Material science notes

Material Science Syllabus
Satish Kailash Vasu/IISc, Bangalore V1/1-6-04/1
MATERIAL SCIENCE
Aim: At the end of the course the student will have an understanding of mechanics,
physical and chemical properties of materials including metals, ceramics, polymers
and composites and the reasons for these properties to exist.
Module 1: Introduction (3)
Historical perspective of Materials Science. Why study properties of materials?
Classification of materials. Advanced Materials, Future materials and modern
materials
Module 2: Atomic Structure, Interatomic Bonding and Structure of Crystalline
Solids (5)
Atomic structure. Atomic bonding in solids, Crystal structures, Crystalline and non-
crystalline materials. Miller indices. Anisotropic elasticity. Elastic behavior of
composites. Structure and properties of polymers. Structure and properties of
ceramics.
Module 3: Imperfections in Solids (2)
Point defects. Theoretical yield point. Line defects and dislocations. Interfacial
defects. Bulk or volume defects. Atomic vibrations
Module 4: Mechanical Properties of Metals (3)
Elastic deformation. Plastic deformation. Interpretation of tensile stress-strain curves
Yielding under multiaxial stress. Yield criteria and macroscopic aspects of plastic
deformation. Property variability and design factors
Module 5: Diffusion (2)
Diffusion mechanisms. Steady and non-steady state diffusion. Factors that influence
diffusion. Non-equilibrium transformation and microstructure
Module 6: Dislocations and Strengthening Mechanisms (3)
Dislocation and plastic deformation. Mechanisms of strengthening in metals.
Recovery, recrystallization and grain growth. Strengthening by second phase
particles. Optimum distribution of particles. Lattice resistance to dislocation motion
Module 7: Phase Diagrams (4)
Equilibrium phase diagrams. Particle strengthening by precipitation. Precipitation
reactions. Kinetics of nucleation and growth. The iron-carbon system. Phase
transformations. Transformation rate effects and TTT diagrams. Microstructure and
property changes in iron-carbon system
Module 8: Failure (5)
Fracture. Ductile and brittle fracture. Fracture mechanics. Impact fracture. Ductile
brittle transition. Fatigue. Crack initiation and propagation. Crack propagation rate.
Creep. Generalized creep behavior. Stress and temperature effects
Module 9: Applications and Processing of Metals and Alloys (2)
Types of metals and alloys. Fabrication of metals. Thermal processing of metals. Heat
treatment. Precipitation hardening.

Module 10: Applications and Processing of Ceramics (1)
Types and applications of ceramics. Fabrication and processing of ceramics.
Module 11: Applications and Processing of Polymers (2)
Mechanical behavior of polymers. Mechanisms of deformation and strengthening of
polymers. Crystallization, melting and glass transition. Polymer types. Polymer
synthesis and processing.
Module 12: Composites (1)
Particle reinforced composites. Fiber reinforced composites. Structural composites
Module 13: Corrosion and Degradation of Materials (1)
Corrosion of metals. Corrosion of ceramics. Degradation of polymers
Module 14: Electrical Properties (1)
Electrical conduction. Semi conductivity. Super conductivity. Electrical conduction in
ionic ceramics and in polymers. Dielectric behavior. Ferroelectricity. Piezoelectricity
Module 15: Thermal Properties (1)
Heat capacity. Thermal expansion. Thermal conductivity. Thermal stresses
Module 16: Magnetic Properties (1)
Diamagnetism and paramagnetism. Ferromagnetism.Antiferromagnetism and
ferrimagnetism. Influence of temperature on magnetic behavior. Domains and
Hysteresis
Module 17: Optical Properties (1)
Basic concepts. Optical properties of metals. Optical properties of nonmetals.
Application of optical phenomena.
Module 18: Economic, Environmental and Social Issues of Material Usage (2)
Economic considerations. Environmental and societal considerations. Recycling
issues. Life cycle analysis and its use in design

