CE
TE 8.0 71.9 91.2 779C
Example Problem 9.4
For a 99.65 wt% Fe 0.35 wt% C alloy at a temperature just below the eutectoid, determine the following:
The mass fractions of total ferrite and cementite phases
The mass fractions of the proeutectoid ferrite and pearlite
The mass fraction of eutectoid ferrite
