MAE 212: Spring 2001
Lecture 14
PHASE DIAGRAMS AND
EQUILIBRIUM MICROSTRUCTURES
N. Zabaras
For more details on the topic read Chapter 9 of the Materials Science
for Engineers by J. Shackelford, pp. 304–353. Also you are strongly
encouraged to read the Appendix on Teaching Yourself Phase Diagrams
from the Mechanics of Materials II of Ashby and Jones. Both books
are on reserve for MAE212 in the Engr. library.
Phase diagrams provide a graphical representation at equilibrium of the structure of an
alloy or ceramic. They tell us what microstructure should exist at a given temperature and
composition. Equilibrium structures give a base line from which non-equilibrium structures
can be inferred.
We will begin with some definitions.
Alloys: A metallic alloy is a mixture of a metal with other metals or non-metals.
For example, Copper (Cu) and Zinc (Zn), when mixed, form the alloy brass. Magnesia
(MgO) and alumina (Al2O3) when mixed in equal proportion form spinel . Iron (Fe) and
carbon (C) mix to give carbon steel .
Components: The alloy components are the chemical elements which make up the
alloy. Alloys are usually made by melting together and mixing the components.
For example, in brass the components are Cu and Zn. In carbon steel the components are
Fe and C. In spinel , they are Mg, Al and O.
Binary alloy: A binary alloy contains two components. Most of the discussion here is
about binary alloys.
Tertiary alloy: A tertiary alloy contains three components, etc.
Concentration: An alloy is described by stating the components and their concentrations.
The weight % of component A in a binary alloy consisting of elements A and B is defined
as follows:
WA =
weight of component A
weights of all components
× 100 (1)
1
The atom (or mol) % of component A can also be introduced:
XA =
number of atoms (or mols) of component A
number of atoms (or mols) of all components
× 100 (2)
Note that from XA and XB, one can calculate WA and WB and the reverse. Recall that:
(Weight in g) / (atomic or molecular wt in g/mol) = number of mols.
Based on this transformation, try to show that
WA =
XAaA
XAaA + XBaB
WB =
XBaB
XAaA + XBaB
(3)
where aA and aB are the atomic weights of A and B.
Note than in many books, the concentration (composition) is simply denoted as C or c. You
always need to pay attention if this is a weight-based concentration or mole-based.
Structure: Alloys are usually made by melting the components and mixing them together
while liquid. A binary alloy can take one of following forms:
• a single solid solution;
• two separated, essentially pure, components;
• two separated solid solutions;
• a chemical compound, together with a solid solution.
Later we will present examples of each of the above structures. The specific form of the
microstructure present is decided by examining a flat surface of the alloys that has been
polished and etched.
Phases: Phase is the part of an alloy with the same physical and chemical properties and
the same composition. Phase must be distinguished from component, which is a distinct
chemical substance from which the phase is formed.
For example, water is one phase, but water mixed with ice is two phases. The Al-Si, Cd-Zn
and Al-Cu alloys are all made up of two phases.
The Constitution of an Alloy: The constitution of an alloy is described by:
• The phases present.
• The weight percentage of each phase.
• The composition of each phase.
2
FIGURE 5-1
Figure 1: Single phase microstructure of commercially pure molybdenum. Although there
are many grains in this microstructure, each grain has the same, uniform composition (From
J. Shackelford, Materials Science for Engineers).
The properties of an alloy depend critically on its constitution and on two further features
of its structure: the scale (nm or µm or mm) and shape (round, or rod-like, or plate-like) of
the phases. The constitution, and the scale and shape of the phases, depend on the thermal
treatment that the material has had.
As a first example, Figure 1 presents the single phase microstructure of pure molybdenum.
Note that a single phase can be polycrystalline, but each grain differs only in orientation,
not in chemical composition.
Cu and Ni are very similar in nature and they are completely soluble in each other in all
proportions. For such alloys, there is a single phase (a solid solution).
When the solid solubility is limited, two phases are formed, each richer in a different component.
