Phase Diagrams

Abhishek Gupta
Assistant Professor, AKGEC
Ghaziabad
Abhishek Gupta
Phase Diagrams

Abhishek Gupta
 Contents
• Basic Terms
• Introduction - Components – Phase
• Phases – Solution
• Solid solutions
• Intermediate Alloy Phases
• Non-homogenous Phases / Mechanical Mixtures
• Hume Rothery Rule’s for Solid Solution
• Solidification
• Equilibrium Phase Diagram - Unary
• Cooling Curves
• Binary phase diagram
• Lever Arm Principle
• Gibbs’s Phase Rule
• Reactions in binary phase diagrams
 Basic terms
1. System
• Thermodynamically, a system is an isolated body of matter
which is under study.
• A substance or a group of substances so isolated from its
surroundings that it is totally unaffected by the surroundings but
changes in its overall composition, temperature, pressure or total
volume can be allowed as per the desire of the person who
investigates it.
• A system may contain solids, liquids, gases or their combination.
• It may have metals ,non-metals separately or in combined form.

2. Phase
• A phase is a substance or a portion of matter
which is
homogenous, physically distinct and mechanically separable..
• Physically distinct and mechanically separable means that the
phase will have a definite boundary surface.
• Different phases are given different names or symbols
like α (alpha),ß (Beta), γ (Gamma), etc.
 Basic terms

Introduction - Components - Phase

• Components are pure metals and/or compounds of
which an alloy is composed. For example, in a
copper–zinc brass, the components are Cu and Zn.
• It refers to a independent chemical species. The
components of a system may be elements, ions
or compounds.
• A component can exist in many phases.
– Water exists as ice, liquid water, and water vapor.
– Carbon exists as graphite and diamond.
 Basic terms
Components and Phases
• Components:
The elements or compounds that are mixed initially (Al and Cu).
• Phases:
A phase is a homogenous, physically distinct and mechanically
separable portion of the material with a given chemical composition
and structure (a and b).
Aluminum-
Copper
Alloy
3. Equilibrium
Basic terms
:• Equilibrium in a system is the state of minimum free energy under any specified
combination of overall composition, temperature, pressure and overall volume.
• Once equilibrium is achieved, even a minor change in these parameters of
composition, temperature, pressure, volume within the system means an increase in
free energy.
4. Degrees of Freedom:
• It is also known as variance of system.
• It is defined as number of external or internal factors of the system (temperature,
pressure and concentration) that can be independently changed without altering
equilibrium i.e. without causing disappearance of a phase or formation of a new
phase in the system.
5. Structural Constituent
• Phase distribution in a system is not necessarily uniform throughout the structure.
• These phases are associated in different ways to form the structure. This association
of phases in a recognizably distinct fashion is referred to as “structural constituent”
of the alloy.
 Basic terms
6.Single and Multiphase Solids
• A single crystal of a material may consist of one phase only while
polycrystalline material may be single or multi-phase depending upon
the nature of individual crystals or grains present.
• Examples : All pure metals are single phase solids
• Alloys likeIron andSteel, Rocks, ceramics, wood, fibre-glass,
polymers, etc. are examples of multi-phase solids.
•Properties of multi-phase solids is dependent upon…
1.Physical and chemical natures of phases present
2.Amount of each phase (%)
3. Distribution of each phase in relation to other phases
4. Size of domain occupied by each phase
7.
Basic terms
Alloys
• Pure metals because of their poor physical and mechanical properties are seldom
used in engineering applications. Most of useful metallic materials are combinations
of metals which are called alloys.
• An alloy can be defined as a substance possessing metallic properties, having
metallic bond and composed of two or more than two elements out of which atleast
one of them is metal.
• Metal present in larger proportion is called base metal while other metallic or non-
metallic element is known as alloying element.
• Elements may combine in different ways to form alloys.
• These elements of alloys usually show complete solubility in liquid state. However,
on cooling them to solid state, they may form mechanical mixtures or
homogenous phases.
•
Phases - Solution
A solution (liquid or solid) is phase with more than one
component; a mixture is a material with more than one phase.
• Solute (minor component of two in a solution) does not change the
structural pattern of the solvent, and the composition of any
solution can be varied.
• In mixtures, there are different phases, each with its own
atomic arrangement. It is possible to have a mixture of two
different solutions!
• For many alloy systems and at some specific temperature, there is
a maximum concentration of solute atoms that may dissolve in
the solvent to form a solid solution; this is called a solubility
limit. Solid Solution cannot have formula so indicated by Greek
letter. Solid Solution are single phase alloy
• The addition of solute in excess of this solubility limit results in
the formation of another solid solution or compound that has a
distinctly different composition.
 Phases
Homogenous Phases Non-Homogenous Phases or
Heterogeneous Phases or
Mechanical Mixtures

