Lecture 17
Phase Diagrams
Department of MME
BUET, Dhaka
Introduction to Phase Diagrams
 Some properties of materials are functions of their microstructures,
and, consequently, of their thermal histories. The microstructures are
controlled by the composition of the material and how it is processed.
 So it is important that we must know


about the structure of a material that has been developed during its
manufacture, and
the method of controlling (and/or modifying) the structure to enhance
its properties.
 Phase diagram is an important tool for materials scientists that
tells which phases are stable in a system under specified
conditions (e.g. of temperature, overall composition, pressure)
 Even though most phase diagrams represent stable (or equilibrium) states and
microstructures,

they are nevertheless useful in understanding the development and preservation of nonequilibrium structures and their attendant properties;
 The understanding of phase diagrams for alloy systems is extremely important
 Because, there is a strong correlation between microstructure and mechanical properties,
 and the development of microstructure of an alloy is related to the characteristics of its phase
diagram
 In addition, phase diagrams provide valuable information about melting, casting,
crystallization, and other phenomena
 Phase diagrams are also known as the equilibrium diagrams or constitutional
diagrams.
 Phase diagram is basically a map that presents the domains of stability of
phases and the limits of stability of phases in a graphical form.
 Reading the map will tell you, at the state when it comes to
equilibrium,
1.
2.
3.
what phases are present,
the state of those phases, and
the relative quantities of each phase.
 Reading a phase diagram will also tell what phase transformations we can expect
when we change one or more parameters of the system (T, P, X).
Limitations of Phase
Diagrams
❑ Rate of phase transformations is missing.
❑ TTT (Temperature-Time-Transformation) diagrams complement the phase
diagrams.
❑ Phase diagram gives information only on the constitution of alloys but not on
the structural distribution of the phases.
❑ Phase diagram show only the equilibrium state whereas alloys in practical use
are rarely in equilibrium.
Definitions and Basic Concepts
Components
❑ Chemically recognisable species that are mixed to form the alloy. Pure metal or
compounds of which alloy is made. Solute and solvent, which are also common
terms.
 In Brass: Cu, Zn (element)
 In steels: Fe, C (element)
 In ceramics: SiO2, Al2O3 (compound)
❑ Binary alloy contains 2 components, ternary 3, etc.
System
❑ relate to the series of possible alloys consisting of the same components, but without
regard to alloy composition (e.g., the iron–carbon system).
❑ An alloy is a substance that has metallic properties and is composed of two or
more chemical elements, of which at least one is a metal. Hence, An alloy is a
combination of metals or of a metal and another element.
❑ Alloying elements are deliberately introduced into a metal to enhance properties
especially, mechanical properties.
Yield strength is defined as the stress at which a material
ceases elastic deformation and begins plastic deformation
Property
60% Ni
Monel
Cu
Wt % Nickel
Tensile strength
Yield Strength
% Elongation
Electrical Conductivity
Ni
Direction
Up
Up
Down
Down
tensile strength: maximum load that a material can support without fracture
when being stretched, divided by the original cross-sectional area of the
material.
An alloy is distinct from an impure metal in that, with an alloy, the added elements are well
controlled to produce desirable properties, while impure metals such as wrought iron are less
controlled, but are often considered useful.
Note the difference
Alloy systems
 Alloying element and impurity element
 Alloy and alloy system
 Binary system (Fe-C system, Cu-Zn system)
 Ternary system (Fe-C-Mn system, Al-Si-Mg system)
o The mechanical properties of alloys will often be quite different from those of its
individual constituents.
o A metal that is normally very soft (malleable), such as aluminium, can be altered by
alloying it with another soft metal, such as copper.
o Although both metals are very soft and ductile, the resulting aluminium alloy will have
much greater strength.
SOLUBILITY LIMIT
❑ 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.
❑ 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.
Phase
❑ A phase is a homogenous, physically distinct and mechanically separable portion of
the material with a given chemical composition and structure.
What and how many phases materials
possess?
 Every pure material is considered to be a phase.
 Solid, liquid, or gas, (and plasma)?
 Is it possible to have more than one solid phases?
Iron, being an allotropic material, has more than one solid phases:
❑ When iron first freezes from its liquid state, it is BCC (d-iron)
❑ As it cools it changes to FCC (g-iron)
❑ Upon further cooling it changes to BCC (a-iron)
Equilibrium state and Metastable state
 A system is at equilibrium if, at
constant T, P and X, the system
does not change with time.
 The equilibrium state always has
the minimum free energy.
❑ Equilibrium state requires sufficient time to achieve. When this time is too long
(due to slow kinetics), another state along the path to the equilibrium may
appear to be stable. This is called a metastable state.
❑ A system at a metastable state is trapped in a local minimum of free energy,
which is not the global one.
Phase Equilibrium
A system is at equilibrium if its free energy is at a minimum under some specified combination
of temperature, pressure, and composition
A change in temperature, pressure, and/or composition for a system in equilibrium will result in
an increase in the free energy and in a possible spontaneous change to another state whereby