An example is the pearlite shown in Fig. 2. Pearlite consists of alternating layers of
ferrite and cementite. The cementite is nearly pure Fe3C, while the ferrite is α − Fe with
a small amount of cementite in solid solution. The components of pearlite are then Fe and
Fe3C.
Equilibrium Constitution: A sample has its equilibrium constitution when, at a given,
constant temperature T and pressure p, there is no further tendency for its constitution to
change with time. This constitution is the stable one.
State Variables: Are the independent variables over which we have control in establishing
microstructures. The constitution variables or state variables are T, p and the composition.
For example, a pure metal at its melting point has two phases (the solid and liquid) at
equilibrium. For a given pressure, any increase or decrease of the temperature will result in
3
FIGURE 5-2
Figure 2: Two phase microstructure of pearlite found in steel with 0.8 wt % C. This carbon
content is an average of the carbon content in each of the alternating layers of ferrite (with
< 0.02 wt % C) and cementite (a compound, Fe3C, which contains 6.7 wt % C). (From J.
Shackelford, Materials Science for Engineers).
change of the microstructure (e.g. higher T will melt the solid phase, etc.). So, a pure metal
at its melting temperature has no degrees of freedom.
Certain thermodynamic relations exist between the state variables. In general for a binary
alloy we choose p, T, and XB as the independent variables – though here we will drop p. The
volume V and the composition XA (= 1 − XB) are then determined: they are the dependent
variables . Of course, the weight percentages WA and WB can be used instead.
For demonstration, let us consider the Al-Cu alloy:
Values of the state variables Equilibrium constitution
(a) T = 500◦
C
p = 1 atm.
WAl = 96%
WCu = 4%



→ Single-phase solid solution of copper in aluminum
(a) T = 20◦
C
p = 1 atm.
WAl = 96%
WCu = 4%



→ Two phases: Al containing 0.1 wt% Cu, and CuAl2
(4)
The microstructures in the Cu-Al alloy above are equilibrium constitutions because they
are the ones reached by very slow cooling; slow cooling gives time for equilibrium to be
reached. An alloy has its equilibrium constitution when there is no further tendency for the
constitution to change with time.
Gibb’s Phase Rule: The number of phases P which coexist in equilibrium is given by the
4
phase rule
F = C − P + 2 (5)
where C is the number of components and F is the number of free independent state variables
or degrees of freedom of the system.
If the pressure p is held constant (as it usually is for solid systems) then the rule becomes
F = C − P + 1 (6)
A one-component system (C = 1 ) has two independent state variables (T and p). At the
triple point three phases (solid, liquid, vapor) coexist at equilibrium, so P = 3. From the
phase rule F = 0 so that at the triple point, T and p are fixed – neither is free but both are
uniquely determined. If T is free but p depends on T then F = 1 and P = 2 that is, two
phases, solid and liquid, say, co-exist at equilibrium. If both p and T are free F = 2 and
P = 1; only one phase exists at equilibrium.
The information obtained from Gibb’s rule is difficult to appreciate without the visual aid
of phase diagrams. The equilibrium diagram or phase diagram summarizes the equilibrium
constitution of the alloy system.
Phase diagram example for one component system: As a simple example, the one-component
phase diagram of H2O is given in Fig. 3, while the one-component phase diagram of pure
iron is given in 4. The equilibrium constitution of a one-component system is fixed by the
variables p and T and so the equilibrium phases can be shown on a diagram with p and T
axes. The one shown in Fig. 3 has only one solid phase, while pure iron in Fig. 4 has several.
Single-phase regions are areas. Two phases co-exist along lines.Three phases co-exist at a
point: the triple point. The behavior at constant p is given by a vertical cut through the
diagram. The solid melts at Tm and vaporizes at Tv. The phase diagram at constant pressure
is a line (shown on the right) along which the span of stability of each phase is marked.
Equilibrium constitution (or phase) diagrams for binary alloys
If the pressure is held constant at 1 atm, then the independent variables which control the
constitution of a binary alloy are T and XB or WB. An equilibrium-constitution diagram
or equilibrium diagram or phase diagram , is a diagram with T and XB (or WB) as axes. It
shows the results of experiments which measure the equilibrium constitution at each T and
XB (or WB). The phase diagram shows the equilibrium constitution for all the binary alloys
that can be made of A and B, in all possible proportions.
