1. Chapter 9: Phase Diagrams
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...
1. How many phases do we get?
2. What is the composition of each phase?
3. How much of each phase do we get?
Phase B
Phase A
Nickel atom
Copper atom

2. Definitions:
Components are pure metals and/or compounds of which an alloy is composed. For example, in a copper–zinc brass, the components are Cu and Zn.
System it may relate to the series of possible alloys consisting of the same components, (e.g., the iron–carbon system).
Solid solution consists of atoms of at least two different types; the solute atoms occupy either substitutional or interstitial positions in the solvent lattice, and the crystal structure of the solvent is maintained.
Mixtures is a systems composed of two or more phases or ‘‘heterogeneous systems. Most metallic alloys, ceramic, polymeric, and composite systems are heterogeneous.

3. Phase: is defined as a homogeneous portion of a system that has uniform physical and chemical characteristics. 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 Each has different physical properties (one is a liquid, the other is a solid); furthermore, each is different chemically (i.e., has a different chemical composition); one is virtually pure sugar, the other is a solution of H2O
If more than one phase is present in a given system, each will have its own distinct properties, and a boundary separating the phases will exist across which there will be a discontinuous and abrupt change in physical and/or chemical characteristics
When two phases are present in a system, it is not necessary that there be a difference in both physical and chemical properties; a disparity in one or the other set of properties is sufficient. Ex. water and ice

4. Heterogeneous Mixtures are composed of two or more components that are: unequally (not uniformly) distributed though out the system, immiscible (won't dissolve), may be of different phase, unable to disperse through most membranes, and separable by mechanical means. There are probably more possibilities for this type of mixture than the first.

5. Phase Equilibria: Solubility Limit
Introduction
Solutions – solid solutions, single phase
Mixtures – more than one phase
• Solubility Limit:
Max concentration for which only
a single phase solution occurs, at
specific temp
Sucrose/Water Phase Diagram
Pure
Sugar
Temperature (°C) 20 40 60 80
100 Co
=Composition (wt% sugar) L
(liquid solution
i.e., syrup)
Solubility
Limit
(liquid) + S
(solid
sugar) 4 6 8 10
Water
Question: What is the
solubility limit at 20°C? 65
Answer: 65 wt% sugar.
If Co < 65 wt% sugar: syrup
If Co > 65 wt% sugar: syrup + sugar.

6. The addition of solute in excess of this solubility limit results in the formation of another solid solution or compound that has a clearly different composition. To illustrate this concept, consider the sugar–water (C12H22O11–H2O) system.
This solubility limit of sugar in water depends on the temperature of the water

7. Components and Phases • Components: • Phases: b (lighter phase) a
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).
Aluminum-
Copper
Alloy b
(lighter
phase) a
(darker
phase)

8. 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)
1 phase
D (100°C,90)
2 phases 70 80
100 60 40 20
Temperature (°C) Co
=Composition (wt% sugar) L (
liquid solution
i.e., syrup)
(liquid) + S
(solid
sugar)
water-
sugar
system
A (20°C,70)
2 phases

9. Phase Equilibria
Free energy is a function of the internal energy of a system, and also the randomness or 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. In a macroscopic sense, this means that the characteristics of the system do not change with time but persist indefinitely; that is, the system is stable.
phase equilibrium, refers to equilibrium as it applies to systems in which more than one phase may exist.
Metastable: non-equilibrium state that may persist for a very long time (specially in solid systems, that a state of equilibrium is never completely achieved because the rate of approach to equilibrium is extremely slow)

10. Phase Equilibria Simple solution system (e.g., Ni-Cu solution) Crystal
Structure
electroneg
r (nm) Ni
FCC
1.9
0.1246 Cu
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.

11. Phase Diagrams
Phase diagram gives information about the control of microstructure or phase structure of a particular alloy system is conveniently and concisely displayed (equilibrium or constitutional diagram)
There are three externally controllable parameters that will affect phase structure – temperature, pressure, and composition – and phase diagram are constructed when combinations of these parameters are plotted against one another

12. One – component (or unary) phase diagram
It is a one component system, in which composition is held constant ( i.e., the phase diagram is for a pure substance); that is means that pressure and temperature are variable.
Ex. Water H2O
liquid
solid
Triple point
0.01
vapour
Temp C
Pressure(atm)
-20
Temperature ( C)