Solid Solutions Intermediate Alloy Phases • Can be any combination i.e.

combination of pure metal and a
2 metals mixed2 me tals mixed solid solution (homogenous
within solubility beyond solubility phase)
limits limi ts • combination of pure metal and
an intermediate alloy phase, etc.

Substitutional Interstitial Intermediate Intermediate

Solid Solid Solid Compounds
Solutions Solutions Solutions

• Chemical Compounds
Substitutional Interstitial • Inter-metallic Compounds
Solid Solid • Interstitial Compounds
Solutions Solutions • Electron Compounds
• Lave’s Phases

Ordered Disordered
Substitutional Substitutional
Solid Solid
Solutions Solutions
 Homogenous phases
• When two elements are completely soluble when coming into solid state
from liquid state and form compounds by chemical reaction, they form
phases known as homogenous phases.
• Each component of such phases loses its own identity, properties and
crystal structure.
1. Solid Solutions
• When two elements completely mix or dissolve in each other in liquid as
well as solid state (during process of solidification), then the resulting
structure or phase is known as a solid solution.
• In a solid solution, there can be more than two components. But in general,
the metal which is in higher proportion is known as base metal or solvent
and the other component (metal or non-metal) is called alloying element
or solute.
• There are two types of Solid Solutions – Substitutional Solid Solution
and Interstitial Solid Solution.
 Solid solutions
• A solid solution is simply a solution in the solid state that
consists of two kinds of atoms combined in one type of space
lattice.
• There is a homogeneous distribution of two or more constituents
in the solid state.
• A solid solution is the result of, metals dissolving in each
other’s crystal lattice.

Solid Solution

Substitutional Solid Solution Interstitial Solid Solution

Ordered

Disordered
 Solid solutions

Disordered Substitutional Solid Solution

Substitutional Solid Solution

Ordered Substitutional Solid Solution

Interstitial Solid Solution

 Hume Rothery Rule’s for Solid
• Solution
Hume Rothery’s rules govern the formation of substitutional solid
solution and aid in the proper selection of such alloying elements :

1. Crystal Structure Factor

2. Relative Size Factor
3. Chemical Affinity Factor
4. Relative Valance Factor

1. Crystal Structure Factor of two metals

(elements) should be same.
 2. Relative Size Factor
• Atomic diameter shall be fairly similar, since atoms differing
directly greatly in size cannot be accommodated readily in the
same structure (as a substitutional solid solution).

• When the term size factor is employed and extensive solid

solubility is encountered only when the two different atoms
differ size by less than 15%,called a favorable size factor.

• If the relative size factor is between 8%-15%, the alloy system

usually shows a minimum and If this factor is greater than
15% substitutional solid solution formation is very limited.
 3. Chemical affinity Factor
• The greater the chemical affinity of two metals, the more
restricted their solubility is their solid solubility.

• When their chemical affinity of two metals is great, two

metals tend to form an intermediate phase rather than a
solid solution.
• Generally, the farther apart the elements are in the
periodic table the greater the chemical affinity.
• If the elements have similar electronegativity, they will
make a solid solution. If the elements have similar
electronegativity, they will make a solid solution.
• Electronegativity & electron affinity of both materilas
should be comparable.
 4. Relative valence Factor
• Consider a two atoms, one with large valance
electrons and the other with small number of
valance electron.