The constitution point: The state variables define a point on the diagram: the “constitution
point.” If this point is given, then the equilibrium number of phases can be read off.
So, too, can their composition and the quantity of each phase.
5
SteamGas
WaterLiquid
IceSolid
1 atm
Pressure (log scale)
(a) (b)
100
0
T( C)Temperature
FIGURE 5-3
Figure 3: (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 point at 0o
C and boiling at
1000
C).
The phase diagram for a binary alloy shows single-phase fields (e.g., liquid) and two-phase
fields . The fields are separated by phase boundaries . When a phase boundary is crossed, a
phase change starts, or finishes, or both.
NOTE 1: When the constitution point lies in a single-phase region, the alloy consists of
a single, homogeneous, phase. Its composition must (obviously) be that of the alloy. The
phase composition and the alloy composition coincide in single-phase fields.
NOTE 2: When the constitution point for an alloy lies in the two-phase field the alloy breaks
up into a mixture of two phases. The composition of each phase is obtained by constructing
the tie line (the isotherm spanning the two-phase region, terminating at the nearest phase
boundary on either side). The composition of each phase is defined by the ends of the tie
line.
We will now discuss in detail some of the above definitions using several phase diagrams for
the A-B alloy. The implications of Notes 1 and 2 will become clear through the following
examples.
Phase diagram example for a binary alloy with a complete solid solution: The simplest phase
diagrams are those associated with binary alloys in which the two components are completely
6
LiquidGas Liquid
α (ferrite)
γ (austenite)
α
γ
δ δ
1 atm
Pressure (log scale)
(a) (b)
1538
1394
910
T( C)Temperature
FIGURE 5-4
Figure 4: (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.
soluble to each other in both the solid and the liquid states (e.g. the Cu-Ni alloy). Figure
5 shows such a phase diagram for an alloy consisting of components A and B. Pay close
attention to the details of this diagram. Between the two single phases (the liquid phase L
and the solid phase SS), there is a two phase mixture labeled L + SS. The phase boundary
which limits the bottom of the liquid field is called the liquidus line. The other boundary of
the two-phase liquid-solid field is called the solidus line.
Figure 6 explains how to calculate the composition at a state point (i.e. at a given temperature
and composition) within the two-phase region. Note that at such a point, an A-rich
liquid exists in equilibrium with a B-rich solid solution. The horizontal line connecting the
two-phase compositions at the system temperature is the tie line. The composition of each
phase is defined by the end points of this line.
7
Melting point
of A
Melting point
of B
Temperature
A
0
100
20
80
40
60
60
40
80
20
Composition (wt %)
B
100 wt % B
0
Solidus
Liquidus
L
L + SS
SS
→
wt % A→
FIGURE 5-5
Figure 5: Binary phase diagram showing complete solid solution. The liquid-phase field is
labeled L and the solid solution is designed SS. Note the two-phase region labeled L + SS
(From J. Shackelford, Materials Science for Engineers).
A
X1
T1
B
L
L + SS
SS
Composition
of L at T1
Composition
of SS at T1
System
composition
System
temperature
State
point
FIGURE 5-6
Figure 6: The compositions of the phases in a two-phase region of the phase diagram designed
by a tie line (From J. Shackelford, Materials Science for Engineers).
8
Temperature
A
Composition
B
F = 2 − 2 + 1
F = C − P + 1
F = 2 − 1 + 1 = 2
F = 2 − 1 + 1 = 2
F = 1 − 2 + 1 = 0
= 1
FIGURE 5-7
Figure 7: Application of Gibbs phase rule to various points in the phase diagram of Fig. 5
(From J. Shackelford, Materials Science for Engineers).
Figure 7 shows the application of the Gibbs rule to the above phase diagram. For example,
within the two phase region (P = 2) of the binary alloy A-B (C = 2), there are F =
C − P + 1 = 2 − 2 + 1 = 1 independent variables. As such, changes in temperature are
possible, however the resulting compositions are not independent and must be established
by the tie line associated with a given temperature.
