The document discusses phase diagrams and their classification. It defines a phase diagram as a graph used to show equilibrium conditions between thermodynamically distinct phases. It classifies phase diagrams as unary, binary, ternary and quaternary depending on the number of components involved. Binary phase diagrams are described in more detail, including examples of eutectic, eutectoid, peritectic and peritectoid diagrams. Gibbs' phase rule and its application to phase diagrams is also covered. Homework questions on interpreting phase diagrams and performing equilibrium calculations are provided.

1. Second Chapter
PHASE DIAGRAM

2. Phase diagram
• a phase diagram is a type of graph used to show the
equilibrium conditions between the thermodynamically-
distinct phases.
• Phase Diagrams, which indicate the phases present at
a given temperature and composition, have often proved
a difficult concept to understand.
• These are known as equilibrium diagrams. Temperature
is plotted on or ordinate (y-axis) and composition (in
binary phase diagram or pressure (unitary phase
diagram) on abscissa (x-axis) in the phase diagram.
• The compositions is expressed in % weight. Phase
diagram are always drawn equilibrium state because the
system always tries to be stable.

3. Classification of phase diagrams
• Unary phase diagram (single components
system).
• Binary phase diagram (two components
system).
• Tertiary phase diagram (three components
System).
• Quarter phase diagrams (four components
systems).

4. Unary phase diagram (single components system).
The diagram indicated
different phases as a
function of temperature and
pressures. Crystal form of
iron such as BCC
(alpha,α), FCC (Gamma, γ)
and HCC (Delta, δ) are
obtain as increasing the
temperatures. The BCC
form converted to HCP
form near a pressure of
about 125 atm. Above the
eutectic point temperature,
i.e., 9100C BCC converted
to FCC. at a peritectic point
temperature, i.e., 14950C
liquid + HCP converted to Fig T-P phase diagram for iron. I am not sure that I
FCP. believe that there is a critical point for liquid and γ-
Temp range for Fe.
BCC = upto 9100C.
FCC = 920-14100C
0

5. Binary phase diagram (two components system).
Such diagram of results of two components
systems. In addition pressure and
temperature, a third variable, composition is
also involved now. It therefore three
dimensional diagram to depict phases.
However for the simplicity of plotting phase
diagrams on paper; the temperature is
always taken on ordinate and composition
on abscissa for a specified pressure.
The binary diagram of two components are
A and B. Percentage weight components.
Percentage weight composions of A raies
from 0 to 100 from left to right while that of B
varies from between 0 to 100 from right to A phase diagram for a binary
left on horizental axis named as composition system displaying a eutectic
or C axis. There are two phase regions, viz point. The eutectic point is the
the solid and liquid. The solid phase region point at which the liquid phase
lies middle of the straight line called as tie- L borders directly on the solid
line. The liquid phase region lies above the phase α + β.
solid phase lines.

6. Classification of binary phase
diagram
• Eutectic Phase diagram
• Eutectoid phase diagram
• Paritactic phase diagram
• Peritectoid phase diagram

7. Eutectic Phase diagram
• An eutectic phase
diagram is obtained when
the melting point of the
two components of the
phase diagram are
neither very close nor
much different .
• The eutectic system
involves the
transformation of a liquid
phase into two other solid
phases on cooling and
vice versa, and
expressed as
• L (liquid phase) →
α+β (solid Phase)

8. Some uses of Eutectic phase diagram
• Some uses include:
• eutectic alloys for soldering, composed of tin (Sn), lead (Pb) and sometimes
silver (Ag) or gold (Au).
• casting alloys, such as aluminum-silicon and cast iron (at the composition
for an austenite-cementite eutectic in the iron-carbon system).
• brazing, where diffusion can remove alloying elements from the joint, so that
eutectic melting is only possible early in the brazing process.
• temperature response, i.e. Wood's metal and Field's metal for fire sprinklers.
• non-toxic mercury replacements, such as galinstan.
• experimental metallic glasses, with extremely high strength and corrosion
resistance.
• eutectic alloys of sodium and potassium (NaK) that are liquid at room
temperature and used as coolant in experimental
fast neutron nuclear reactors.

9. Eutectoid Phase diagram
• In eutectoid system, a
solid phase replaces the
liquid phase of eutectic
system.
• The eutectoid system
involves the
transformation of a solid
phase into two other solid
phases on cooling and
vice versa, and
expressed as
• γ (solid phase) →
α+β (solid Phase).
• In the Fe-C system, there
is a eutectoid point at
approximately 0.8wt% C,
723°C.

10. The compositions of the
two new phases are given
by the ends of the tie-line
through the eutectoid
point. The general
eutectoid reaction is
therefore:
Solid γ –> solid α + solid β
or using the names given
to these phases:
Austenite –> ferrite +
cementite (Fe3C)

11. Eutectoid
When the solution above the
transformation point is solid, rather than
liquid, an analogous eutectoid
transformation can occur.
For instance, in the iron-carbon system,
the austenite phase can undergo a
eutectoid transformation to produce
ferrite and cementite (iron carbide),
often in lamellar structures such as
pearlite and bainite.
This eutectoid point occurs at 727°C
(1340.6 ºF) and about 0.83% carbon[5];
alloys of nearly this composition are
called high-carbon steel, while those Iron-carbon phase diagram, showing
which have less carbon are termed the euctectoid transformation
mild steel. The process analogous to between austenite (γ) and pearlite.
glass formation in this system is the
martensitic transformation.