• It has been found that high valance can dissolve

only a small amount of a lower valance metal ,
while the lower valance metal may have good
solubility for higher valance metal.
• Valency of both the material should be same
Solidification …
 Phase Diagram
• Phase Diagram are important and essential tools to
understand compositional concentrations of two or
more elements.
• It is a plot of all temperature composition space
showing the stability of various phases. In other words
what will be the melting point of alloy that can be
understood from the phase diagram
• C+2=F+P
• C=1 (Unary Phase Diagram)
• C=2 (Binary Phase Diagram)
 Equilibrium Phase Diagram
• A diagram that depicts existence of different phases of
a system under equilibrium is termed as phase
diagram.
• It is actually a collection of solubility limit curves. It is
also known as equilibrium or constitutional diagram.
• Equilibrium phase diagrams represent there relationships
between temperature, compositions and the quantities of
phases at equilibrium.
• These diagrams do not indicate the dynamics when one
phase transforms into another.
 Equilibrium Phase Diagram
• Important information, useful in materials development and
selection, obtainable from a phase diagram.
• It shows phases present at different compositions and
temperatures under slow cooling (equilibrium) conditions.
• It indicates equilibrium solid solubility of one element /
compound in another.
• It suggests temperature at which an alloy starts to solidify
and the range of solidification.
• It signals the temperature at which different phases start to
melt.
• Amount of each phase in a two-phase mixture can be
 Unary phase diagram
• If a system consists of just one component(e.g.:water),
equilibrium of phases exists depicted by unary phase diagram.
The component may exist in different forms, thus variables here
are–temperature and pressure.
Cooling Curves
Cooling Curves
Cooling Curves
Cooling Curves
 Binary phase diagram
If a system consist soft components, equilibrium of phases exist is
depicted by binary phase diagram. Pressure is constant, thus in
dependently variable parameters are– temperature and
composition.
Two component
systems are classified
based on extent of
mutual solid solubility
• completely soluble in
both liquid and solid
phases (isomorphous
system)
• completely soluble in
liquid phase where as
solubility is limited in
Binary phase diagram
 Lever Arm
• Proportion ofPrinciple
co-existing phase at any given temperature.

• Determine the relative

amount of two phases, erect
an ordinate at a point
(30%Bi) on the composition
scale which gives the total
or overall composition of
the alloy.
 Lever Arm
Principle
• The intersection of this composition vertical (AL) and a given isothermal
line OP (i.e., point M is the fulcrum of a simple lever system and OM
and MP are two lever arms.)
• The relative lengths of the
lever arms multiplied by the
amounts of the phase present
must balance.

• This is called 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 (i.e.,other) lever arm.
 Lever Arm
• Principle
It can also be seen that the proportion of solid corresponds to
the length of the segment adjacent to liquidus line, whereas
the fraction of liquid corresponds to the length of segment
adjacent to the solidus line.
• The isotherm (line OMP) can be
considered as a tie line, since it joins
the composition of two phases in
equilibrium at a specific
temperature.
 Gibbs’s Phase
• Rule
The Phase Rule, known as 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
expressed mathematically as follows:
P+F=C+2

– where, P is the number of phases (e.g., solid, liquid etc.)

– F is the number of degrees of freedom or the number of
physical ' variables (pressure, temperature and concentration)
that can be independently changed without altering the
equilibrium, i.e., without causing disappearance of a phase
or the formation of a new phase in the system.
– C is the number of components in the system (for example, Pb
and Sn are the components of Pb-Sn equilibrium diagram.
 Gibbs’s Phase
Rule
• “Provided the equilibrium between any no. of phases is not influenced by
gravity or electrical forces or magnetic forces or surface tension, and
influenced only by the temperature, pressure and concentration then the no. of
degrees of freedom (F) of the system is related to no. of components (C) and
phases (P) can be related by the phase rule equation. F = C – P + 2
• In studying the chemical equilibrium, temperature and pressure are
considered as external factors determining the state of the system. Therefore
in the phase rule equation, the digit 2 stands for these two variables –
temperature and pressure.
• In applying the Gibb’s phase rule to the metal systems, the pressure is
considered as remaining fixed at one atmosphere. Thus, the effect of pressure
is neglected, leaving only one variable factor i.e. temperature.
• The phase rule equation then simplifies to F = C – P + 1
• since the degrees of freedom F cannot be less than zero
• C + 1 – P => 0, OR P <= C + 1 which means the number of Phases can not
exceed the number of component plus one.
 Reactions
CLASIFICATION OF EQUITIBRIUM DIAGRAMS
-An equilibrium diagram has been defined as a plot of the composition of phases is
function of temperature in any alloy system under equilibrium conditions
-Equilibrium diagrams may be classified according to the relation of the component
in the liquid and solid states as follows:
❑ Components completely soluble in the liquid state,
• and also completely soluble in the solid state,
• but partly soluble in the solid state (EUTECTIC REACTION Type I).
• but insoluble in the solid state (EUTECTIC REACTION Type II)
• The PERITECTIC Reaction
❑ Transformation in solid state
• Eutectoid reaction
• Peritectoid reaction
❖ Types of reactions in binary phase diagrams
• Eutectic Reaction
• Peritectic Reaction
• Eutectoid reaction
• Peritectoid reaction
Eutectic Reaction
I-Type
Eutectic Reaction
II-Type
Peritectic Reaction
Eutectoid reaction
Types of reactions in binary phase
diagrams
 1. Eutectic
❖In an eutectic reaction, when a liquid solution of fixed
Transformation
composition, solidifies at a constant temperature, forms a
mixture of two or more solid phases without an intermediate
pasty stage. This process reverses on heating.
❖A eutectic reaction is a three-phase reaction, by
which, on cooling, a liquid transforms into two
solid phases at the same time. It is a phase
reaction, but a special one.
❖ For example: liquid alloy becomes a solid
mixture of alpha and beta at a specific
temperature (rather than over a temperature
range).
❖In eutectic system, there is always a specific alloy, known
as eutectic composition, that freezes at a lower temp.
than all other compositions.
❖At the eutectic temp. two solids form simultaneously
form a single liquid phase.

