palanivendhan palani vendan pHASE DIAGRAMS SRM UNIVERSITY MATERIALS TECHNOLOGY

2. Introduction
 Phase diagrams , are also known by the names equilibrium/constitutional
diagrams , are a very important tool used in the study of alloys.
 A phase diagram consists of two parameters – temperature , taken on the
ordinate and the alloy composition taken on the abscissa.
 Role of the phase diagram :-
 Shows the phases in equilibrium for a given allow composition, at a glance.
 Shows the relationship between the composition , temperature, and alloy
structure in series.
 Permits to study and control processes such as Phase separation ,Solidification of
metals and alloys , Purification of materials ,The growth and doping single crystals,
and the structural changes produced by heat treatment ,casting ,etc. .

3. Solid Solutions
• A solid solution is defined as a solid
mixture containing a minor
component uniformly distributed
within the crystal lattice of the
major component. ( as shown in
the two possible cases )
• The key feature of a solid solution is
that the metals retain their
homogeneity and hence their
solubility after their transformation
to a solid crystalline state.
• An example of a solid solution
would be Copper 64% and Zinc 36%
• The solid solutions comprise of
atoms of almost the same atomic
radius , and they tend to form a
single phase and the elements are
soluble in both their solid and liquid
states .

4. Classification of Solid solutions :
Substitutional Interstitial
Disordered Ordered
• Substitutional Solid Solutions have a direct substitution of one type of atom for another
so that solute atoms (Cu) enter the crystal to take positions normally occupied by solvent
atoms (eg . Ni atoms).
• Disordered Substitutional Solid Solutions are those type of solid solutions in which the
solute atoms are randomly distributed in the solvent lattice structure , hence disordered.
• Ordered Substitutional Solid Solutions are those in the disordered solution is cooled
slowly , causing atomic re-arrangement because of the diffusion due to cooling causing
uniform distribution of solute and solvent atoms.
• Interstitial Solid Solutions are those in which the solute atoms occupy the interstitial
positions in the solvent crystal lattice , without any replacement of solvent atoms , on
account of a very small solute atomic size relative to that of the solvent. (around a factor
of 70 )

6. Intermediate phases
• In many binary alloy systems, when the chemical affinity of metals is great, their
mutual solubility becomes limited or reduced and a so called “intermediate
phase” is formed.
• The intermediate phase may have either narrow or wide ranges of homogeneity
and may or may not include a composition having a simple chemical formula.
• For example the phase CuAl exists in a homogeneity ,that does not include the
composition CuAl.
• Intermediate phases may range between ideal solid solutions and the ideal
chemical compound.
• The intermediate phases are the phases that form in the intermediate regions of
the equilibrium diagram.
• They are usually classified into two types : Intermetallic compounds of
• a)fixed composition or b)variable composition.

7. Comparison between the types
Intermetallic compounds of
fixed composition
• They obey the usual valency
laws ,like ordinary chemical
compounds. Eg. NaCl.
• An example could be Mg2Sn
has 29.08% of Mn.
Intermetallic compounds of
variable composition
• They do not obey the
valence laws and are also
known as electron
compounds.
• Examples could be Ratio 3/2
–beta , like Cu3Al,Ratio
21/13-gamma like Cu9Al4 or
ratio 7/4-Epsilon like Cu3Al

8. Phase rules
• The following are the rules which are to be
followed while interpreting the phase diagrams :
• Prediction of Phases
• From a phase diagram , specific information can
be obtained only if a temperature and a
composition is specified.
• This can be done by using both temperature and
composition parameters to identify the point on
the phase diagram.
• Once done , depending on its location ,identify
the phase present at that particular point .
• Phase composition
• To find the phase composition at a particular
temperature like 500 degrees Celsius , draw a
horizontal line OP , that hits the liquidus and a
vertical line that hits the solidus curve from P .
This would automatically indicate the phase
composition for the required temperature.

