A phase diagram contains a “map” of a materials state (liquid only, solid only, coexisting as liquid with solid, or even various crystal structures of solid phases verses changes in material temperature, composition or pressure. We will only examine phase diagrams at a single pressure.
A diagram that depict 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.
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Equilibrium phase diagrams represent the relationships between temperature, compositions and the quantities of phases at equilibrium.

These diagrams do not indicate the dynamics when one phase transforms into another.
Phase diagrams are classified according to the number of component present in a particular system.
1) Unary phase diagram.
2) Binary phase diagram.
3) Ternary 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 obtained.
The change in the number of phases in an alloy under equilibrium condition are expressed by the
Gibbs phase rule
In a system under a set of conditions, number of phases ( P ) exist can be related to the number of components ( C ) and degrees of freedom ( F ) by Gibbs phase rule.

Thermodynamically derived Gibbs phase rule :
F+P=C+2
In practical conditions for metallurgical and materials systems, pressure can be treated as a constant (1 atm.).
Thus Condensed Gibbs phase rule is written as:
F+P=C+1
Phase is derived from the Greek verb fasis, "appearance, assertion, and accusation"
A phase can be defined as a homogeneous portion of a system that has uniform physical and chemical characteristics i.e. it is a physically distinct from other phases, chemically

homogeneous and mechanically separable portion of a system.
Phase Symbol Description
Liquid L
 -Ferrite 
Austenite 
Liquid solution of Fe and C
Interstitial solid solution of C in
 -Fe (high temperature bcc phase)
Interstitial solid solution of C in
 -Fe (FCC phase of Fe)
Ferrite  Interstitial solid solution of C in
 -Fe (room temperature bcc phase)
Soft and Ductile
Cementite Fe
3
C Intermetallic compound of Fe and C
(orthorhombic system)
Hard and Brittle
Component is either pure metal and/or compounds of which an alloy is composed. The components of a system may be elements, ions or compounds. They refer to the independent chemical species that comprise the system.
A component can exist in many phases. E.g.: Water exists as ice, liquid water, and water vapor.
Carbon exists as graphite and diamond.
2
2

3
A single component phase diagram is Unary diagram
A two-component phase diagram is Binary diagram
A three-component phase diagram is Ternary diagram
Degrees of freedom refers to the number of independent variables (e.g.: pressure, temperature) that can be varied individually to effect changes in a system. The maximum number of variables

which may be independently altered in value without disturbing the equilibrium in the system.
This number is obtained as the difference between the total number of variables available to the system and the minimum number of equations among these variables that is required for maintenance of the equilibrium

The degrees of freedom cannot be less than zero
The key idea behind the degrees of freedom is to ask: what can be changed without changing the mineral or assemblage? In the case of an invariant point, the answer is nothing. If P or T change, the conditions no longer fall on the invariant point. There are no degrees of freedom ( F = 0). In the case of a reaction, we can change P and T, but we must change them together or we will no longer be on the reaction line. So, there is one degree of freedom ( F = 1). If we are out in some general regions of PT space, we can change (within some limits) both P and T in arbitrary ways without crossing a reaction and changing the assemblage. So, the degrees of freedom is 2 ( F = 2). To summarize: where on the diagram? at an invariant point along a reaction line in general PT space
Degrees of freedom
F = 0
F = 1
F = 2
It refers to the set of conditions where more than one phase may exist. It is best described in terms of a thermodynamic quantity called the free energy. In brief, free energy is a function of the internal energy of a system, and also the randomness or disorder of the atoms or molecules
(or entropy). A system is at equilibrium if its free energy is at a minimum under some specified combination of temperature, pressure, and composition. In a macroscopic sense, this means that the characteristics of the system do not change with time but persist indefinitely; that is, the system is stable. 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. g
 g g
S g
L
 g
Gibbs free energy as a function of temperature, Problem 2.3


 
 g
T


 p
  s


  g
L
2

T g
2



< g p
S
  c
T p
Solid is stable g
S
< g
L
Liquid is stable g
S g
L
T freesing
T m
T

In most metallurgical and materials systems, phase equilibrium involves just solid phases.
However the state of equilibrium is never completely achieved because of very slow rate of approach of equilibrium in solid systems. This leads to non-equilibrium or meta-stable state, which may persist indefinitely and of course, has more practical significance than equilibrium phases. An equilibrium state of solid system can be reflected in terms of characteristics of the microstructure, phases present and their compositions, relative phase amounts and their spatial arrangement or distribution
If a system consists of just one component (e.g. water), equilibrium of phases exist is depicted by unary phase diagram. The component may exist in different forms, thus variables here are – temperature and pressure. r
Critical Point
P
Liquid r
Vapor
T
Temperature
1 If a system consists of two components, equilibrium of phases exist is depicted by binary phase diagram. For most systems, pressure is constant, thus independently variable parameters are –temperature and composition.
2 Two components can be either two metals (Cu and Ni), or a metal and a compound (Fe and Fe3C), or two compounds (Al2O3 and Si2O3), etc.
3 Two component systems are classified based on extent of mutual solid solubility (a) completely soluble in both liquid and solid phases (isomorphous system) and (b) completely soluble in liquid phase whereas solubility is limited in solid state.
An isomorphous system phase diagram and corresponding microstructural changes

1 System: A body of matter with finite boundaries (physical or virtual)
2 Closed System: Does not exchange matter with surroundings but may exchange energy
(heat).
3 Open System: Does exchange matter and energy with surroundings.
4 Homogeneous System: Intensive properties change continuously and uniformly
(smoothly)
5 Heterogeneous System: System made up of two or more phases in which the intensive

properties change abruptly at phase-contact surfaces
6 Phase: A portion of the system which has homogeneous intensive properties and it is bounded by a physical surface.
7 Interface: Separates two or more phases. These phases are solid, liquid(s), and gas.
8 Intensive Properties: Independent of system mass (i.e. density)
9 Extensive Properties: Dependent of system mass (i.e. volume )