❖The eutectic temp. & composition determine a point on the

phase diagram, called the eutectic point.
Eutectic or invariant point. Liquid and two solid phases exist in
equilibrium at the eutectic composition and the eutectic
temperature.

Note:
❖the melting point of the eutectic alloy is lower than that of the
components (eutectic = easy to melt in Greek).
❖At most two phases can be in equilibrium within a phase field.

❖Single-phase regions are separated by 2-phase regions.

◆Binary alloy eutectic system can be classified
as:
1. One in which, two metals are completely soluble in the
liquid state but are insoluble in each other in the solid
state.
2. two metals are completely soluble in the liquid state but
are partly soluble in each other in the solid state.
1. Two metals completely soluble in the liquid state but completely insoluble
in the solid state.
◆ Technically, no two metals are completely insoluble in each other. However, in some
cases the solubility is so restricted that for practical purposes they may be
considered insoluble.
❖ Alloy-1: 20% Cd and 80% Bi
❖ Contrary to alloy 3, in this case crystal of pure Bi form first, enriching the melt
with Cd.
❖ The composition of the melt (or liquid) moves to right until Ultimately the point E
is reached and the remaining liquid solidi-fies as eutectic (40% Cd and 60% Bi).
❖ Alloy-2: 40% Cd and 60% Bi (eutectic
alloy)
❖ No solidification occurs until the melt reaches the eutectic temperature (140°)

❖ At the eutectic temperature, the two pure metals crystallize together to give a
characteristically line aggregate known as
eutectic. consists of alternate layers of Cd and Bi which form at the eutectic
❖ Eutectic
temperature (140°C in this case).
 Alloy-3: 80% Cd and 20% Bismuth.
❖ As the temperature falls to T1, crystal nuclei of pure Cd begin to form. Since
pure Cd is deposited, it follows that the liquid becomes richer in Bi; the
composition of liquid move s to left 3’ and as indicated by the diagram, no
further Cd deposits until temperature falls to T2.
❖ At T2 more Cd is deposited and dendrites begin to develop from the already
formed nuclei.
❖ The growth of the Cd dendrites, on the one hand, and the consequent enrichment of
the remaining liquid in Bi, on the other, continues until the temperature has fallen
to 140°C, the eutectic temperature in this case.
❖ The remaining liquid then contains 40% Cd and 60% Bi, the eutectic
composition.
2. Two metals completely soluble in the liquid state, but only partly soluble in
the solid state
❖ Sincemost metals show some solubility for each other in the solid state, this type is
the most common and, therefore, the most common alloy system.
❖ Metals such as Pb-Sn and Pb-Sb are partly soluble in each other in the solid state. ❖

