1. Chapter 9
Sections:9.2, 9.3, 9.4, 9.5

2. Chapter 9: Phase Diagrams
Why study?
One of the reason why a knowledge and understanding of phase diagrams is important to the engineers related to the design and control of heat treating processes.
Some properties are functions of their microstructures, and, consequently, of their thermal histories.

3. Definitions and Basic Concepts
Components : Pure metals and/or compounds of which an alloy is composed
Example: in a copper-zinc brass, the components are Cu and Zn.
System
First meaning: refer to a specific body of material under consideration ( e.g., a ladle of molten steel)
Second meaning: relate to the series of possible alloys consisting of the same components, but without regard to alloy composition (e.g., the iron-carbon system)
Solid solution: Consists of atoms of at least two different types
Solute  an element or compound present in a minor concentration
Solvent  an element or compound in greater amount; host atoms.
Solute atoms occupy either substitutional or interstitial positions in the solvent lattice
Crystal structure of the solvent is maintained

4. 9.2 Solubility Limit
Solubility Limit: The maximum concentration of a solute atoms that may dissolve in the solvent to form a solid solution at some specific temperature.
The addition in excess results in the formation of another solid solution or compound that has a distinctly different composition.
Example: Sugar-Water (C12H22O11-H2O) system
Initially, as sugar added to water, a solution of syrup forms.
As more sugar is added, solution becomes more concentrated
Solution becomes saturated with sugar Solubility limit is reached
Not capable to dissolving more  further addition simply settle to the bottom
System now consists of two separate substances:
A sugar-water syrup liquid solution, and
Solid crystals of undissolved sugar

6. 9.3 Phases
Phase: defined as a homogeneous portion of a system that has uniform physical and chemical characteristics.
Every pure material is considered to be a phase
Also every solid, liquid, and gaseous solution
e.g., syrup solution is one phase, and solid sugar is another
If more than one phase is present, it is not necessary that there be difference in both physical and chemical properties:
A disparity in one or both is sufficient
e.g., water and ice in a container ( two phase, identical chemically)
When a substance can exist in two or more polymorphic forms (e.g. having both FCC abd BCC)  each structure is a separate phase because of difference in physical properties.

7. A single-phase system is termed “homogeneous”
Systems composed of two or more phases are termed “mixture” or heterogeneous systems”.
Most metallic alloys, ceramics, polymeric, and composite systems are heterogeneous.
Ordinarily, in multiphase systems
The phases interact such that the property is different and more attractive than individual phases.

8. 9.4 Microstructure
Physical properties and mechanical behavior depend on the microstructure.
In metal alloys, microstructure is characterized by
Number of phases present
Their proportions
The manner they are distributed or arranged
The microstructure of an alloy depends on such variables as
Alloying elements present
Their concentrations
The heat treatment
Microstructure studies:
surface preparation (Polishing and etching)
For two phase alloys, one phase may appear light and other dark

9. 9.5 Phase Equilibria
Free energy is a function of the internal energy of a system, and also of 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 macroscopic sense, this means that the characteristics of the system do not change with time but persist indefinitely
 The system is stable
A change in temperature, pressure, and/or composition in equilibrium  increase in free energy  another equilibrium state whereby the free energy is lowered.

10. Phase equilibrium  refers to equilibrium as it applied to systems in which more than one phase may exist.
Example:
Sugar-water syrup is contained in a closed vessel
solution is in contact with solid sugar at 20oC
If system is in equilibrium,
Composition of syrup is 65wt% C12H22O11-35wt% H2O (Fig 9.1)
Amount and composition of syrup and sugar will remain constant
If temperature is raised to 100oC
Equilibrium is temporarily upset
Solubility limit of sugar has increased to 80 wt%
Some of the solid sugar will dissolve until new equilibrium is reached

11. Metastable state:
Nonequilibrium state
A state of equilibrium is never completely achieved because the rate of approach to equilibrium is extremely slow
Common in many metals or solid solutions
Persist indefinitely with imperceptible changes with time.
Metastable structure:
More practical than equilibrium
Some steel and aluminum rely on this for heat treatment designing