Finally, Fig. 8 summarizes the different microstructures obtained in the different regions of
the phase diagram.
Eutectic diagram example for a binary alloy with no solid solution: We consider a binary
alloy where the components A and B have negligible solubility in each other (see Fig. 9). At
low temperatures there is a two phase region that consists of pure A and pure B. The solidus
line is horizontal and the corresponding temperature is known as the eutectic temperature.
The liquidus lines start from the melting points of the pure components. Almost always,
alloying lowers the melting point, so the liquidus lines descend from the melting points of the
pure components, forming a shallow V. The bottom point of the V formed by two liquidus
lines is the eutectic point .
Note that the solid at the eutectic composition (Fig. 9) will melt completely at the eutectic
temperature. For other compositions, complete melting will require heating to the liquidus
line after passing the two-phase region A + L (or B + L).
9
A
L1
Lsystem
T1
Temperature
B
SS1
All liquid (Lsystem)
Crystallites of SS1
in matrix of L1
Polycrystalline solid
(SSsystem)
System
composition
Composition
SSsystem
FIGURE 5-8
Figure 8: Various microstructures characteristic of different regions in the complete solidsolution
phase diagram (From J. Shackelford, Materials Science for Engineers).Temperature
A B
Solidus
Liquidus
L
L + B
A + L
A + B
Eutectic
composition
Eutectic
temperature
Composition
FIGURE 5-9
Figure 9: Binary eutectic phase diagram showing no solid solution. The general appearance
can be contrasted to the opposite case of complete solid solution illustrated in Fig. 5 (From
J. Shackelford, Materials Science for Engineers).
10
Temperature
A B
Leutectic
L2
Composition
Crystallites of B
in matrix of L2
Eutectic microstructure—
fine, alternating layers of
A and B
All liquid (Leutectic)
Crystallites of A
in matrix of L1 L1
FIGURE 5-10
Figure 10: Various microstructures characteristic of different regions in a binary eutectic
phase diagram with no solid solution (From J. Shackelford, Materials Science for Engineers).
Figure 10 shows the different microstructures. Note that the liquid and (solid+liquid) microstructures
are similar in nature with those shown in Fig. 8. However, the solid microstructure
(known as the eutectic structure) consists of fine-grained alternating layers of
pure A and pure B.
Eutectic phase diagram example for a binary alloy with limited solid solution: Here A and B
are partially soluble in each other. Figure 11 presents such a phase diagram. It is similar to
that of Fig. 9 except for the solid solution regions α and β. The crystal structure of α will
be that of A (α consists of B atoms in the lattice of A), while the crystal structure of β will
be that of B (β consists of A atoms in the lattice of B).
Figure 12 shows the microstructures in the different regions of the phase diagram. Also, the
tie lines needed to calculate the compositions of the different phases are shown as well.
The transformation of eutectic liquid to the fine grained microstructure upon cooling is called
the eutectic reaction. It can be written as follows:
Liquid
cooling
−→ solid α + solid β (7)
Example of the eutectoid phase diagram: In addition to the eutectic reaction, some phase
diagrams contain the so called eutectoid reaction upon cooling. This reaction has the form:
Solid
cooling
−→ solid α + solid β (8)
11
Temperature
A B
L
L + βα + L
α β
α + β
Composition
FIGURE 5-11
Figure 11: Binary eutectic phase diagram with limited solid solution. The only difference
from Fig. 9 is the presense of solid-solutions α and β (From J. Shackelford, Materials Science
for Engineers).
12
Temperature
A B
Leutectic
L1 L2
β2
β1
α3
α2α1
Composition
All liquid (Leutectic)
Crystallites of β1
in matrix of L2
Eutectic microstructure—
fine, alternating layers of
α2 and β2
Crystallites of α3
in matrix of L1
Polycrystalline
solid (α1)
FIGURE 5-12
Figure 12: Various microstructures characteristic of different regions in the binary eutectic
phase diagram with limited solid solution. This illustration is essentially equivalent to Fig.