Lecture Plan
Module Learning Units Hours
per topic
Total
Hours
1. Historic perspective and Materials Science 1
2. Why study properties of materials.
Classification of materials
1
1) Introduction
3. Advanced materials, Future materials and
Modern materials
1
3
4. Atomic Structure and atomic bonding in
solids
1
5. Crystal structures, Crystalline and non-
crystalline materials
1
6. Miller indices, Anisotropic elasticity and
elastic behavior of composites
1
7. Structure and properties of polymers 1
2) Atomic Structure,
Interatomic Bonding
and Structure of
Crystalline Solids
8. Structure and properties of Ceramics 1
5
9. Pint defects, theoretical yield point, line
defects and dislocations
13) Imperfections in
Solids
10. Interfacial defects, bulk or volume defects
and atomic vibrations
1
2
11. Elastic deformation and plastic deformation 1
12. Interpretation of tensile stress-strain curves 1
4) Mechanical
Properties of Metals
13. Yielding under multiaxial stress, Yield
criteria and macroscopic aspects of plastic
deformation and property variability and
design factors
1 3
14. Diffusion Mechanisms and steady state and
non-steady state diffusion
15) Diffusion
15. Factors that influence diffusion and non-
equilibrium transformation and
microstructure
1 2
16. Dislocation and plastic deformation and
mechanisms of strengthening in metals
1
17. Recovery, recrystallization and grain growth 1
6) Dislocations and
Strengthening
Mechanisms
18. Strengthening by second phase particles,
optimum distribution of particles and lattice
resistance to dislocation motion
1 3
19. Equilibrium phase diagrams, Particle
strengthening by precipitation and
precipitation reactions
1
20. Kinetics of nucleation and growth 1
21. The iron-carbon system, phase
transformations
1
7. Phase Diagrams
22. Transformation rate effects and TTT
diagrams, Microstructure and property
changes in iron-carbon system
1
4
23. Fracture, ductile and brittle fracture 1
24. Fracture mechanics 1
8. Failure
25. Impact fracture, ductile brittle transition 1

26. Fatigue, crack initiation and propagation,
crack propagation rate
1
27. Creep, generalized creep behavior, stress and
temperature effects
1
5
28. Types on metals and alloys, fabrication of
metals, thermal processing of metals
19. Applications and
Processing of Metals
and Alloys 29. Heat treatment and precipitation hardening 1
2
Processing of
Ceramics
30. Types and applications of ceramics,
fabrication and processing of ceramics 1 1
31. Mechanical Behavior of polymers,
Mechanisms of deformation and
strengthening of polymers
1
Processing of
Polymers
32. Crystallization, melting and glass transition,
polymer types and polymer synthesis and
processing
1
2
12. Composites 33. Particle reinforced composites, fiber
reinforced composites, structural composites 1 1
13. Corrosion and
Degradation of
Materials
34. Corrosion of metals, Corrosion of ceramics,
Degradation of polymers 1 1
14. Electrical
Properties
35. Electrical conduction, Semi conductivity,
Super conductivity, Electrical conduction in
ionic ceramics and in polymers, Dielectric
behavior, Ferroelectricity, Piezoelectricity
2 1
15. Thermal
Properties
36. Heat capacity, Thermal expansion, Thermal
conductivity, Thermal stresses
1 1
16. Magnetic
Properties
37. Diamagnetism, paramagnetism,
ferromagnetism, antiferromagnetism, and
ferrimagnetism. Influence of temperature on
magnetic behavior, domains and hysteresis
1 1
17. Optical
Properties
38. Basic concepts, Optical properties of metals,
Optical properties of nonmetals, Application
of optical phenomena
1 1
39. Economic considerations, Environmental
and societal considerations, Recycling issues 1
18. Economic,
Environmental and
Social Issues of
Material Usage
40. Life Cycle analysis and its use in design 1
2

Material Science/Introduction Learning Material
Introduction
Historical Perspective
Materials are so important in the development of civilization that we associate ages with
them. In the origin of human life on earth, the Stone Age, people used only natural
materials, like stone, clay, skins, and wood. When people found copper and how to make
it harder by alloying, the Bronze Age started about 3000 BC. The use of iron and steel, a
stronger material that gave advantage in wars started at about 1200 BC. The next big step
was the discovery of a cheap process to make steel around 1850, which enabled the
railroads and the building of the modern infrastructure of the industrial world.
Materials Science and Engineering
Understanding of how materials behave like they do, and why they differ in properties
was only possible with the atomistic understanding allowed by quantum mechanics, that
first explained atoms and then solids starting in the 1930s. The combination of physics,
chemistry, and the focus on the relationship between the properties of a material and its
microstructure is the domain of Materials Science. The development of this science
allowed designing materials and provided a knowledge base for the engineering
applications (Materials Engineering).
Satish V. Kailas/IISc M1/L1/V1/Aug 2004/1

