Introduction to phase diagram of alloy

1. B.Tech. 7th Semester
Metals and Alloys [CHOE12]
UNIT 1: Introduction to metals and alloys
Phase diagram

2. Phase diagram is a graphical representation of the phases that are present in a
material at various temperatures and pressures and compositions.
It usually describes the equilibrium conditions.
It is a “map” that tells us which state(s) of matter (solid, liquid, gas) exist for a
given set of temperature and pressure conditions.
Almost all materials have more than one phase in them. Thus engineering materials
attain their special properties.
Macroscopic basic unit of a material is called component. It refers to a
independent chemical species. The components of a system may be elements, ions
or compounds.
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.
A component can exist in many phases. E.g.: Water exists as ice, liquid water, and
water vapor. Carbon exists as graphite and diamond.

3. A solution (liquid or solid) is phase with more than one component; a mixture is a material
with more than one phase.
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.
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.
Thermodynamically derived Gibbs phase rule: The constant “2” in the equation implies that
both temperature and pressure are allowed to change.
In practical conditions for metallurgical and materials systems, pressure can be treated as a
constant (1 atm.). The constant pressure will reduce the degrees of freedom from “2” in
Gibb’s equation to “1” for a binary phase diagram
Thus Condensed Gibbs phase rule is written as:

4. Temperature
A measure of the average kinetic energy
(energy of motion) of particles (atoms or
molecules) in matter in Celsius, Kelvin, or
Fahrenheit.

5. Pressure
A measure of how tightly matter is squeezed
together in units of atmospheres (atm), bars,
torrs, Pascals (Pa) or even pounds/in2 (psi).

6. In other words….for most cases
Solids Liquids
Temperature
Pressure
Gases

7. Unary phase diagram
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.
For the triple point of water:
• One component, i.e., water.
• 3 phases present, i.e. vapor, liquid, and solid.
• F = 1 – 3 + 2 = 0, so this is an invariant
point on the diagram

8. The H2O Phase Diagram
 = 1.00 g/ml
 = .92 g/ml
 = .0006 g/ml

9. Binary phase diagram
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.
There are two general types of alloys having phase diagrams.
Substitutional alloys
Interstitial alloys
• Subtitutional alloys have elements, which are incorporated into regular lattice positions
within the unit cell. e.g. Tin and Zinc alloying additions to Copper to form bronze and
brass, respectively
• Interstitial alloys have elements, which are incorporated into the interstitial sites of the
unit cell. E.g. carbon in iron to form steel.

10. The liquidus temperature is the temperature above which a material is completely liquid.
The solidus temperature is the temperature which the alloy is 100% solid.
The freezing range of the alloy is the temperature difference between the liquidus and
solidus where the two phases exists, ie., the liquid and solid.
A binary phase diagram between two
elements A and B. When an alloy is
present in a two phase region, a tie line
at the temperature of interest fixes the
composition of the two phases. This is
a consequence of the Gibbs phase rule,
which provides for only one degree of
freedom.
liquidus temperature
solidus temperature

11. Hume-Ruthery conditions
• Extent of solid solubility in a two element system can be predicted based on Hume-
Ruthery conditions.
• If the system obeys these conditions, then complete solid solubility can be expected.
Hume-Ruthery conditions
 Crystal structure of each element of solid solution must be the same.
 Size of atoms of each two elements must not differ by more than 15%
 Elements should not form compounds with each other i.e. there should be no appreciable
difference in the electronegativities of the two elements.
 Elements should have the same valence.

12. Phase diagram of Lead-Tin Solder
• Soldering is using the fusible metal alloy to create a permanent bond between different
metal pieces.
• The solder must be melted first in order to adhere to and connect the pieces together after
cooling down. This requires the alloy suitable as solder should have a lower melting
point than the two pieces being joined.
• The solder should be also resistant to both corrosive and oxidative effects which can
degrade the joint over time.
• Also, the solder used in electrical conductive connections needs to possess proper
electrical characteristics.
The Soft solder normally has a melting point in the range of 90 to 450 °C and is usually used
in electronics and sheet metal work. Alloys that have melting point between 180 and 190 °C
are the most commonly used alloys. Soldering which is performed using alloys that have a
melting point above 450 °C is named hard soldering,

14. A eutectic system is a system of a homogeneous mixture of substances that either melts or
solidifies at a particular given temperature that is lower than the melting point of any of the
mixture of any of the constituent elements. This particular temperature is known as the
eutectic point. Thus, for a liquid mixture eutectic point or the eutectic temperature is the
lowest temperature at which a liquid can exist before solidifying in a eutectic system.

15. Phase diagram
of Lead-Tin system
Lead is soluble in Tin only up to 2.6 %, while Tin is soluble in Lead up to 19.5 %.
Lead-Tin mixture makes good eutectic mixture, melting point of pure lead is 327 °C and
melting point of Tin is 232 °C. A good example of this is Tin 63% / Lead 37% solder which
melts and freezes at 183 °C. This melting point is much lower than the melting points of
either pure metal which are 232 °C (tin) and 327 °C (lead).
Lead
100 %
Tin
100 %
Melting point of Lead
Melting point of Tin

16. Phase diagram
of Lead-Tin system
Lead 100 %
& 0 % Tin
Tin 100 %
& 0% Lead
Melting point of Lead
Melting point of Tin
Lead rich phase is called α-phase and lies at left hand side of phase diagram.
Tin rich phase is called β-phase and lies at right hand side of phase diagram.
Three phases- α, β, and liquid phases coexist in the phase diagram.
Curves AE and BE are liquidus curves. Curves ADE and BCE are solidus curves.
Point D indicate maximum solubility of tin in lead. Point C indicate maximum solubility of lead in
tin. Solubility decreases with decrease in temperature. Point E is eutectic point (lowest melting
point composition), liquid and solid curves exist in equilibrium. It melts at 183 °C and contain Tin
63% / Lead 37%. Curves DF and CG indicate variation of composition of conjugate solid solutions as a
function of temperature. As temperature increases, solubility increases.

17. At curves AE and BE, solid and liquid phases exist together, indicating univariant systems.
F = C - P + 1
F = 2 – 2 + 1
F = 1
The area above AEB curve, there is only liquid phase exist, represent bivariant system,
where both the temperature and composition have to be specified to define system.
F = C - P + 1
F = 2 – 1 + 1
F = 2
At eutectic point E, three phase solid lead, solid tin and their solution exist together.
F = C - P + 1
F = 2 – 3 + 1
F = 0
At eutectic point system has no freedom and system is invariant. This means that the system
consisting of two solid and solution can exist only at definite temperature and definite
composition.

18. There are a variety of common solder alloys used for electronics assembly, but only a few
are eutectic solders as shown in the table below.