Week 5

Phase Diagrams
Chapter 10
Callister, 2006

Sibel Uludag-Demirer IE 114 Cankaya University 2
Outline of the Lecture
1) Definitions
2) Equilibrium Phase Diagrams
----Binary Isomorphous Systems
----Binary Eutectic Systems
3) The Iron-Carbon System

Why do we study phase diagrams?
There is a strong correlation between microstructure and mechanical
properties and development of microstructure can be understood from the
phase diagrams. Moreover phase diagrams can be used to obtain
information about melting, casting, crystallization, etc.
Preeutectoid ferrite
Pearlite (dark layer is ferrite,
Light layer is cementite)
SEM micrograph of plain C steel
with 0.44 wt% C (3000X).

Major terms used in this lecture:
Component: pure metals or elements in the composition of an alloy.
Solute and solvent (Week 4)
System: specific body of material or series of alloys consisting the same
components ( iron-carbon system)
Solubility Limit: The maximum amount of solute that may dissolve in
solvent to form a solid solution. Addition of solute beyond the solubility
limit causes the formation of another phase.
Phase: is a homogeneous portion of a system that has uniform physical
and chemical characteristics. Gas, liquid and solid phase.

Sugar and Water
65%
(a single phase)
(two-phase system)
how many phases are there?

For example if a substance can exist in two or more polymorphic forms
(BBC and FCC) each of these structures is a separate phase because their
physical properties are different.
A single phase system is called homogeneous system.
System of two or more phases is called a mixture or heterogeneous
system. Therefore most of the metallic alloys,ceramics, polymeric and
composite systems are heterogeneous.
Microstructure: is subject to direct microscopic observation using
microscopic techniques. The number of phases, their proportions, and the
way they are distributed or arranged can be characterized by the same
techniques.
Phase Equilibria: A system is said to be at equilibrium when the free
energy, which is the internal energy and randomness of the atoms, is at
minimum under some specified combination of temperature, pressure
and composition.
In other words, at equilibrium the characteristics of the system do not
change with time but persist indefinetely. This system is also called
stable.

The diagrams showing the solubility (solubility charts) do not give
information about the time necessary to achieve the equilibrium. It is
often the case that a state of equilibrium is never completely achieved
because the rate of approach to equilibrium is slow. Such a system is
said to be nonequilibrium or metastable state.
Therefore not only the understanding of equilibrium states are important
but also the rate at which they are established, and the factors affecting
this rate.
Equilibrium Phase Diagrams
Phase diagram is also called equilibrium or constitutional diagram.
These diagrams defines the relationship between the temperature and
compositions or quantities of phases at EQM. External pressure could
also be another parameter affecting the phase distribution but it remains
constant at 1 atm in most of the applications.

Isomorphous Binary Systems:
Binary systems are composed of two components and they are isomorphous since
there is a complete solubility of liquids and solids.
Example: Cu-Ni
Liquid forms of Cu and Ni (L)
Substitutional
Solid solution of
Cu and Ni (α)
Structure is FCC.
Mixture of solid and
Liquid phases (α+L)
Below 10850
C, Cu and
Ni are soluble in each other
at all compositions.
m.p. of Ni
m.p. of Cu

The lower case Greek letters (α, β, γ, etc.) indicate solid solutions.
The line separating L and α+L phases is liquidus line.
The line separating α and α+L phases is called solidus line.
Take 50 wt% Ni and 50 wt% Cu alloy: melting begins around 12800
C and
the amount of liquid increases with temperature until about 13200
C
and above this temperature the alloy is completely liquid.
From the phase diagrams we can learn the followings:
1) Phases that are present
2) Composition of the phases
3) Fractions of the phases
Example: 60 wt % Ni-40 wt % Cu alloy at 11000
C (pt A). There is a single
phase, which solid (α).
Pt B (35 wt % Ni-65 wt% Cu) is the mixture of solid and liquid on the
same plot.

Determination of the composition in a single phase is trivial. But in two
phase, the calculation is as follows:
1) A tie line (horizontal line passing from the temperature) is
constructed.
2) The intersections of tie line and phase boundaries are noted.
3) Each respective composition is read from the composition axis.
For example point B in Figure 10.2a:
35 wt% Ni-65 wt% Cu at 12500
C : α+L
CL (Composition of the liquid phase)
Cα (Composition of the solid phase)

Phase Amounts: For a single phase it is 100 % of solid or liquid.
For two phase systems: Lever rule
1) Draw the tie line
2) Locate the overall composition of the alloy on the line
3) The fraction of one phase is computed by taking the length of the line
from the overall composition to the phase boundary of the other phase.
4) Do the same thing for the other phase.
5) Multiply each fraction by 100.

Similary for solid phase:
For multiphase alloys relative phase amounts can be reported in volume fraction
rather than mass fraction. For an alloy with α and β phases, the volume fraction of
the α phase, Vα
volume of α
volume of β
Conversion from mass fraction to volume fraction can be accomplished using the
equations:

Mechanical properties of solid isomorphous alloys can be improved by solid
solution strengthening or by the addition of other components.
Tensile strength and elongation are two opposite mechanical properties of the material
This is why one has the maximum value while the other has the minimum.

Binary Eutectic Systems: Cu and Ag system
Three single phase
α = FCC structure
β = FCC structure
Max.
Solubility
of Ag in Cu
8 wt% Ag at
7790
C
max. solubility of Cu
in Ag (8.8 wt%)
maximum solubility line,
which is also solidus. This
line shows the minimum
temperature for the liquid
phase existence.

