PHASE TRANSFORMATION

KNUST
PHY 392 - Lec. One (1)

H. Martin (PhD)

June 16, 2024

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Outline of Presentation

1 Objectives & Goals of the Course

2 Course Outline

3 Books Recommended

4 Assessment

5 Revision
Electronic, Atomic bonding and Crystal Structure
Thermodynamics & Kinetic

6 Phase Transformation

.
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Objectives & Goals of the Course

To understand the underlying Principles of the formation of metal

alloys structures and the evolution within it. Thus, the mechanisms
by which metal alloys attempts to reach a stable or equilibrium state
and how long it takes.

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Course Outline
1 Revision
Electronic, Atomic bonding & Crystal structure
Thermodynamics & Kinetics
2 Solid solution
Substitutional and Interstitial Solid solution
3 Phase Equilibria of alloys
Phase, Component, Phase Rule, ... , Single component
4 Phase Diagram
Binary and Ternary
Time Temperature Transformation (TTT diagram)
Continuous Cooling Transformation (CCT diagram)
5 Solidification
Nucleation: Homogeneous and Heterogeneous
Growth: Continuous, Lateral, Constitutional supercooling, ...
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Books Recommended

1 Materials Science and Engineering: An Introduction: William D.

Callister, Jr., David G. Rethwisch. 8th ed.
2 Fundamentals of Materials Science - The Microstructure
Property Relationship using Metals as Model Systems: Eric J.
Mittemeijer. Springer-Verlag Berlin Heidelberg, 2010
3 Physical Metallurgy Principles: Reza Abbaschian, Lara
Abbaschian, Robert E. Reed-Hill. 4th Ed. 2004

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Assessment

1 Assignments: 20 mins of Individual presentation on Article

Review. One (1) Student per a week. Each other student is
required to ask at least 2 questions during the presentation.
2 Oral Exams:
3 Mid-Sem:
4 Oral Exams:
5 Main Exams:

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Electronic, Atomic bonding and Crystal Structure

Principal quantum number - n, Azimuthal quantum number -

l = n − 1 and Magnetic quantum number - m.
n l m
2 0s 0
L
1 p -1 0 +1
3 0s 0
M 1 p -1 0 +1
2 d -2 -1 0 +1 +2
Examples: Li -1s 2 2s 1 , Ar - 1s 2 2s 2 2p 6 3s 2 3p 6
Types of Solid bonding
Metallic, Ionic, Covalent bond
Metallic bonds: Is the electrostatic attractive force between
valence electrons (delocalized electron cloud) and metal atom(s).
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The ordered arrangements of material constituents (atoms, ions)
are described by Crystal structure
This is form from a symmetry array of points in space - Crystal
Lattice
The smallest group is the unit cell, the repetitive pattern along a
direction describes a Periodic Structure
Classified as follows:
Lattice System
Bravais Lattices
Point group
Space group

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Thermodynamic & Kinetic

Thermodynamics is the theory that deals with the flow of energy

between material systems. A thermodynamic system is the
macroscopic space/domain defined with its physical boundary.

A system can either be homogeneous or heterogeneous.

A homogeneous system is a system with a uniform phase and a
heterogeneous system is a system that has more than one phase i.e.
combination of solid, liquid and gaseous state.

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The surrounding space interacting with the system is called
environment.
This has three (3) ways of classifying a system. Namely, Isolated,
Closed and Opened.

An isolated system cannot exchange energy or matter with the

environment.
A closed system can exchange energy with the environment but not
matter.
An open system can exchange both energy and matter with the
environment.

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Macroscopic observables that affect the behaviour of a
thermodynamics system in an equilibrium state are known as state
variables. These has four main independent state variables, given as
Number of particles, N, Volume, V, Temperature, T and Pressure, p.
Laws of Thermodynamics
The zeroth law is a statement about the relationship between bodies
in thermal equilibrium.
The first law is a statement of the conservation of energy.

∆U = ∆q + ∆w (1)
δw = −pδV (2)

The second law deals with the directionality of thermodynamic

processes.  
dq
S= (3)
T rev
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The third law states that as a system with T → 0 all processes cease
and the entropy of the system approaches a minimum value.

dS = (∂S)E ,V ≥ 0 (4)

Hence, combining all the thermodynamic laws and other measure

energy changes in systems as they evolve from an initial state to a
final state.
Internal energy, U = TdS − pdV + · · ·
Helmholtz free energy, F = U − TS
Enthalpy, H = U + pV
Gibbs free energy, G = U + pV − TS

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Kinetic: Is the study of transformation rates (how fast processes
occur) in physical chemistry.
Transition or Activated state - For an atom to vibrate/move from an
initial state to a final state. The probability of an atom reaching an
activated state is:  
−∆G
exp (5)
kB T
Hence, the rate at which a transformation occurs will depend on the
frequency with which atoms reach the activated state - Arrhenius law.

Reference:
Callister - Ch 1 to Ch 3
Physical Metallurgy - Ch 1 and Ch 3

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Phase Transformation
Phase transformation is the phenomena where the state of a material
changes or the changes that occur in a solid crystal structure by
adding other element(s) (thus, solid solution)
during a cooling/heating process (thus, heat treatment)

Composition (Solid solution) + Processing (heat treatment)

↘⇓↙
Phase transformation (Properties change)

Examples:
casting: filling a mould with molten metal, (solidification and
cooling)
thermo-mechanical deformation (cold/hot rolling) forming
shapes metal billets
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Table 1: Techniques for observing phases and phase transformations in a
microstructure

Technique Physical basis

Measurement of dimensional changes at high resolution to detect changes
Dilatometry
density and symmetry caused by phase change
Measurement of electrical resistivity changes associated with difference in
Electrical resistivity
electron mean free path before and after phase change
Sensitive differential measurement of release or take-up of latent heat
Calorimetry
associated with phase change
Differential reflection of light, either in color or intensity, by phases or by
Optical microscopy
a surface film created by chemical or electro-etching
Differential back-scattering of electrons by differing phases giving both
SEM
an image and compositional information
Diffraction of an electron beam by the crystal lattice of each phase, giving
TEM
both an image of the structure and, from the diffraction pattern, its crystal

Reference:
Physical Metallurgy - Ch 2
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 THANK YOU

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