10 except that the solid phases are now solid solutions (α and β) rather than pure components
(A and B) (From J. Shackelford, Materials Science for Engineers).
13
Figure 13 presents the eutectoid phase diagram, while Fig. 14 presents the related microstructures.
Note that both the eutectic and eutectoid (eutectic like) microstructures are
fine-grained.
Temperature
A B
L
α + β
L + β
γ + β
γ + L
Eutectoid
composition
Eutectoid
temperature
Composition
Eutectic
composition
Eutectic
temperature
α + γ
α
γ
β
FIGURE 5-13
Figure 13: The eutectoid phase diagram contains both a eutectic reaction as well as a
eutectoid reaction. (From J. Shackelford, Materials Science for Engineers).
Temperature
A B
Composition
α1
γeutectoid
β2
β1γ1
Eutectic microstructure—
fine-grained nodules of
γ1 in matrix of β1
Polycrystalline
solid (γeutectoid)
Eutectoid microstructure—
fine, alternating layers of
α1 and β2
FIGURE 5-14
Figure 14: Microstructures in the different regions of the eutectoid phase diagram. (From J.
Shackelford, Materials Science for Engineers).
14
Temperature
A AB B
L L + B
AB + B
A + AB
Composition
Composition of
liquid formed upon
melting of AB
L+ABA+L
FIGURE 5-15
Figure 15: Peritectic phase diagram showing a peritectic reaction. For simplicitly, no solid
solution is shown (From J. Shackelford, Materials Science for Engineers).
Example of a peritectic phase diagram: Here we consider a binary alloy system in which A
and B form a stable compound AB, which does not melt at a single temperature as do the
components A and B. To simplify, we assume that there is no solid solution formed between
the components and the intermediate compound. The preritectic reaction upon heating of
AB is defined as follows:
compound AB
heating
−→ liquid + solid B (9)
where the liquid composition is defined in Fig. 15. The microstructures for this phase
diagram are shown in Fig. 16. The liquid formed upon melting of the components has the
same composition as the solid from which it was formed. On the other hand, the liquid
formed by melting AB has composition other than that of AB.
The Lever Rule
You can get the relative amounts of each phase in a two-phase alloy microstructure from the
phase diagram. Let us start with the familiar phase diagram given in Fig. 17. Let mL be the
mass of the liquid phase and mSS the mass of the solid solution phase of the alloy. Also, let
mtotal be the total mass of the alloy. We consider the alloy here to have a wt % composition
of 50%. Simple mass balance gives that:
mL + mSS = mtotal (10)
15
Temperature
A AB B
L
Composition
Polycrystalline solid
(compound AB)
Crystallites of B
in matrix of L1
FIGURE 5-16
Figure 16: Microstructures for the peritectic diagram of Fig. 15 (From J. Shackelford,
Materials Science for Engineers).
A mass balance tells us that the amount of B in the alloy is the sum of the amounts of B in
the liquid and solid phases, i.e.
0.30mL + 0.80mSS = 0.50mtotal (11)
From the two equations above, we can show that mL = 0.6mtotal and mSS = 0.4mtotal.
The above calculation can be easily generalized. Let x be the composition of the alloy and
xα and xβ the compositions of the two phases α and β at equilibrium (see Fig. 18(a)). The
final results are as follows:
mα
mα + mβ
=
xβ − x
xβ − xα
(12)
mβ
mα + mβ
=
x − xα
xβ − xα
These equations represent the so called lever rule. The name of this rule becomes apparent
from its mechanical analog (see Fig. 18(b)).
Phase Reactions During Slow Cooling
In all of the following examples, we will assume slow cooling of an alloy of given composition
from a single-phase melt. As we mentioned earlier, slow cooling is essential to maintain
equilibrium microstructures.
16
Temperature
A
0 30 50 80 100
Composition (wt % B) B
L
L + SS
SS
T1
mL + mSS = mtotal
0.30mL + 0.80mSS = 0.50mtotal
←mL = 0.60mtotal
mSS = 0.40mtotal
FIGURE 5-19
Figure 17: A more quantitative treatment of the tie line allows the amount of each phase
(L and SS) to be calculated by means of a mass balance (From J. Shackelford, Materials
Science for Engineers).