13. Phase Diagrams • Indicate phases as function of T, Co, and P.
• For this course:
-binary systems: just 2 components.
-independent variables: T and Co (P = 1 atm is almost always used).
• 2 phases region : L
(liquid) a
(FCC solid solution)
• 3 phase fields:
L +
wt% Ni 20 40 60 80
100
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid)
(FCC solid
solution) +
liquidus
solidus
• Phase
Diagram
for Cu-Ni
system

14. Ex. copper–nickel system
The liquid L is a homogeneous liquid solution composed of both copper and nickel.
The phase is a substitutional solid solution consisting of both Cu and Ni atoms, and having an FCC crystal structure. At temperatures below about 1080C, copper and nickel are mutually soluble in each other in the solid state for all compositions.
This complete solubility is explained by the fact that both Cu and Ni have the same crystal structure (FCC), nearly identical atomic radii and electro-negativities, and similar valences. The copper–nickel system is termed isomorphous because of this complete liquid and solid solubility of the two components.

15. Phase Diagrams: # and types of phases
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
wt% Ni 20 40 60 80
100
1000
1100
1200
1300
1400
1500
1600
T(°C)
L (liquid) a
(FCC solid
solution) L +
liquidus
solidus
Cu-Ni
phase
diagram
• Examples:
A(1100°C, 60):
1 phase: a B
(1250°C,35) B
(1250°C, 35):
2 phases: L + a
A(1100°C,60)

16. Phase Diagrams: composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 30 40 50
Cu-Ni system
• Examples: T A C o
= 35 wt% Ni
tie line 35 C o
At T A
= 1320°C:
Only Liquid (L) C L
= C o
( = 35 wt% Ni) B T 32 C L 4 C a 3
At T D
= 1190°C: D T
Only Solid ( a ) C
= C o
( = 35 wt% Ni
At T B
= 1250°C:
Both a
and L C L
= C
liquidus
( = 32 wt% Ni here) C a
= C
solidus
( = 43 wt% Ni here)

17. 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%).
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 3 4 5
Cu-Ni system T A 35 C o 32 B D
tie line R S
• Examples: C o
= 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, W
= 100 wt%
At T B :
Both a
and L
= 27 wt% WL = S R + Wa
- Composition need be specified in terms of only one of the constituents for a binary alloy

18. The Lever Rule
Tie line – connects the phases in equilibrium with each other - essentially an isotherm
wt% Ni 20
1200
1300
T(°C)
L (liquid) a
(solid) L +
liquidus
solidus 3 4 5 B T
tie line C o S R
How much of each phase? Think of it as a lever (teeter-totter) ML M R S

19. DEVELOPMENT OF MICROSTRUCTURE IN ISOMORPHOUS ALLOYS
EQUILIBRIUM COOLING
NONEQUILIBRIUM COOLING

20. Ex: Cooling in a Cu-Ni Binary
1. EQUILIBRIUM COOLING
Ex: Cooling in a Cu-Ni Binary
• Phase diagram:
Cu-Ni system.
wt% Ni 20
120
130 3 4 5
110
L (liquid) a
(solid) L +
T(°C) A 35 C o
L: 35wt%Ni
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.
a: 46 wt% Ni
L: 35 wt% Ni B 46 35 C 43 32 a :
43 wt% Ni
L: 32 wt% Ni D 24 36
L: 24 wt% Ni a :
36 wt% Ni E
• Consider
Co = 35 wt%Ni.

21. NONEQUILIBRIUM COOLING

22. 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
Uniform C :
35 wt% Ni
Last
< 35 wt% Ni

23. Mechanical Properties: Cu-Ni System
• Effect of solid solution strengthening on:
--Tensile strength (TS)
--Ductility (%EL,%AR)
Tensile Strength (MPa)
Composition, wt% Ni Cu Ni 20 40 60 80
100
200
300
400
TS for
pure Ni
TS for pure Cu
Elongation (%EL)
Composition, wt% Ni Cu Ni 20 40 60 80
100 30 50
%EL
for
pure Ni
for pure Cu
--Peak as a function of Co
--Min. as a function of Co

24. 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)
(L,
a, b )
1000 a
• Limited solubility: a L + L + b
800
779°C b a TE
: mostly Cu
8.0
71.9
91.2 b
: mostly Ag
600
• TE
: No liquid below TE a + b
solvus
• CE
: Min. melting TE
400
composition
200 20 40 60 CE 80
100
• Eutectic transition
L(CE) (CE) + (CE) Co ,
wt% Ag