Three two phase regions.
Composition and the fraction of the phases can be determined by lever rule.

As Ag is added to Cu, the melting point of alloy decreases along the
liquidus line, which is the same for Ag. The minimum melting point is
at point E (invariant point), which is defined CE (71.9 wt% Ag) and TE
(7790
C).
There is an imp. Rxn (eutectic reaction) for the alloy with a composition of
CE as the temperature decreases:
Eutectic=easily melted
Eutectic isotherm

Notice that in the eutectic phase diagram α and β phases exist over the
composition ranges near the concentration extremities, this is why they
are also called terminal solid solutions. For other alloy systems, there
may be intermediate solid solutions, such as Cu-Zn (brass) system.

For some alloy systems, discrete intermediate compounds rather than solid
solutions may be observed in phase diagrams. For example; Mg-Pb
system. These are called intermetallic compounds. The compound Mg2Pb
is shown as a vertical line on the diagram rather than a phase region
since it exists precisely at the composition defined.
This diagram can be
thought as two eutectic
phase diagrams of
Mg-Mg2Pb and Mg2Pb-Pb
systems.

Eutectoid and Peritectic Reactions:
Consider Cu-Zn system.
Eutectoid reaction: 5600
C and 74 wt% Zn
-26 wt% Cu
Notice that one solid phase forms two other
solid phases upon cooling.
This is also seen in Fe-C systems.
Peritectic reaction: 5980
C and 78.6 wt% Zn-
21.4 wt% Cu
Notice that a solid transforms into another
solid and a liquid.

Phase transformations can be classified according to whether or not there is
any change in composition. Those which have no changes in
composition are called as congruent transformations. The opposite is
incongruent transformation. Allotropic transformations are congruent
as well as melting pure metals. Eutectic, eutectoid or melting alloy
systems are incongruent transformations.
Phase diagrams of the metallic systems composed of more than two metal
(or component) are very complex. There is a need for 3-D diagram to
analyze such systems.

Iron-Carbon System
This is the most important system in manufacturing since primary
structural materials are essentially Fe-C alloys, such as, steel and
cast iron.
The Iron-Iron Carbide System -Phase Diagram:
Pure Fe at room T is stable and
it has a BCC structure. This
form of the Fe is called
ferrite or α Fe.
As T increases, ferrite experiences
a polymorphic transformation
to FCC austenite (γ-Fe) at 9120
C.
At 15380
C FCC austenite
transforms back to BCC δ ferrite.
This system is Fe rich
graphite

At 6.70 wt% C composition, an intermediate compound, iron carbide (Fe3C)
or cementite is formed. In practice all steels and cast irons have C
content less than 6.70 wt%C, which corresponds to 100% Fe3C.
C is an interstitial impurity and can form solid solutions with each of the iron (ferrite,
austenite, and δ ferrite.
relatively soft, can be made
magnetic at 7680
C and
has a density of 7.88 g/cm3
.
max. solubility of C is 0.022
wt% at 7270
C.
max. solubility of C is
2.14 wt% at 11470
C. This
is nonmagnetic.

δ-ferrite and α-ferrite are virtually the same except the temperatures over
which they exist.
Cementite forms when the solubilty limit of C is exceeded in α-ferrite below
7270
C. Cementite is hard and brittle, which enhances the strength of the
steel. Cementite is a metastable at RT. When it is heated to 650-7000
C for
several years, then it will transform in to α iron and carbon. Therefore
cementite in the phase diagram is not compound at equilibrium, but since
the rate of its transformation is very slow we can assume the compound to
be stable in steel for instance.
Eutectic reaction at 4.30 wt% Cand 11470
C
Eutectoid reaction 7270
C
These equations are extremely important in the heat treatment of steels.

Ferrous Alloys
(Iron is the primary component)
based on C content of the alloy
Iron
<0.008 wt% C
ferrite
Steel
0.008-2.14 wt% C
α and Fe3C
Cast Iron
2.14-6.70 wt%C
Development of Microstructure in
Iron-Carbon alloys:
Microstructures of Fe-C alloys
depend on C content and heat
treatment.
Assume here that cooling is very
slow and equilibrium is maintained
continuously.
For a phase of a eutectic alloy cooling
from the temperature range of
austenite:
Pearlite
properties b/w
soft, ductile ferrite
and hard brittle
cement.

The alternating α and Fe3C
layers in pearlite causes
the redistribution of C by
diffusion as shown
during phase
transformation:
Hypoeutectoid
alloys: Alloys with
C content between
0.022 and 0.76 wt%
are
hypoeutectoid alloys.

proeutectoid
ferrite
pearlite
some pearlite grains
look darker because
of the magnification
used.

The fractions of the phases can be calculated using lever rule.
Fraction of pearlite:
Fraction of proeutectoid ferrite:
Fraction of total α and
cementite is determined
by using tie line extending
from 0.022 to 6.70 wt% C

Hypereutectoid Alloys: alloys with C content of b/w 0.76 - 2.14 wt% cooled
from austenite T range.
proeutectoid
cementite
pearlite

Things learned
What is a phase diagram?
Interpretation of the phase diagrams.
Types of the phase diagrams.
Phase diagram of Fe-C alloy system.
Changes in the microstructure of Fe-C alloys during slow cooling.

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