(b)
(a)
Fulcrum
α + βα β
mα
mβ
FIGURE 5-20
Figure 18: The lever rule is a mechanical analogy to the mass balance calculation. The (a)
tie line in the two-phase region is analogous to (b) a lever balanced on a fulcrum (From J.
Shackelford, Materials Science for Engineers).
17
A
L2
L3
L1
Lsystem
T2
T1
T3
Temperature
B
SS1
SS2
SS3
100% liquid
(Lsystem)
10% SS1 in
matrix of L1
Composition
40% SS2 in
matrix of L2
90% SS3 in
matrix of L3
SSsystem
100% solid
(SSsystem)
FIGURE 5-21
Figure 19: Microstructural development during the slow cooling of a 50%A − 50%B composition
in a phase diagram with complete solid solution. At each temperature, the amounts of
the phases in the microstructure correspond to a lever rule calculation. (From J. Shackelford,
Materials Science for Engineers).
When the compositions of the phases change with temperature, we say that a phase reaction
takes place. Figure 19 shows the phase reactions that take place during the slow cooling of
50%A − 50%B alloy from its melt. Both the % of each phase as well as the composition of
each phase are shown during the cooling process.
Figure 20 shows the phase reactions during the slow cooling of an alloy at the eutectic
composition.
The obtained microstructures are slightly more complicated if the alloy composition is different
from the eutectic composition. In Fig. 21, the reactions upon cooling are presented
for an alloy with higher than the eutectic composition. For example, consider the cooling
of an alloy with 80 % B. Starting from above the liquidus curve, the regions of interest are
shown in Figure 21.
• Upon reaching the liquidus curve, phase β appears in growing amounts as we further
cool towards the eutectic temperature.
• Just before reaching the eutectic temperature, 33% of the microstructure is liquid.
This amount of liquid undergoes the eutectic reaction and it is transformed to the
18
Temperature
A
T2
T1
B
Leutectic
β2
β1
α2
α1
Composition
100% liquid
(Leutectic)
Eutectic microstructure—
fine, alternating layers of
α2 and β2*
Eutectic microstructure—
fine, alternating layers of
α1 and β1
*The only differences from the T1 microstructure are
the phase compositions and the relative amounts of
each phase. For example, the amount of β will be
proportional to:
xeutectic − xα
xβ − xα
FIGURE 5-22
Figure 20: Microstructural development during the slow cooling of a eutectic composition
(From J. Shackelford, Materials Science for Engineers).
fine grained eutectic microstructure (17%α3 and 83%β3). At this point the phase β
is present in two distinct forms: The large grains produced during cooling in the (L
+ β) region (called pro-eutectic β); and the finer β (called eutectic β) in the eutectic
microstructure.
Figure 22 presents the reactions during slow cooling of an alloy with composition lower than
the eutectic one.
Finally, Figure 23 present some microstructural developments that avoid the eutectic reac-
tion.
19
Temperature
A
T2 (= Teutectic + 1 )
T3 (= Teutectic − 1 )
B
100908060300
L2
L1
β2
&
β3
β1
α3
Composition (wt % B)
100% liquid
(Lsystem = 80% B)
Lsystem
67% β2 ( 90% B)
in matrix of L2
( 60% B)
67% β3 ( 90% B)
in matrix of eutectic
microstructure
= 17% α3 ( 30% B)
+ 83% β3 ( 90% B)
10% β1 in
matrix of L1
∼=
∼=
∼=
∼=
∼=
FIGURE 5-23
Figure 21: Microstructural development during the slow cooling of a hypereutectic composition
(From J. Shackelford, Materials Science for Engineers).