12. Chapter 9
Sections: 9.6

13. Equilibrium Phase Diagrams
Represents the relationships between temperature and the compositions and the quantities of phases at equilibrium.
Also known as phase, equilibrium or constitutional diagram
A binary alloy is one that contains two components.
Temperature and composition are the variable parameters for binary alloys.
Of more than two components, phase diagrams become extremely complicated and difficult to represents

14. 9.6 Binary Isomorphous systems
Phase diagram of the copper-Nickel system is shown in Fig 9.2a.
Ordinate  Temperature
Abscissa  composition
Composition ranges from 0 wt% Ni (100 wt% Cu) to 100 wt% Ni (0 wt% Cu)
Three different phase regions, or fields, appear
An alpha (a) field
A liquid (L) field
A two-phase (a+L) field

15. Liquid L: homogeneous liquid solution composed of both copper and nickel
a phase: a substitutional solid solution consisting of both Cu and Ni atoms, and having an FCC crstal structure.
Isomorphous: complete liquid and solid solubility of two components
Copper-Nickel system is Isomorpous
At temperatures below about 1080oC, mutually soluble in solid state for all compositions
Complete solubility is due to same crystal structure (FCC), nearly identical atomic radii and electronegativities, and similar valences

16. Nomenclature
For metallic alloys, solid solutions are designated by a, b, g, etc.
Liquidus line: liquid phase at all temperature and composition above this line
Solidus line: solid phase below this line at all temperatute and composition
Liquidus and solidus lines intersect at two extreme points
Correspond to melting temperature of pure components
Copper (1085oC) and Nickel (1453oC)
Heating of pure copper
Moving vertically on left-temperature axis
Remains solid until its melting temperature is reached
No further heating possible, until this transformation is complete

17. For any composition other than pure components
Melting phenomenon occurs over the range of temperature between the solidus and liquidus lines
Both solid a and liquid will be in equilibrium within this range

18. Interpretation of Phase Diagrams
For binary system of known composition and temperature that is in equilibrium, at least three kinds of information are available:
The phases that are present
The composition of these phases
The % or fraction of the phases
1.0 Phases present
Relatively simple
Example (refer to Fig 9.2a),
60 wt% Ni-40 wt% Cu at 1100oC Point A a phase
35 wt% Ni-65 wt% Cu at 1250oC Point B a + liquid phases

19. • Tell us about phases as function of T, Co, P. • For this course:
PHASE DIAGRAMS
• Tell us about phases as function of T, Co, P.
• For this course:
--binary systems: just 2 components.
--independent variables: T and Co (P = 1atm is always used).
• Phase
Diagram
for Cu-Ni
system
Adapted from Fig. 9.2(a), Callister 6e.
(Fig. 9.2(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH (1991). 5

20. PHASE DIAGRAMS: # and types of phases
• Rule 1: If we know T and Co, then we know:
--the # and types of phases present.
• Examples:
Cu-Ni
phase
diagram
Adapted from Fig. 9.2(a), Callister 6e.
(Fig. 9.2(a) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991). 6

21. PHASE DIAGRAMS: composition of phases
• Rule 2: If we know T and Co, then we know:
--the composition of each phase.
Cu-Ni system
• Examples:
Adapted from Fig. 9.2(b), Callister 6e.
(Fig. 9.2(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 7

22. 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%).
Cu-Ni
system
• Examples:
= 27wt%
Adapted from Fig. 9.2(b), Callister 6e.
(Fig. 9.2(b) is adapted from Phase Diagrams of Binary Nickel Alloys, P. Nash (Ed.), ASM International, Materials Park, OH, 1991.) 8

23. • Sum of weight fractions:
THE LEVER RULE: A PROOF
• Sum of weight fractions:
• Conservation of mass (Ni):
• Combine above equations:
• A geometric interpretation: 9