25. Binary-Eutectic Systems
Depending on composition, several different types of microstructures are possible for the slow cooling of alloys belonging to binary eutectic systems.
Ex. Lead(Pb)–tin(Sn) phase diagram
The first case is for compositions ranging between a pure component and the maximum solid solubility for that component at room temperature [20C (70F)].
For the lead–tin system, this includes lead-rich alloys containing between 0 and about 2 wt% Sn (for the phase solid solution), and also between approximately 99 wt% Sn and pure tin (for the β phase)

27. The second case considered is for compositions that range between the room temperature solubility limit and the maximum solid solubility at the eutectic temperature.
For the lead–tin system (Figure 10.7), these compositions extend from about 2wt%Sn to 18.3 wt%Sn (for lead-rich alloys) and from 97.8 wt%Sn to approximately 99 wt% Sn (for tin-rich alloys).
The third case involves solidification of the eutectic composition, 61.9 wt% Sn (C3 in Figure). Consider an alloy having this composition that is cooled from a temperature within the liquid-phase region (e.g., 250C) down the vertical line yy in Figure. As the temperature is lowered, no changes occur until we reach the eutectic temperature, 183C. Upon crossing the eutectic isotherm, the liquid transforms to the two and phases. This transformation may be represented by the reaction

28. The fourth and final micro structural case for this system includes all compositions other than the eutectic that, when cooled, cross the eutectic isotherm. Consider, for example, the composition C4 , see figure, which lies to the left of the eutectic; as the temperature is lowered, we move down the line zz, beginning at point j.

30. EX: Pb-Sn Eutectic System (1)
• For a 40 wt% Sn-60 wt% Pb alloy at 150°C, find...
--the phases present:
a + b
Pb-Sn
system
--compositions of phases: L + a b
200
T(°C)
18.3
C, wt% Sn 20 60 80
100
300
L (liquid)
183°C
61.9
97.8
CO = 40 wt% Sn
Ca = 11 wt% Sn
Cb = 99 wt% Sn
--the relative amount of each phase: W a =
C - CO
C - C 59 88
= 67 wt% S
R+S
150 R 40 Co S 11 C 99 C W  =
CO - C
C - C R
R+S 29 88
= 33 wt%

31. EX: Pb-Sn Eutectic System (2)
• For a 40 wt% Sn-60 wt% Pb alloy at 200°C, find...
--the phases present:
a + L
Pb-Sn
system
--compositions of phases: L + b a
200
T(°C)
C, wt% Sn 20 60 80
100
300
L (liquid)
183°C
CO = 40 wt% Sn
Ca = 17 wt% Sn
CL = 46 wt% Sn
--the relative amount of each phase:
220 17 C R 40 Co S 46 CL W a =
CL - CO
CL - C 6 29
= 21 wt% W L =
CO - C
CL - C 23 29
= 79 wt%

32. Microstructures in Eutectic Systems: I
• Co < 2 wt% Sn
• Result:
--at extreme ends
--polycrystal of a grains
i.e., only one solid phase. L + a
200
T(°C) Co ,
wt% Sn 10 2 20
300
100 30 b
400
(room T solubility limit) TE
(Pb-Sn
System)
L: Co wt% Sn a L
a: Co wt% Sn

33. Microstructures in Eutectic Systems: II
L: Co wt% Sn
• 2 wt% Sn < Co < 18.3 wt% Sn
• Result:
Initially liquid + 
then  alone
finally two phases
a polycrystal
fine -phase inclusions
Pb-Sn
system L + a
200
T(°C) Co ,
wt% Sn 10
18.3 20
300
100 30 b
400
(sol. limit at TE) TE 2
(sol. limit at T
room ) L a
a: Co wt% Sn a b

34. Microstructures in Eutectic Systems: III
• Co = CE
• Result: Eutectic microstructure (lamellar structure)
--alternating layers (lamellae) of a and b crystals.
160 m
Micrograph of Pb-Sn
eutectic
microstructure
Pb-Sn
system
L
a
200
T(°C)
C, wt% Sn 20 60 80
100
300 L a b +
183°C 40 TE
L: Co wt% Sn CE
61.9
18.3
: 18.3 wt%Sn
97.8
: 97.8 wt% Sn

35. Lamellar Eutectic Structure

36. Microstructures in Eutectic Systems: IV
• wt% Sn < Co < 61.9 wt% Sn
• Result: a crystals and a eutectic microstructure WL
= (1- W a )
= 50 wt% C
= 18.3 wt% Sn CL
= 61.9 wt% Sn S R + =
• Just above TE :
Pb-Sn
system L + b
200
T(°C)
Co, wt% Sn 20 60 80
100
300 a 40 TE
L: Co
wt% Sn L a L a
18.3
61.9 S R
97.8 S R
primary a
eutectic b
• Just below TE : C a
= 18.3 wt% Sn b
= 97.8 wt% Sn S R + W =
= 73 wt%
= 27 wt%