Temperature
A
T2 (= Teutectic + 1 )
T3 (= Teutectic − 1 )
B
1009040 60300
L1
β3
α2 &
α3
α1
Composition (wt % B)
100% liquid
(Lsystem = 40% B)
Lsystem
10% α1 in
matrix of L1
67% α2 ( 30% B)
in matrix of L2
( 60% B)
∼=
∼=
67% α3 ( 30% B)
in matrix of eutectic
microstructure
= 83% α3 ( 30% B)
+ 17% β3 ( 90% B)
∼=
∼=
∼=
FIGURE 5-24
Figure 22: Microstructural development during the slow cooling of a hypoeutectic composition
(From J. Shackelford, Materials Science for Engineers).
20
Temperature
A B
100100
L1
α1
αsystem
Composition (wt % B)
(a)
100% liquid
(Lsystem = 10% B)
50% α1 in
matrix of L1
Lsystem
100% α
(αsystem = 10% B)
Temperature
A B
100200
L1α1
α2
α3
β2
β3
αsystem
Composition (wt % B)
(b)
50% α1 in
matrix of L1
100% liquid
(Lsystem = 20% B)
Lsystem
100% α
(αsystem = 20% B)
1% β2 in
matrix of α2
5% β3 in
matrix of α3
FIGURE 5-25
Figure 23: Microstructural development for a composition that avoids the eutectic reaction.
(a) Solidification leads to a single solid-solution that remains stable upon further cooling
(b) Upon cooling the α phase becomes saturated with B atoms. Further cooling leads to
precipitation of a small amount of the β phase along grain boundaries (From J. Shackelford,
Materials Science for Engineers).
21
The Fe − Fe3C phase diagram
Atomic percentage carbon
C
Weight percentage carbon
Fe 1 2 3 4 5 6 7
1700
2 5 10 15 20 25
1600
1500
1400
1300
912
0.02 0.77
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
α
(ferrite)
α + Fe3C
Fe3C
(cementite)
2.11
γ + Fe3C
γ + L
1148
4.30 6.69
L + Fe3C
1495
1538
L
(austenite)
γ
1394
727
1227 C
FIGURE 5-26
Figure 24: The Fe−Fe3C phase diagram. Note that the composition axis is given in wheight
percent carbon even though Fe3C, and not carbon is a component.
Figure 24 is one of the most important phase diagrams. The phases are:
Ferrite α (b.c.c.) iron with up to 0.035 wt% C dissolved in solid solution.
Austenite γ (f.c.c.) iron with up to 1.7 wt% C dissolved in solid solution.
δ-iron δ (b.c.c.) with up to 0.08 wt% C dissolved in solid solution.
Cementite Fe3C, a compound, at the right of the diagram.
The boundary between “irons” and “steels” is approximately at carbon content of 2.0wt%
(the carbon solubility limit of austenite). Ferrite (or α) is the low-temperature form of iron.
22
On heating, it changes to austenite (or γ) at 914◦
C when it is pure, and this form remains
stable until it reaches 1391◦
C when it changes to δ-iron (see Fig. 4).
Note that in Fig. 24 carbon (and not Fe3C) is given as the composition axis.
At the eutectic point the phase reaction, on cooling, is
Liquid
cooling
−→ austenite + cementite (13)
At the V at the bottom of the austenite field (eutectoid point), austenite, transforms on
Figure 25: The general pearlite reaction γ − Fe → α − Fe + Fe3C.
cooling to two other solids. Recall that a eutectoid reaction is a three-phase reaction by which,
on cooling, a solid transforms into two other solid phases at the same time. The compositions
of the two new phases are given by the ends of the tie line through the eutectoid point.
Eutectoid structures are like eutectic structures, but much finer in scale. The original solid
decomposes into two others, both with compositions which differ from the original, and in
the form (usually) of fine, parallel plates. In the eutectoid decomposition of iron, carbon
diffuses to the carbon-rich Fe3C plates, and away from the (carbon-poor) α-plates, just
ahead of the interface. The colony of plates then grows to the right, consuming the austenite
(γ) (see Fig. 25). The eutectoid structure in iron is called pearlite (because it has a pearly
look). The micrograph (Figure 2) shows pearlite.
Figure 26 presents the development of microstructures for a 3.0 wt % C (the so called white
cast iron). The production of pearlite through the eutectoid reaction is shown in Fig. 27 for
0.77 wt % C carbon steel.