24. Composition need to be specified in terms of only one of the constituents
For example, composition of Ni is used
Identical results if composition of Cu is used
Co = 35 wt% Ni
Ca = 42.5 wt% Ni
CL = 31.5 wt% Ni
WL = ( 42.5 – 35) / (42.5 – 31.5) = 0.68
Wa = (35 – 31.5) / (42.5 – 31.5) = 0.32
Volume fraction: See equations 9.5 – 9.7

25. Volume Fractions

26. Development of Microstructure in Isomorphous alloys -- Equilibrium Cooling
35 wt% Ni-65wt% Cu
as cooled from 1300oC
Cooling very slowly  phase equilibrium is maintained
Cooling  Moving down
At 1300oC, completely liquid
At b (1260oC), solidification starts
At d (1220oC), solidification completes

27. Development of Microstructure -- Non-Equilibrium Cooling
Extremely slow cooling not valid
Temperature change  readjustment in composition  diffusional processes
Diffusion rates are low for the solid phase and, for both phases, decrease with diminishing temperature
Practical solidification processes, cooling rates are much too rapid to allow these compositional readjustments and maintenance of equilibrium  different microstructure develops

29. At b’, a phase begin to form [a(46Ni)]
At c’,
liquid composition: 29wt% Ni-71 wt% Cu
Solid phase: 40 wt% Ni-60 wt% Cu [a(40Ni)]
Since diffusion in solid is relatively slow, a phase formed at b’ has not changes composition appreciably  still [a(46Ni)]
Composition of a grains continuously changes radially from 46 wt% Ni at center to 40 wt% Ni at the outer grains  average composition (say 42 wt%Ni)
Solidus line has shifted

30. Chapter 9
Sections: 9.7

31. 9.7 Binary Eutectic Systems
Binary Eutectic Phase Diagram
Another type of common and relatively simple phase diagram
Figure 9.6 shows for the copper-silver system
Features of Binary Eutectic Phase Diagram
Feature 1: Three single-phase regions ( a, b, and liquid )
The a phase: solid solution rich in copper, silver as solute, FCC
The b phase: solid solution rich in silver, copper as solute, FCC
Solubility in each of these solids phases is limited
Solubility limit for a phase
Line ABC ( Increases with temperature, maximum, decreases to minimum)
Solvus line (BC)
Solidus line (AB)

32. Line FGH ( Increases with temperature, maximum, decreases to minimum)
Solubility limit for b phase
Line FGH ( Increases with temperature, maximum, decreases to minimum)
Solvus line (GH)
Solidus line (FG)
Line BEG is also solidus line
Maximum solubility in both a and b phases occur at 779oC
Feature 2: Three two-phase regions
a + L
b + L
a + b

34. As silver is added to copper,
The melting temperature of copper is lowered by silver additions.
Line AE: the liquidus line
Same is true as copper is added to silver
Point E is called the invariant point (CE = 71.9 wt% Ag, TE = 779oC)
At E, an important reaction occurs
Upon cooling, a liquid phase is transformed into a and b solid phases
The opposite reaction occurs upon heating
This is called eutectic reaction ( Eutectic means easily melted)
CE and TE represents eutectic composition and temperature
Horizontal solidus line at TE is called the eutectic isotherm

35. The eutectic reaction, upon cooling, is similar to solidification of pure components:
Reaction proceeds to completion at a constant temperature
Isothermal at TE
Solid products of eutectic solidification is always two solid phases
Another common eutectic system is that for lead and tin
The phase diagram is shown in Figure 9.7
Example 9.2
Example 9.3

36. Development of Microstructure in Eutectic Alloys
Depending on composition, several different types of microstructures
These possibilities considered in terms of the lead-tin phase diagram
Figure 9.7

37. First case: Composition C1
Range:
Composition ranging between a pure metal and the maximum solid solubility for that component at room temperature (20oC)
Lead-rich alloy (0-2 wt% Sn)
Slowly cooled down

38. Second Case: Composition C2
Range:
Composition ranging between the room temperature solubility and the maximum solid solubility at the eutectic temperature.
Corresponds: 2 wt% Sn to 18.3 wt% Sn

39. Third Case: Composition C3
Solidification of the eutectic composition
Corresponds: 61 wt% Sn
The microstructure at i is known as eutectic structure.