9. Lever arm Principle
• Besides indicating the number of phases and phase composition , the phase
diagram also tells the proportion of co-existing phases at a given temperature.
• To determine the relative amount of the two phases , erect an ordinate at a point
say (85% Sb) on the scale which gives the total composition of the alloy.
• The intersection of this vertical blue line and a given isothermal line OP (at a given
temperature) is the fulcrum of the simple lever system and OM and MP are the two
lever arms as shown in the previous figure.
• This is commonly referred to as the lever rule because the amount of a given phase
multiplied by its lever arm is equal to the amount of the other phase multiplied by
its (or the other) lever arm.
• The isothermal line is also referred to as the Tie line since it joins the composition
of the two phases in equilibrium at a specific temperature.
• When expressed mathematically it gives us the foll :
• 1.The amount of solid phase
• i.e. (MP/OP)*100
• 2.The amount of liquid phase
• i.e. (OM/OP)*100

10. • The phase rule, also known as the Gibbs Phase Rule, establishes the relationship
between the number of degrees of freedom (F),the number of components(C) and
the number of phases(P).
• It is mathematically expressed as follows :
P+F=C+2
• P->Number of phases (Solid or liquid and so on) ;
• F->Number of degrees of freedom (pressure ,temperature ,concentration and so
on) without altering the equilibrium
• C->Number of Components n the system (For example Pb-Sn)
• In metallurgical systems the pressure is regarded as remaining fixed at one atm
and hence the pressure variation is neglected.
• Phase rule applies to dynamic and reversible processes, where a system is in
heterogeneous equilibrium and where the external variable are only temperature ,
pressure and concentration.
• It is used while dealing with multicomponent systems to determine whether the
microstructures are in equilibrium or not.
Gibbs Phase rule

11. Energy in the intermediate phase
• The formation of a new intermediate phase in
a system is associated to the change in free
energy of the system.
• The free energy has two components :-
1)Chemical energy 2)Non chemical free
energies.
• Let us assume that “x” be the width of the
new intermediate phase formed in the
system.
• If “G” is the amount of decrease in free
energy/unit volume , then the total free
energy decrease would be G*x , considering
unit cross sectional area of the couple.
• Non chemical free energy is brought into play
for the creation of the new intermediate
phase , and a mechanical work is done while
doing so due to volume change.
• Hence the total free energy change is the sum
of the interfacial energies and the mechanical
work done .

12. Phase diagram
• A great deal of information concerning to phase
changes in many alloy systems has been
accumulated and the best method of recording
the data is in the form of phase diagram.
• A phase diagram shows the limits of
composition and temperature within which
the various constituents or phases of the
alloys are stable.
• The structural changes and compositional
changes of the constituents in equilibrium at a
fixed temperature can be ascertained using the
phase diagrams.
• If two metals of a binary solution ( such as Cu-
Ni) are mixed in different proportions, melted
and cooled , and a cooling curve is constructed
for each composition,.
• When the temperatures at which solidification
starts and completes for various compositions
with respect to time would lead to the phase
diagram.

13. Classification of Phase diagram
• The classification is as follows :-
• Unary (or one component) phase diagram which is plotted as pressure on the
vertical axis and temperature on the horizontal axis .
• Binary (or two components) phase diagram which is plotted with temperature
taken on the vertical axis and the various concentrations taken on the horizontal
axis commonly.
• Ternary (or three components) phase diagram which is plotted three
dimensionally between three components and the equilibrium associated with
each other and the vertical axis usually taken comprises of the temperature as the
common parameter (discussed more in the successive slides).

14. Phase changes in alloys
• Phase changes can be analyzed for the alloys in two ways :-
• 1)For two metals completely soluble in liquid state and insoluble in the solid state
• 2) For two metals completely soluble in liquid state and partially soluble in the
solid state
For two metals completely soluble in liquid state and insoluble in the solid state
Consider the Bismuth Cadmium system as shown :

15. Four phase fields are seen on Fig. 5 above:
• a fully molten region,
• two regions in which liquid and solid coexist,
• a completely solid region.
• The two liquidus lines slope downwards from the
melting points of the pure materials to meet at a
point known as the eutectic point (E).
• Material of the eutectic composition will undergo
the transformation liquid -> solid (Bi+Cd) at the
temperature 144 degrees Celsius.
• Since the formation of the two solids occurs
simultaneously, this will be also reflected in the
microstructure.
• The two solids are strongly mixed in this eutectic
structure, sometimes as particles or ”stars” of one
solid surrounded by the other, or maybe as
laminations as shown in the drawing.
• Note that unlike all other alloys, eutectic
compositions have no extended freezing range but
they freeze at a definite temperature similarly to
pure metals.