23
Weight percentage carbon
0
Temperature
100% liquid
(3% C)
γ2 in matrix of
eutectic
microstructure
(γ + Fe3C
“islands”)
γ1 in matrix
of L1
L1
γ1
γ2
3.0 6.7
Fe3C islands
(from eutectic)
+ pearlite (α +
Fe3C, from
eutectoid)
FIGURE 5-27
Figure 26: Microstructural development for white cast iron shown with the aid of the Fe −
Fe3C phase diagram (From J. Shackelford, Materials Science for Engineers).
24
Weight percentage carbon
0 0.77 6.7
Temperature
Eutectoid microstructure—
fine, alternating layers of
α and Fe3C
100% γ
(0.77% C)
FIGURE 5-28
Figure 27: Microstructural development of eutectoid steel (of composition 0.77 wt % C)
(From J. Shackelford, Materials Science for Engineers).
25
Weight percentage carbon
0 1.13 6.7
Temperature
100% γ
(1.13% C)
Proeutectoid cementite
at γ grain boundaries
Proeutectoid cementite
+ pearlite
FIGURE 5-29
Figure 28: Microstructural development of hypereutectoid steel (of composition 1.13 wt %
C) (From J. Shackelford, Materials Science for Engineers).
26
The microstructure development for a hypereutectoid (composition higher than 0.77 wt % C)
steel can be found in Fig. 28. Note that the proeutectic Fe3C is the matrix in the final
microstructure ( compare with the proeutectic phase in Fig. 21 which was the isolated
phase).
Weight percentage carbon
0 0.50 6.7
Temperature
100% γ
(0.50% C)
Proeutectoid ferrite at
γ grain boundaries
Proeutectoid ferrite
+ pearlite
FIGURE 5-30
Figure 29: Microstructural development of hypoeutectoid steel (of composition 0.5 wt % C)
(From J. Shackelford, Materials Science for Engineers).
Finally, the microstrutructure development for a hypoeutectoid (composition less than 0.77 wt % C)
steel is shown in Fig. 29.
27
The Fe-C system
Atomic percentage carbon
C
Weight percentage carbon
Fe 1 2 3 4 5 6 99 100
1700
1800
1900
2000
2100
2200
2 5 10 15 20 25
1600
1500
1400
1300
1200
1100
1000
900
800
700
600
500
400
300
200
100
0
L + C
α
(ferrite)
γ
(austenite)
α + C
C
(graphite)
0.02
0.68
γ + L
γ + C912
1394
1154
738
1538
1495
2.08 4.26
FIGURE 5-31
Figure 30: Very slow cooling can produce the Fe − C phase diagram. The left side of this
diagram is nearly identical to that for the Fe − Fe3C diagram (Fig. 24). In this case,
however, the intermediate compound Fe3C does not exist. The precipitation of graphite can
be promoted by addition of small amount of silicon (not shown here).
The Fe − Fe3C phase diagram presented earlier is not truly an equilibrium diagrams
(graphite C is more stable than Fe3C). The precipitation of graphite is enormously slow
and as such the Fe-C phase diagram is not very common (see Fig. 30). This precipitation
can be promoted by adding a small amount of silicon.
28
Weight percentage carbon
0 1003
Temperature
γ1
γ2
γ1 in matrix
of L1
γ2 in matrix of
eutectic microstructure
(γ + C flakes)
C flakes (from eutectic
and eutectoid reactions)
in matrix of ferrite
L1
100% liquid
(3% C)
FIGURE 5-32
Figure 31: Microstructural development for gray cast iron (of composition 3.0 wt % C) shown
in the Fe-C phase diagram. In the actual microstructure, a substantial amount of metastable
pearlite was formed at the eutectoid temperature. It is also interesting to compare this sketch
with that for white cast iron in Fig. 26. The small amount of silicon added to promote
graphite precipitation is not shown in this two-component diagram (From J. Shackelford,
Materials Science for Engineers).
The structure development for gray cast iron (composition in wt 3%) is shown in Fig. 31 on
the Fe-C system. As before, silicon was added to promote graphite precipitation.
29