37. Hypoeutectic & Hypereutectic
Hypoeutectic: alloy with a composition C to the left
eutectic point (less than eutectic)
Hypereutectic: alloy with a composition C to the right
eutectic point (more than eutectic)

38. Hypoeutectic & Hypereutectic
300 L
T(°C) L + a a
200 L + b b
(Pb-Sn TE
System) a + b
100
175 mm a
hypoeutectic: Co = 50 wt% Sn
hypereutectic: (illustration only) b
Co, wt% Sn 20 40 60 80
100
eutectic
61.9
eutectic: Co = 61.9 wt% Sn
160 mm
eutectic micro-constituent

39. Intermetallic Compounds
Terminal solid solution: the solid phase which exist over composition ranges near the concentration extremities.
Intermediate solid solution:(or intermediate phases )
A solid solution or phase having a composition range that does not extend to either of the pure components of the system. may be found at other than the two composition extremes
Intermetallic compounds: ( for metal – metal system)
A compound of two metals that has a distinct chemical formula. On a phase diagram it appears as an intermediate phase that exists over a very narrow range of compositions.
; Ex. The magnesium – lead system

40. Intermetallic Compounds
Mg2Pb
Note: intermetallic compound forms a line - not an area - because stoichiometry (i.e. composition) is exact.

41. Characteristics noting for magnesium – lead system:
The compound Mg2Pb melts at approximately 550 C as indicated by point M in figure
The solubility of lead in magnesium is rather extensive, as indicated by the relatively large composition span for the a phase field
The solubility of magnesium in lead is extremely limited. This is evident from the very narrow β terminal – solid solution region on the right or lead – rich side of the diagram
This phase diagram may be thought of as two simple eutectic diagrams joined back to back, one for the Mg-Mg2Pb system and the other for Mg2Pb-Pb; as such the compound Mg2Pb is really considered to be a component

42. Eutectoid & Peritectic
Eutectic - liquid in equilibrium with two solids
L  + 
cool
heat
intermetallic compound - cementite
cool
heat
Eutectoid - solid phase transforms into two solid phases
S S1+S3
  + Fe3C (727ºC)
cool
heat
Peritectic - liquid + solid 1  solid 2 (Fig 9.21)
S1 + L S2
 + L  (1493ºC)
Invariants point: the different phases in equilibrium
( ex. Eutectic, eutectoid, peritectic)

43. Eutectoid & Peritectic
Peritectic transition  + L 
Cu-Zn Phase diagram
Eutectoid transition   + 

44. THE GIBBS PHASE RULE
Gibbs phase rule for construction of phase diagram
Gibbs phase rule: For a system at equilibrium, an equation that expresses the relationship between the number of phases present and the number of externally controllable variables.
P is the number of phases present
F is the number of these variables that can be changed
independently without altering the number of phases
that coexist at equilibrium(T, p, C)
C is the number of components in the system.
N is the number of non compositional variables (e.g.,
temperature and pressure).(p=1atm constant, so N =1)

45. Example: the copper–silver system
Since pressure is constant (1 atm), the parameter N is 1 (temperature is the only non compositional variable)
the number of components C is 2 (viz Cu and Ag),
Consider the case of single-phase fields on the phase diagram (e.g., , , and liquid regions). Since only one phase is present
This means that to completely describe the characteristics of any alloy that exists within one of these phase fields, we must specify two parameters; these are composition and temperature, which locate, respectively, the horizontal and vertical positions of the alloy on the phase diagram.

46. Iron-Carbon (Fe-C) Phase Diagram
In the classification scheme of ferrous alloys based on carbon content, there are three types: iron, steel, and cast iron
Commercially pure iron contains less than wt% C and, from the phase diagram, is composed almost exclusively of
the ferrite phase at room temperature.
2. The iron–carbon alloys that contain between and 2.14
wt% C are classified as steels. In most steels the
microstructure consists of both α and Fe3C phases.
3. Cast irons are classified as ferrous alloys that contain
between 2.14 and 6.70 wt% C. However, commercial cast
irons normally contain less than 4.5 wt% C