16. • For two metals completely soluble in liquid state and partially soluble in the solid
state

17. • A eutectic system can occur when terminal solid solutions exist on both ends of the
binary equilibrium phase diagram. An example of a binary eutectic system is lead (Pb) -
tin (Sn).
• Although the atomic size difference is less than 10%, Pb has an FCC crystal
structure while Sn is an unusual metal with a non-cubic tetragonal structure. This results
in limited solid state solubility with the maximum solubility of Sn in the FCC Pb equal to
19.2 wt%Sn while only 2.5wt% of Pb is soluble in the tetragonal Sn structure.
• At compositions and temperatures, which exceed these solubility limits, two solid
phases
will exist in equilibrium. The phase is the FCC Pb with some substitutional Sn atoms
and the phase is tetragonal Sn with only a few substitutional Pb atoms.
• These maximum solid-state solubility both occur at 183 deg. Cel. which is referred to
as the eutectic temperature.
• At this temperature, there exists a point on the phase diagram
(a single combination of composition and temperature) where three phases (the two
solids and a liquid) can exist simultaneously in equilibrium.

18. Ternary Phase diagrams
• The properties of a pure metal are improved
by the addition of alloy elements.
• Simple binary alloys process certain improved
properties than the pure metals.
• Further improvement in qualities or
properties of a binary alloy is frequently
gained by adding a third element, eg , the
addition of nickel to Steel (Fe-C) improves
toughness and the addition of lead to brass
(Cu-Zn) improves machinability.
• A ternary equilibrium diagram presents a
three component system , that is it deals
with three metals say A,B and C.
• The complete equilibrium is indicated in a
three dimensional figure.
• The temperature is always plotted vertically.
• We have liquidus and solidus planes in a
ternary system unlike the liquidus and solidus
lines in a binary system .

19. Cooling Curves
• A mathematical curve while plotting the temperature as a function of
time as different alloys in the system are very slowly cooled.
• This method is basically used to determine the temperature at which
phase change ( from solid to liquid ) occurs.
• The study is useful in :-
– Studying the changes that occur during solidification of alloys, and
– In determining transformations subsequent to solidification .

20. Cooling curve of pure metal or compound
• The liquid metal initially cools at a rate
called as the cooling rate until we
reach the beginning of the thermal
arrest.
• During thermal arrest the phase
change occurs and the metal liberates
its latent heat of fusion while keeping
the temperature constant to reach to
the end of the thermal arrest.
• This point is referred to as the freezing
point of the metal.
• On further cooling the metal tends to
reach the room temperature.
• The Slopes before and after thermal
arrest ,by value , depend upon the
specific heats of the liquid and solid
metals , respectively.

21. Equilibrium diagrams of Iron and Iron -Carbide diagram
• Iron is molten above 1536 deg.
Celsius. It solidifies in a BCC
Structure (Delta).
• On further cooling at 1400 Celsius
, a phase change occurs and the
atoms rearrange themselves into
the Gamma from which is FCC
and non magnetic.
• On further cooling at 910 Celsius,
another phase change occurs
from FCC non magnetic gamma
iron to BCC non magnetic alpha
iron.
• Finally at 768 Celsius ,the alpha
iron becomes magnetic without a
change in the lattice structure . Cooling curve for Iron

22. Equilibrium diagram for Iron Carbide System

23. • The iron carbon equilibrium diagram indicates the phase changes that occur during heating
and cooling and the nature and amount of the structural components that exist in any
temperature. It also establishes a relation between the microstructure and properties of steel
and cast irons and provides a basis for the understanding of the principles of heat treatment.
• The iron carbon equilibrium has a peritectic point , eutectic and eutectoid point.
• When Delta iron + liquid when cooled below peritectic point causes it to be converted to
Austenite. (Occurs around 2720 Fahrenheit)
• The liquid cools to an eutectic mixture of austenite and cementite at a temperature of 2066
Fahrenheit and the reaction is called as a eutectic reaction.
• Eutectic point is at 4.3% carbon content and the eutectic mixture is not usually seen in the
microstructure, because austenite is not stable at room temperature and must undergo
another reaction during cooling.
• The eutectoid reaction occurs at 1333 Fahrenheit and is represented by a horizontal line with
the eutectic point at 0.83% carbon content .
Features :-
1)When steel of 0.4 % carbon (hypoeutectoid steel) is converted entirely into austenite above
• The upper critical temperature line and whencooled below the line the structure of iron
changes from FCC TO BCC causing ferrite crystals to grow in size at the expense of austenite.
At 1344 Fahrenheit , austenite has 0.83 % (max limit it can hold in solid solution) , the
temperature drops further , and carbon precipitates as cementite at 723 degrees Celsius.

24. • Cementite and still separating Ferrite form alternate layers until all the remaining austenite is
consumed. The lamellae structure contains 0.83% of carbon and is known as pearlite.
• Other transformations are also possible such as eutectoid steel into pearlite as well as
hypereutectoid steel to cementite.
Ledeburite Structure