the free energy is lowered.
The term phase equilibrium, often used in the context of this discussion, refers to equilibrium as
it applies to systems in which more than one phase may exist. Phase equilibrium is reflected by
a constancy with time in the phase characteristics of a system.
Degrees Of Freedom, F
• The degrees of freedom is essentially the number of independent variables (that can be varied
independently without changing the number and state of phases at equilibrium), both internal
(composition of phases) and external ones(temperature, pressure etc.) whose values must be
specified in order to define completely the state of the system.
• Factors (variables) that might come in to an equation of state:
–
–
–
–
–
–
–
–
Number of components
Number of Phases
Composition of the phases
Amount of phases
Overall composition of the alloy
Temperature
Pressure
Volume
Gibb’s Phase Rule:
F = C–P+2
F = # degrees of freedom
C = # components
P = # phases
13
Classification of Phase Diagrams
One component (unary) phase diagrams
❑ Also known as P-T diagrams.
❑ The simple case is Water.
 How many single-phase
regions?
 How many two-phase
regions?
 Is there any three-, or
more-phase regions?
Unary phase diagram of water
This one-component phase diagram (or unary phase diagram) is represented as a two dimensional plot of pressure (ordinate, or
vertical axis) versus temperature (abscissa, or horizontal axis). Most often, the pressure axis is scaled logarithmically.
Two-component (binary) phase diagrams
❑ How does mixing of A into B effect the bond energies and the
melting temperature of the resultant alloy?
❑ Interaction of A and B resulted three bonds: A-A, B-B and A-B
bonds.
❑ Example: Copper - Nickel, Silicon - Germanium
➔ Completely miscible/soluble phase diagrams
Ge-Si phase diagram (completely miscible)
Humayun Kabir, Dept of MME, BUET
Ni-Cu phase diagram (completely miscible)
Working with Binary Phase Diagrams
Most Important Information:
 Overall composition of the alloy
 Liquidus and solidus temperatures
 Limits of solid solubility
 Identification of equilibrium phases at any given condition
 Chemical composition of phases at any temperature
 Amount of phases (relative amount) at any temperature
Phase Diagram Nomenclatures
Concentration/Overall Composition of alloy
❑ Relative amounts of each constituent
❑ It is the horizontal axis in all binary phase diagrams
❑ The scale can be in weight %, atomic % or mole %
Liquidus temperature
❑ Start of solidification (or, end of liquification) temperature
Solidus temperature
❑ End of solidification (or, start of liquification) temperature
Liquidus
Liquid
Freezing range
Liquid +
Solid
Solidus
Solid
X
% Y added
Y
Phase diagram with complete solubility of one component into another
The copper–nickel phase diagram
The liquid L is a homogeneous liquid solution composed of both
copper and nickel. The Alpha phase is a substitutional solid solution
consisting of both Cu and Ni atoms and having an FCC crystal
structure.
The copper–nickel phase diagram
❑ At temperatures below about 1085ºC, copper and nickel are
mutually soluble in each other in the solid state for all compositions.
❑ This complete solubility is explained by the fact that both Cu and Ni
have the same crystal structure (FCC), nearly identical atomic radii and
electro-negativities, and similar valences, as discussed previously.
❑ The copper–nickel system is termed isomorphous because of this
complete liquid and solid solubility of the two components.
Chemical composition of Phases
❑ It is the chemical composition of each phase in the system.
❑ In a system having more than one phase, each phase will have a
unique chemical composition which will be different from each other,
and will also be different from the overall composition.
❑ Not to be confused with overall composition of the alloy.
Relative amounts of Phases
❑ When a system contains more than one phases, then it is the amount
of each phase relative to overall amount of the alloy.
❑ Depends on temperature and composition of the alloy.
❑ Not to be confused with composition of phases.
 Composition of each phase
Phase diagram rule #2:
Tie Line Rule
If we know C0, then we can tell the composition
of each phase at any temperature.
In a system having more than
one phase, each phase will have
a unique chemical composition
which will be different from each
other, and will also be different
from the overall composition of
the system.
Not to be confused with overall
composition.
tie line
At TA: L phase only
CL = 35%Ni
At TB: L and a phases
CL = Cliquidus = 32%Ni
Ca = Csolidus = 43%Ni
At TD: a phase only
Ca = 35%Ni

Relative amount of each
phase
Phase diagram rule #3:
Lever Rule
If we know C0, then we can tell the weight
fraction of each phase at any temperature.
Consider C0 = 35 wt.%Ni
 At TA, only L phase  WL = 100 wt.%
 At TD, only a phase  Wa = 100 wt.%
 At TB, both L and a phases 
Lever
Rule
100 S
100 (43-35)
WL =
=
= 73 wt.%
R+S
43-32
100 R 100 (35-32)
Wa =
=
= 27 wt.%
R+S
43-32
It is the relative amount
(as in kg) of each phase in
the whole alloy.
Not to be confused with
composition (i.e., %A and
%B) of the alloy.
To summarise:
Finding the composition in a two phase region:
1.
2.
3.
Locate composition and temperature in the diagram.
In the two phase region, draw a tie line at the given temperature.
The liquid composition will be on the liquidus line and the solid
composition will be on the solidus line. Note the intersections with
phase boundaries. Read compositions at the intersections.
Finding the amounts of phases in a two phase region:
1.
2.
3.
Locate composition and temperature in the diagram.
In the two phase region, draw a tie line at the given temperature.
Fraction of a phase is determined by taking the length of the tie line
to the phase boundary for the other phase, and dividing by the total
length of tie line.