40. Lamellae :
The microstructure of a solid consisting of alternating layers
Shown in Figure 9.12

41. Fourth Case: Composition C4
All composition other than the eutectic composition
At m, a phase will be present in both :
Eutectic a
Primary a

42. Microconstituents
An element of the microstructure having an identifiable and characteristic structure.
At m, two microconstituents ( primary a and the eutectic structure )

43. Relative amounts of both eutectic and primary a microconstituents
Eutectic microconstituents forms from liquid having eutectic composition (61 wt% Sn, Fig 9.11, point i)
Apply lever rule using tie line
Eutectic fraction
We = WL = P / (P+Q)
Primary a fraction
Wprimary a = Q / (P+Q)
Total a fraction (primary plus eutectic)
W a = (Q+R) / (P+Q+R)
Total b fraction (primary plus eutectic)
W b = P / (P+Q+R)

45. Chapter 9
Sections: 9.8, 9.9, 9.13

46. 9.8 Equilibrium Diagrams Having Intermediate Phases or Compounds
Terminal solid solutions
Solid phases exist over the composition ranges near the concentration extremities of the phase diagram
Examples: Copper-Silver system (Figures 9.6)
Lead –Tin system (Figure 9.7)
Intermediate solid solutions
Intermediate phases
Solid phases at other than the two composition extremes
Example: Cupper-Zinc system (Figure 9.17)

50. Intermetallic compounds
Discrete intermediate compounds rather than solid solutions
These compounds have distinc chemical formulas

51. 9.9 Eutectoid and Peritectic Reactions
Eutectoid Reaction
Invariant point E, Figure 9.19
Upon cooling, a solid phase transforms into two other solid phases
Reverse reaction occurs on heating
Horizontal line at 560oC: eutectoid or eutectoid isotherm
Eutectic  liquid on cooling transforms into two solids
Importance: iron-carbon diagram
Peritectic Reaction
Another invariant reaction (Point P, Figure 9.19)
Upon heating, one solid phase transforms into a liquid phase and another solid phase
(d + L) on cooling e

53. THE IRON-CARBON SYSTEM 9
THE IRON-CARBON SYSTEM The iron-iron carbide (Fe-Fe3C) phase diagram
Of all binary alloys, the most important is the iron-carbon phase diagram.
A portion is shown in Figure 9.22
Practically all steels and cast irons have less than 6.70 wt% C.
Pure iron:
Upon heating, experiences two changes in crystal structure before it melts
At room temperature, the stable form ( ferrite or a iron ) has a BCC.
At 912oC, Ferrite experiences polymorphic transformation FCC austenite, or g iron.
At 1394oC, reverts back to a BCC phase ( d ferrite )
At 1538oC, d ferrite melts

55. At 6.7 wt% C
Intermediate compound iron carbide, or cementite (FE3C), is formed.
6.7 wt% C corresponds to 100 wt% Fe3C
Carbon is an interstitial impurity in iron
Forms a solid solution with each of a and d ferrites and g austenite
BCC a ferrite
Small concentration of carbon are soluble (0.022 wt% at 727oC)
Even though small concentration, significantly influences mechanical properties
Relatively soft, magnetic at temperature below 768oC, density of 7.88 g/cm3
Figure shows photomicrograph

57. Austenite or g phase iron
Not stable below 727oC
FCC structure
Maximum solubility of carbon in austenite: 2.14 wt% C at 1147oC.
Figure 9.23b shows photomicrograph
BCC d ferrite is virtually same as a ferrite
Stable only at relatively high temperatures  no technological importance
Cementite (Fe3C) forms when the solubility limit of carbon in a ferrite is exceeded below 727oC
Coexist with g phase between 727 and 1147oC
Cementite is very hard and brittle  strength of steel is enhanced by its presence

58. One eutectic reaction for iron-carbon system
At 4.30 wt% C and 1147oC
L  on cooling  g + Fe3C
L  on heating  g + Fe3C
Eutectoid invariant point at 0.76 wt% C and 727oC
g (0.76 wt% C)  on cooling  a (0.022 wt% C) + Fe3C(6.7 wt%C)
g (0.76 wt% C)  on heating  a (0.022 wt% C) + Fe3C(6.7 wt%C)