Fig. shows the Tin-Lead equilibrium diagram with micro-structures (of course)
obtained under non-equilibrium condition of
solidification.
I. Tin will dissolve up to maximum of 2.6% Pb at the temperature, forming the solid
solution α.
II. Lead will dissolve up to a maximum of (100-80.5) i.e. 19 .5% tin at the eutectic
temperature, giving the solid solution β.
III. Slope of BA and CD indicate that the solubility of Pb in Sn (α) and that of Sn in Pb (β)
decrease as temperature falls
◆ Consider an alloy of composition Z (70% Pb-30% Sn). As the melt temperature
falls to T1, dendrites of composition Y will deposit.
◆ The alloy solidifies as a solid solution until at 183°C, the last layer of solid to form is
of composition C (80.5% Pb-19.5% Sn).
◆ The remaining liquid which has the eutectic composition (38% Pb-62% Sn) then
solidifies by depositing, in the form of a eutectic, i.e., alternate layers of α and β, of
compositions B and C respectively.
◆ If cooled slowly to room temperature the compositions of the solid solutions α and β
will follow the line BA and CD, i.e., α will become progressively poorer in lead and
β in tin.
◆ Take another alloy of composition Z' (95% Pb-5% Sn). When cooled slowly,
solidification starts at R and is complete at P, the resultant solid being a
homogeneous single phase, the β solid solution.
◆ As the alloy cools, the solvus line is reached at point Q. The β solution is now
saturated in tin. Below this temperature, under conditions of slow cooling, the
excess tin must come out of solution. Since tin is soluble in lead, the precipitate does
not come out as the pure metal tin, but rather the α solid solution.
 2. Eutectoid Transformation
◆ Eutectoid reaction is an isothermal reversible reaction in which a solid phase (usually
solid solution) is converted into two or more intimately mixed solids on cooling, the
number of solids formed being the same as the number of component in the system.
❖Definition: A eutectoid reaction is a three-phase reaction by which,
on cooling, a solid transforms into two other solid phases at the
same time. If the bottom of a single-phase solid field closes (and
provided the adjacent two-phase fields are solid also), it does so
❖The eutectoid(eutectic-like)
with aeutectoid point. reaction is similar to the eutectic
reaction but occurs from one solid phase to two new solid phases. It
also shows as V on top of a horizontal line in the phase diagram.
There are associated eutectoid temperature (or temperature),
eutectoid phase, eutectoid and proeutectoid microstructures.
❖Solid Phase 1 à Solid Phase 2 + Solid Phase 3
❖The eutectoid structure in iron has a special name: it is called
pearlite (because it has a pearly look). The schematic and
micrograph below show pearlite. It is important to note that
pearlite is not a phase, but a mixture of two phases: ferrite and
cementite.
❖During slow cooling of an iron-carbon alloy, pearlite forms by
a eutectoid reaction as austenite cools below 727 °C (1,341 °F)
(the eutectoid temperature). Pearlite is a microstructure
occurring in many common grades of steels.
❖Eutectoid decomposition of iron as an example, austenite containing
0.8% C changes into ferrite (iron containing almost no carbon) and
cementite (Fe3C, containing 25 at% carbon). Hence carbon atoms
must diffuse together to form Fe3C, leaving ferrite.
❖Nuclei of small plates of ferrite and cementite form at the grain
boundaries of the austenite, and carbon diffusion takes place on a
very local scale just ahead of the interface (schematic below). Thus
the plates grow, consuming the austenite as they go, to form pearlite.
❖The difference is of % of Carbon present in the
steel.
❖Eutectoid steel has 0.8% C.
❖Hypereutectoid steel has greater than 0.8% C whereas
hypoeutectoid steel has less than 0.8% C. ...
❖Thus, if the steel is hypoeutectoid it will produce
proeutectoid ferrite and if it is hypereutectoid it will
produce proeutectoid cementite.
 3. Peritectoid
❖ The peritectoid reaction is the transformation of two solid into a third
Transformation
solid.
 It is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle

Thus, combining these two phases in solution an alloy can be

obtained with intermediate properties. (Mechanical properties
also depend on the microstructure, that is, how ferrite and
cementite are mixed.)
 4. Peritectic reaction
❖The peritectic reaction also involves three solid in
equilibrium, the transition is from a solid + liquid phase
to a different solid phase when cooling. The inverse
reaction occurs when heating.
❖Solid Phase 1 + liquid = Solid Phase
2
◆ Itis the reaction that occurs during the solidification of some alloys where
the liquid phase reacts with a solid phase to give a solid phase of different
structure.
◆ Assuming very slow rates of cooling, the peritectic reaction will occur
only in those Pt- Ag alloys that Contain between 12 and 69% silver (Ag).

◆ Consider a liquid (melt) of composition Z, i.e., containing 25% Ag.

Solidification commences at T1 and dendrites of α, initially of
composition W, begin forming.
◆ Selective crystallization of α continues down to Tp, the peritectic
temperature; when the alloy reaches. this temperature, it is composed of
solid α-dendrites of composition B and liquid of composition D in the
proportion α : liquid = RD : RB.