47. Pure iron, upon heating, experiences two changes in crystal structure before it melts.
At room temperature the stable form, called ferrite, or α iron, has a BCC crystal structure.
At 912C (1674F ) Ferrite experiences a polymorphic transformation to FCC austenite, or iron. This austenite persists to 1394C (2541F), at which temperature the FCC austenite reverts back to a BCC phase known as  ferrite,
which finally melts at 1538C (2800F).
3. The composition axis extends only to 6.70 wt% C; at this concentration the intermediate compound iron carbide, or cementite (Fe3C), is formed, which is represented by a vertical line on the phase diagram. Thus, the iron–carbon system may be divided into two parts: an iron-rich portion, and the other (not shown) for compositions between 6.70 and 100 wt% C (pure graphite). In practice, all steels and cast irons have carbon contents less than 6.70 wt% C;

48. Iron-Carbon (Fe-C) Phase Diagram
• 2 important
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+Fe3C a +
L+Fe3C d
(Fe)
Co, wt% C
1148°C
T (°C)
727°C = T
eutectoid
points
-Eutectic (A): L Þ g +
Fe3C A S R
4.30
-Eutectoid (B): g Þ a +
Fe3C g
Result: Pearlite =
alternating layers of a
and Fe3C phases
120 mm
0.76 C
eutectoid B R S
Fe3C (cementite-hard) a
(ferrite-soft)

49. The two-phase regions are labeled in Figure.
1. It may be noted that one eutectic exists for the iron–iron carbide system, at 4.30 wt% C and 1147C (2097F); for this eutectic reaction,
the liquid solidifies to form austenite and cementite phases. Of course, subsequent cooling to room temperature will promote additional phase changes.
2. It may be noted that a eutectoid invariant point exists at a composition of 0.76 wt% C and a temperature of 727C (1341F). This eutectoid reaction may be represented by

50. Hypoeutectoid Steel T (°C) d L +L g (austenite) Fe3C (cementite) a
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+ Fe3C a
L+Fe3C d
(Fe)
Co , wt% C
1148°C
T (°C)
727°C
(Fe-C
System) C0
0.76 g g r s w a = /( + ) g
(1-
proeutectoid ferrite
pearlite
100 mm
Hypoeutectoid
steel R S a w = /( + )
Fe3C
(1- g

51. Hypereutectoid Steel Fe3C (cementite) L g (austenite) +L a d T(°C) g g
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+Fe3C a
L+Fe3C d
(Fe)
Co , wt%C
1148°C
T(°C)
(Fe-C
System) g g s r w
Fe3C = /( + ) g
=(1-
Adapted from Fig. 9.33,Callister 7e.
proeutectoid Fe3C
60 mm
Hypereutectoid
steel
pearlite R S w a = /( + )
Fe3C
(1- g Co
0.76

52. Example: Phase Equilibria
For a 99.6 wt% Fe-0.40 wt% C at a temperature just below the eutectoid, determine the following
composition of Fe3C and ferrite ()
the amount of carbide (cementite) in grams that forms per 100 g of steel
the amount of pearlite and proeutectoid ferrite ()

53. Chapter 9 – Phase Equilibria
Solution:
a) composition of Fe3C and ferrite ()
the amount of carbide (cementite) in grams that forms per 100 g of steel
CO = 0.40 wt% C Ca = wt% C CFe C = 6.70 wt% C 3
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+ Fe3C a
L+Fe3C d
Co , wt% C
1148°C
T(°C)
727°C CO R S
CFe C 3 C

54. Chapter 9 – Phase Equilibria
the amount of pearlite and proeutectoid ferrite ()
note: amount of pearlite = amount of g just above TE
Co = 0.40 wt% C Ca = wt% C Cpearlite = C = 0.76 wt% C
Fe3C (cementite)
1600
1400
1200
1000
800
600
400 1 2 3 4 5 6
6.7 L g
(austenite) +L
+ Fe3C a
L+Fe3C d
Co , wt% C
1148°C
T(°C)
727°C CO R S C C
pearlite = 51.2 g proeutectoid  = 48.8 g

55. Alloying Steel with More Elements
• Teutectoid changes:
• Ceutectoid changes: T
Eutectoid
(°C)
wt. % of alloying elements Ti Ni Mo Si W Cr Mn C
eutectoid
(wt%C)

56. Summary • Phase diagrams are useful tools to determine:
--the number and types of phases,
--the wt% of each phase,
--and the composition of each phase
for a given T and composition of the system.
• Alloying to produce a solid solution usually
--increases the tensile strength (TS)
--decreases the ductility.
• Binary eutectics and binary eutectoids allow for
a range of microstructures.
Steels are alloyed for:
--improve their corrosion resistance
--to render them amenable to heat treatment