59. Chapter 9
Sections: 9.14, 9.15

60. 9.14 Development of Microstructures in Iron-Carbon Alloys
Microstructure depends on both the carbon content and heat treatment.
Discussion confined to very slow cooling  equilibrium is continuously maintained.
Phase change from g austenite region into the a + Fe3C phase field
Relatively complex, similar to eutectic system
Consider cooling of an alloy of eutectoid composition
(Point a at 0.76 wt% C and 800oC)
No changes until the eutectoid temperature (727oC)
At b, pearlite microstructure
Figure 9.25, photomicrograph of eutectoid steel showing the pearlite.

62. The pearlite exists as grains
Often termed colonies
Layer orientation is same in each colony
Thick light layers  ferrite phase
Thin lamellae, mostly dark  cementite
Ferrite  soft and ductile
Cementite  hard and brittle
Pearlite  intermediate between ferrite and cementite

64. Hypo-Eutectoid Alloys
Consider a composition Co to the left of eutectoid
Between and 0.76 wt% C
Termed a hypoeutectoid (less than eutectoid) alloy
Cooling is shown in Figure 9.27
At d, about 775oC, a + g phase
Composition of ferrite (a iron) changes along MN
Slight changes
Composition of austenite (g iron) changes dramatically along MO
At f, just below the eutectoid
All g-phase having eutectoid composition transforms to pearlite
No change in a-phase (ferrite )
Ferrite exist in two phases:
Eutectoid ferrite  ferrite that is present in pearlite
Proeutectoid ferrite  pre- or before eutectoid; formed above Te

66. Figure 9.28: photomicrograph of a 0.38 wt% C steel
Large white regions: proeutectoid ferrite
Pearlite
Dark regions
Spacing between a and Fe3C layers vary from grain to grain

67. Hyper-Eutectoid Alloys
Right side of eutectoid ( between 0.76 and 2.14 wt% C)
At g, only g phase (austenite ) of composition C1
Upon cooling at h, g  g + Fe3C phase field
Proeutectoid cementite  that forms before the eutectoid reaction
Cementite composition remains constant as the temperature changes
Austenite composition changes along line PO towards eutectoid
Below eutectoid temperature at i,
All remaining austenite of eutectoid composition  pearlite (a+Fe3C)
Microconstituents of resulting microstructure
 pearlite and proeutectoid cementite (Fig 9.30)

69. Photomicrograph of hypereutectoid alloys
Photomicrograph of 1.4 wt% C steel is shown in Fig. 9.31
Consists of pearlite and proeutectoid cementite
Proeutectoid cementite appears light
Same appearance as proeutectoid ferrite
 difficulty in distinguishing between hypoeutectoid and hypereutectoid steels on the basis of microstructure

70. Photomicrograph of hypereutectoid alloys (Contd.)
Comparison with hypoeutectoid alloys photomicrograph

71. Relative amounts for hypoeutectoid steel alloys
Using lever rule
Tie line extends between and 0.76 wt% C
Fraction of pearlite,
Wp = T / (T+U) = (Co’ – 0.022) / (0.76 – 0.022)
Fraction of proeutectoid a,
Wa’ = U / (T+U) = ( Co’) / (0.76 – 0.022)

73. Relative amounts for hypereutectoid steel alloys
Using lever rule
Tie line extends between 0.76 and 6.7 wt% C
Fraction of pearlite,
Wp = X / (V+X) = (6.70 – C1’) / ( )
Fraction of proeutectoid cementite (Fe3C)
WCementite’ = V / (V+X) = (C1’ ) / ( )

74. 9.15 The Influence of Other Alloying Elements
Other alloying elements (Cr, Ni, Ti, etc.) bring about dramatic changes
Changes in the position of phase boundaries and shapes
One important change  shift in eutectoid position w.r.t temperature and composition
These effects are illustrated in Figures 9.32 and 9.33