Chapter 9

Sections:9.2, 9.3, 9.4, 9.5


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.


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


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 (C
12
H
22
O
11
-H
2
O) 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


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.


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.


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

 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.


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 20 o C
–
If system is in equilibrium,
»
Composition of syrup is 65wt% C
12
H
22
O
11
-35wt% H
2
O (Fig 9.1)
»
Amount and composition of syrup and sugar will remain constant
– If temperature is raised to 100 o C
» 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


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

Chapter 9

Sections: 9.6


Equilibrium Phase diagram :
– 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


Phase diagram of the
is shown in Fig 9.2a.


Temperature
 composition

Composition ranges from 0 wt% Ni (100 wt% Cu) to 100 wt% Ni (0 wt% Cu)

regions, or fields, appear
– An alpha ( a
) field
– A liquid (L) field
– A two-phase ( a
+L) field

 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


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 (1085 o C) and Nickel (1453 o C)

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


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


For binary system of known composition and temperature that is in equilibrium, at least three kinds of information are available:
1.
The phases that are present
2.
The composition of these phases
3.
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 1100 o C Point A a phase
35 wt% Ni-65 wt% Cu at 1250 o C Point B a
+ liquid phases

o
o (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

PHASE DIAGRAMS: # and types of phases
o
--the # and types of phases present.
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

PHASE DIAGRAMS: composition of phases
o
--the composition of each phase.
Cu-Ni system
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

PHASE DIAGRAMS: weight fractions of phases
o
--the amount of each phase (given in wt%).
Cu-Ni system
W
L

R
S

S

43

35
43

32

73 wt %
W a 
R
R

S
= 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

WL

W a 
Co

1
WLCL

W a C a
moment equilibrium:
WLR
 W a
S
1
 W a solving gives Lever Rule
9

 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

C o
= 35 wt% Ni
C a
= 42.5 wt% Ni
C
L
= 31.5 wt% Ni
W
L
= ( 42.5 – 35) / (42.5 – 31.5) = 0.68
W a
= (35 – 31.5) / (42.5 – 31.5) = 0.32
 Volume fraction : See equations 9.5 – 9.7

V a
 v a v
 a v b
V b
 v a v b
 v b
V a

W a
 a
W a
 a

W b
 b
V b

W a
 a
W b
 b

W b
 b
W a

V a
 a
V a
 a

V b
 b
W b

V a

V b
 b a

V b
 b

 35 wt% Ni-65wt% Cu as cooled from 1300 o C
 Cooling very slowly  phase equilibrium is maintained
Cooling

Moving down
At 1300 o C , completely liquid
At b (1260 o C), solidification starts
At d (1220 o C), solidification completes


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

 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

Chapter 9

Sections: 9.7


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)


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 779 o C

Feature 2:
 a
+ L
 b
+ L
 a
+ b
Three two-phase regions


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 (C
E
= 71.9 wt% Ag, T
E
= 779 o C)

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)
–
C
E and T
E represents eutectic composition and temperature
– Horizontal solidus line at T
E is called the eutectic isotherm


The eutectic reaction, upon cooling , is similar to solidification of pure components:
– Reaction proceeds to completion at a constant temperature
– Isothermal at T
E
– 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

 Depending on composition, several different types of microstructures
 These possibilities considered in terms of the lead-tin phase diagram
–
Figure 9.7

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

 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

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


Lamellae :
– The microstructure of a solid consisting of alternating layers
– Shown in Figure 9.12

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

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


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

W e
= W
L
= P / (P+Q)

a
W primary a
= Q / (P+Q)

a
W a
= (Q+R) / (P+Q+R)

b
W b
= P / (P+Q+R)

Chapter 9

Sections: 9.8, 9.9, 9.13


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)


Intermetallic compounds
 Discrete intermediate compounds rather than solid solutions
– These compounds have distinc chemical formulas

 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 560 o C: 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

3

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 912 o C , Ferrite experiences polymorphic transformation FCC austenite , or g iron .
– At 1394 o C , reverts back to a BCC phase ( d ferrite )
– At 1538 o C , d ferrite melts


At 6.7 wt% C
– Intermediate compound iron carbide , or cementite (FE
3
C), is formed.
– 6.7 wt% C corresponds to 100 wt% Fe
3
C

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 727 o C)
–
Even though small concentration, significantly influences mechanical properties
– Relatively soft, magnetic at temperature below 768 o C, density of 7.88 g/cm 3
– Figure shows photomicrograph


or g phase iron
– Not stable below 727 o C
– FCC structure
– Maximum solubility of carbon in austenite: 2.14 wt% C at 1147 o C.
–
Figure 9.23b shows photomicrograph
 BCC d
is virtually same as a ferrite
– Stable only at relatively high temperatures  no technological importance

Cementite (Fe
3
C) forms when the solubility limit of carbon in a ferrite is exceeded below 727 o C
– Coexist with g phase between 727 and 1147 o C
–
Cementite is very hard and brittle
 strength of steel is enhanced by its presence


One eutectic reaction for iron-carbon system
– At 4.30 wt% C and 1147 o C
L  on cooling  g
+ Fe
3
C
L
 on heating
 g
+ Fe
3
C

Eutectoid invariant point at 0.76 wt% C and 727 o C g
(0.76 wt% C)  on cooling  a
(0.022 wt% C) + Fe
3
C(6.7 wt%C) g
(0.76 wt% C)
 on heating
 a
(0.022 wt% C) + Fe
3
C(6.7 wt%C)

Chapter 9

Sections: 9.14, 9.15


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
+ Fe
3
C phase field
– Relatively complex , similar to eutectic system
– Consider cooling of an alloy of eutectoid composition
( Point a at 0.76 wt% C and 800 o C)
– No changes until the eutectoid temperature (727 o C)
–
At b, pearlite microstructure
– Figure 9.25, photomicrograph of eutectoid steel showing the pearlite.


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

 Consider a composition Co to the left of eutectoid
– Between 0.022 and 0.76 wt% C
– Termed a hypoeutectoid (less than eutectoid) alloy
– Cooling is shown in Figure 9.27
 At d , about 775 o C, 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


Figure 9.28: photomicrograph of a 0.38 wt% C steel
– Large white regions: proeutectoid ferrite
–
Pearlite
» Dark regions
» Spacing between a and
Fe
3
C layers vary from grain to grain

 Right side of eutectoid ( between 0.76 and 2.14 wt% C)

At g , only g phase (austenite ) of composition C
1

Upon cooling at h , g  g
+ Fe
3
C 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
+Fe
3
C)
– Microconstituents of resulting microstructure
 pearlite and proeutectoid cementite (Fig 9.30)


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


Comparison with hypoeutectoid alloys photomicrograph


Using lever rule
 Tie line extends between 0.022 and 0.76 wt% C

Fraction of pearlite,
W p
= T / (T+U) = (C o
’ – 0.022) / (0.76 – 0.022)
 Fraction of proeutectoid a
,
W a
’
= U / (T+U) = (0.76 - C o
’
) / (0.76 – 0.022)


Using lever rule
 Tie line extends between 0.76 and 6.7 wt% C

Fraction of pearlite,
W p
= X / (V+X) = (6.70 – C
1
’
) / (6.70 - 0.76)
 Fraction of proeutectoid cementite (Fe
3
C)
W
Cementite
’
= V / (V+X) = (C
1
’
- 0.76 ) / (6.70 - 0.76)


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