12. Paritactic phase diagram
• Peritectic transformations are also
similar to eutectic reactions. Here, a
liquid and solid phase of fixed
proportions react at a fixed
temperature to yield a single solid
phase.
• L + β phase → α Phase
• Since the solid product forms at the
interface between the two reactants, it
can form a diffusion barrier and
generally causes such reactions to
proceed much more slowly than
eutectic or eutectoid transformations.
Because of this, when a peritectic
composition solidifies it does not show
the lamellar structure that you find with
eutectic freezing.
• Such a transformation exists in the iron
-carbon system, as seen near the
upper-left corner of the figure. It
resembles an inverted eutectic, with
the δ phase combining with the liquid
to produce pure austenite at 1495 °C
and 0.17 mass percent carbon

13. • Peritectic
• Peritectic transformations are also similar to eutectic
reactions.
• Here, a liquid and solid phase of fixed proportions react
at a fixed temperature to yield a single solid phase.
Since the solid product forms at the interface between
the two reactants, it can form a diffusion barrier and
generally causes such reactions to proceed much more
slowly than eutectic or eutectoid transformations.
Because of this, when a peritectic composition solidifies
it does not show the lamellar structure that you find with
eutectic freezing.
• Such a transformation exists in the iron-carbon system,
as seen near the upper-left corner of the figure. It
resembles an inverted eutectic, with the δ phase
combining with the liquid to produce pure austenite at
1495 °C and 0.17 mass percent carbon.

14. Peritectoid phase diagram
• Peritectoid phase diagrams involve
transformation of two solid phases into a
different solid phase on cooling and vise
versa. Contrary peritectic reaction where
sodid liquid phase L + β changed to another
solid phase α; here solid phase changed to
another solid phase. It is given by
• γ + β phase → α solid Phase

15. Gibbs' phase rule
• Gibbs' phase rule, stated by
Josiah Willard Gibbs in the 1870s, is the
fundamental rule on which phase diagrams are
based.
F=2−π+C
• where π is the number of phases present in
equilibrium (Types of solid, liquid, gas phases
etc). F is the number of degrees of freedom or
independent variables taken from temperature,
pressure and composition of the phases
present. C is the number of chemical
components required to describe the system

16. • Condensed phase rule
• In many solids with high melting
temperature; the vapour pressure of the
solids and even that of the liquid is
negligible in comparison with
atmospheric pressure.
F=1−π+N

17. Figure 1 shows the
equilibrium diagram for
combinations of carbon in a
solid solution of iron. The
diagram shows iron and
carbons combined to form
Fe-Fe3C at the 6.67%C end
of the diagram. The left side
of the diagram is pure iron
combined with carbon,
resulting in steel alloys.
Three significant regions can
be made relative to the steel
portion of the diagram. They
are the eutectoid E, the
hypoeutectoid A, and the
hypereutectoid B. The right
side of the pure iron line is
carbon in combination with
various forms of iron
called alpha iron (ferrite),
gamma iron (austenite),
and delta iron. The black
dots mark clickable
sections of the diagram. Fig 1: Fe-Fe3C Phase Diagram
Iron-Iron Carbide Phase Diagram

18. Continue...
• Allotropic changes take place when there is a change in crystal
lattice structure. From 2802º-2552ºF the delta iron has a
body-centered cubic lattice structure.
• At 2552ºF, the lattice changes from a body-centered cubic to a
face-centered cubic lattice type.
• At 1400ºF, the curve shows a plateau but this does not signify
an allotropic change. It is called the Curie temperature, where
the metal changes its magnetic properties.
• Two very important phase changes take place at 0.83%C and at
4.3% C. At 0.83%C, the transformation is eutectoid, called
pearlite.
• gamma (austenite) --> alpha + Fe3C (cementite)
• At 4.3% C and 2066ºF, the transformation is eutectic, called
ledeburite.
• L(liquid) --> gamma (austenite) + Fe3C (cementite)

19. Home assignments
• Equilibrium Calculations
1. Given the Fe-Fe3C phase diagram, Fig. 1, calculate the phases present
at the eutectoid composition line at:
a. T = 3000ºF
b. T = 2200ºF
c. T = 1333ºF
d. T = 410ºF
2. Calculate the phases in the cast-iron portion of the diagram at the
eutectic composition of 4.3% C in combination with 95.7% ferrite at:
a. T = 3000ºF
b. T = 1670ºF
c. T = 1333ºF
3. A eutectoid steel (about 0.8%C) is heated to 800ºC (1472ºF) and cooled
slowly through the eutectoid temperature. Calculate the number of
grams of carbide that form per 100g of steel.
4. Determine the amount of pearlite in a 99.5% Fe-0.5%C alloy that is
cooled slowly from 870ºC given a basis of 100g of alloy.

20. Lever Rule
• To determine compositions of
phases and the relative
proportions of phases to each
other in Binary diagrams the
LEVER RULE is used.
• Using the lever rule one can
determine quantitatively the
relative composition of a mixture in
a two-phase region in a
phase diagram. The distances l
from the mixture point along a
horizontal tie line to both phase
boundaries give the composition:
• Nα lα = nβ lβ
• nα represents the amount of
phase α and nβ represents the
amount of phase β.

21. 1. Point "I" lies above the liquidus within the
liquid field.
What is the composition, in terms of the two end
member components, A and B, of the liquid
represented by this point?
To determine the composition of "I" you must
complete the following steps:
1. Draw a line through "I" perpendicular to the
AB join, i.e., the base of the diagram. This line
represents a line of constant composition and is
referred to as an isopleths.
2. The liquid at "I" consists of a mixture of A and
B, the proportions of which can be determined
simply by measuring the length of three lines,
AI', BI' and AB and then ratio these lengths.
%A = I'B/AB *100
%B = I'A/AB *100
This gives us the bulk composition of the liquid
at this point. If the composition point for the
moves then we get a new bulk composition for
that point represented by the new liquid

22. Home Assignment