The document discusses phase transformations in solids. It defines phases as homogeneous regions of a material that are physically distinct. Phase transformations occur when an initial state becomes unstable relative to a final state. The stability of a system is determined by its Gibbs free energy (G), which depends on enthalpy (H), entropy (S), temperature (T), and pressure (P). Binary phase diagrams illustrate the phases present at various compositions and temperatures. Common diagram types include eutectic systems where components are soluble in liquid but not solid, and partially soluble solid systems. Determining phase amounts uses the lever rule based on composition and phase boundaries.

1. MM-501 Phase Transformation in
Solids
Fall Semester-2015
Engr. Muhammad Ali Siddiqui
Lecturer,
Metallurgical Engineering Department,
NED UET
BE: Mehran UET, 2007
ME: NED UET, 2011

2. Lecture No: 02
1. Equilibrium
2. One-component systems
– Enthalpy and entropy dependence on P and T
– Gibbs free energy dependence on P and T
– Effect of pressure on the equilibrium phase
diagram for pure iron
3. Phase Diagrams (Binary System)
– Type I, II and III Phase Diagrams,
2

3. • Study of phase transformation concerned with how one or
more phases in an alloy (or in a system) change into new
phase or mixture of phases.
• The reason why a transformation occur….? because the initial
state of the alloy is unstable relative to the final slate.
• A phase can be defined as a portion of a system whose
properties and composition are homogeneous but physically
distinct from other parts of the system.
• The Transformations that occur at constant temperature and
pressure ,the stability of a system is determined by its Gibbs
free energy (G).
3
Equilibrium

4. • The Gibbs free energy, G of a system is
defined by the equation.
G = H - TS
Where
• H is the enthalpy, is the measure of the heat
content of the system.
• T the absolute temperature, and
• S the entropy of the system, is the measure of
the randomness of the system.
4

5. • Enthalpy is a measure of the heat content of the
system and is given
H = E + PV
• Where E, the internal energy of the system, P the
pressure, and V the volume.
• E = internal energy arises from the total kinetic and
potential energies of the atoms within the system.
• Kinetic energy can arise from atomic vibration in solids
or liquids and from translational and rotational
energies for the atoms and molecules within a liquid or
gas; whereas
• potential energy arises from the interactions, or
bonds, between the atoms within the system.
5

6. H = E + PV…… For reference
• If a transformation or reaction occurs the heat
that is absorbed or evolved will depend on the
change in the internal energy of the system.
• However it will also depend on changes in the
volume of the system and the term PV takes
this into account, so that at constant pressure
the heat absorbed or evolved is given by the
change in H.
6

7. • When dealing with condensed phases (solids and
liquids) the PV term is usually very small in
comparison to E, that is H = E + PV. This is the very
first approximation.
• A system is said to be in equilibrium when it is in the
most stable state, i.e. shows no desire to change.
• An important consequence of the laws of classical
thermodynamics is that at constant temperature and
pressure a closed system will be in stable equilibrium
if it has the lowest possible value of the Gibbs free
energy, or in mathematical terms
• dG = 0 and graphically is shown as :
• 7

8. 8
Fig: A schematic variation of Gibbs free energy with the
arrangement of atoms.
Configuration 'A' has the lowest free energy and is therefore
the arrangement when the system is at stable equilibrium.
Configuration 'B' is a metastable equilibrium.
Arrangment of Atoms


9. 9
Equilibrium States:
dG = 0 dG = 0 dG ≠ 0

10. 10
One-component systems

11. 11
• Cp = Specific heat, quantity of heat (in joules) required
to raise the temperature of the substance by one
degree Kelvin
• The specific heat of most substances is easily measured
and easily available.
• In general it varies with temperature as shown.

12. 12
a. Variation of Specific Heat with Temperature
b. Variation of enthalpy (H) with absolute Temperature of a pure
substance
c. Variation of entropy (S) with absolute Temperature of a pure
substance

13. • Finally the variation of G with temperature
shown in next Fig.
• which is obtained by combining Fig. b and c &
using Equation G = H-TS.
13

14. 14
• G decreases with increasing T at a rate given by - S.
Fig. Variation of Gibbs free energy with temperature.

15. • The relative positions of the free energy curves of
solid and liquid phases are illustrated in Fig.
15
• Variation of enthalpy
(H) and free energy
(G) with temperature
for the solid and
liquid phases of a
pure metal.
• L is the latent heat of
melting,
• T m the equilibrium
melting temperature.

16. 16

17. 17

18. 18
Fig. Effect of pressure on the equilibrium phase
diagram for pure iron
Pressure, Kbar

23. Type-I –Two Metals Completely Soluble in liquid and solid state

24. Figure: Determination o f a phase diagram by thermal analysis.
A) Cooling curves of six alloys of various compositions are determined
experimentally.
Temperature is shown on the vertical axis as a function of time on the
horizontal axis.
B) The fusion temperature and the liquidus and solidus temperatures are then
plotted ,IS a function of composition to form the phase diagram.

26. Determination of Phase Composition

27. If an alloy consists of more than one phase, the amount of each
phase present can be found by applying the lever rule to the
phase diagram.
The lever rule can be explained by considering a simple
balance. The composition of the alloy is represented by the
fulcrum, and the compositions of the two phases by the ends
of a bar. The proportions of the phases present are determined
by the weights needed to balance the system.
So,
fraction of phase C1 = (C2 - C) / (C2 - C1)
and,
fraction of phase C2 = (C - C1) / (C2 - C1).
Lever Rule: Determine the Phase Amount

33. Type-II- Two Metals Completely Soluble in Liquid State and Completely
insoluble in the solid state. (Eutectic phase diagram)
 Eutectic phase
diagram describes
behavior of the
alloys, two components
of
which are completely so
luble in liquid state and
entirely
insoluble in solid state.
 This diagram
has two liquidus curves,
starting from the
freezing points of
the two metals and inte
rsecting in a minimum
point – eutectic point.

34. Type-III- Two Metals Completely Soluble in Liquid State but Partly
soluble in the solid state

45. Summary

46. Thanks
46