Why Study Materials Science and Engineering?
• To be able to select a material for a given use based on considerations of cost and
performance.
• To understand the limits of materials and the change of their properties with use.
• To be able to create a new material that will have some desirable properties.
All engineering disciplines need to know about materials. Even the most "immaterial",
like software or system engineering depend on the development of new materials, which
in turn alter the economics, like software-hardware trade-offs. Increasing applications of
system engineering are in materials manufacturing (industrial engineering) and complex
environmental systems.
Classification of Materials
Like many other things, materials are classified in groups, so that our brain can handle
the complexity. One could classify them according to structure, or properties, or use. The
one that we will use is according to the way the atoms are bound together:
Metals: valence electrons are detached from atoms, and spread in an 'electron sea' that
"glues" the ions together. Metals are usually strong, conduct electricity and heat well and
are opaque to light (shiny if polished). Examples: aluminum, steel, brass, gold.
Semiconductors: the bonding is covalent (electrons are shared between atoms). Their
electrical properties depend extremely strongly on minute proportions of contaminants.
They are opaque to visible light but transparent to the infrared. Examples: Si, Ge, GaAs.
Ceramics: atoms behave mostly like either positive or negative ions, and are bound by
Coulomb forces between them. They are usually combinations of metals or
semiconductors with oxygen, nitrogen or carbon (oxides, nitrides, and carbides).
Examples: glass, porcelain, many minerals.
Polymers: are bound by covalent forces and also by weak van der Waals forces, and
usually based on H, C and other non-metallic elements. They decompose at moderate
temperatures (100 – 400 C), and are lightweight. Other properties vary greatly.
Examples: plastics (nylon, teflon, polyester) and rubber.
Other categories are not based on bonding. A particular microstructure identifies
composites, made of different materials in intimate contact (example: fiberglass,
concrete, wood) to achieve specific properties. Biomaterials can be any type of material
that is biocompatible and used, for instance, to replace human body parts.

Advanced Materials
Materials used in "High-Tec" applications, usually designed for maximum performance,
and normally expensive. Examples are titanium alloys for supersonic airplanes, magnetic
alloys for computer disks, special ceramics for the heat shield of the space shuttle, etc.
Modern Material's Needs
• Engine efficiency increases at high temperatures: requires high temperature
structural materials
• Use of nuclear energy requires solving problem with residues, or advances in
nuclear waste processing.
• Hypersonic flight requires materials that are light, strong and resist high
temperatures.
• Optical communications require optical fibers that absorb light negligibly.
• Civil construction – materials for unbreakable windows.
• Structures: materials that are strong like metals and resist corrosion like plastics.

Satish V. Kailas ME/MS 1
Module-1
Introduction

1. Historic perspective and Materials Science
2. Why study properties of materials, Classification of
materials
3. Advanced materials, Future materials and Modern
materials’ needs
Contents

Historic Perspective
Materials are very important in development of human
civilization. In respect, their names are associated in
history, e.g. stone age, Bronze age, Iron age, etc.
With time humans discovered new materials and also
techniques to produce known materials. This is an
ongoing process for coming centuries, i.e. no end in sight!

Materials Science
It can be defined as science dealing the relationships that
exist between the structures and properties of materials,
which are useful in practice of engineer’s profession.
Basic components and their interrelationship:
Structure
Properties Processing
Performance

Properties Of Materials
All solid engineering materials are characterized for their
properties.
Engineering use of a material is reflection of its properties
under conditions of use.
All important properties can be grouped into six categories:
Mechanical, Electrical, Thermal, Magnetic, Optical, and
Deteriorative.
Each material possess a structure, relevant properties, which
dependent on processing and determines the performance.

Why Study Properties Of Materials? - 1
Since there are thousands of materials available it is almost
impossible to select a material for a specific task unless
otherwise its properties are known.
There are several criteria on which the final decision is
based on.
There are less chances of material possessing optimal or idle
combination of properties.
A need to trade off between number of factors!

The classic example involves strength and ductility:
Normally material possessing strength have limited
ductility.In such cases a reasonable comprise between two
or more properties are important.
A second selection consideration is any deterioration of
material properties during service operations.
Finally the overriding consideration is economics.
Why Study Properties Of Materials? - 2

Classification Of Materials
Three basic groups of solid engineering materials based on
atomic bonds and structures:
Metals
Ceramics
Polymers
Classification can also be done based on either properties
(mechanical, electrical, optical), areas of applications
(structures, machines, devices). Further we can subdivide
these groups.
According to the present engineering needs:
Composites, Semiconductors, Biomatrials

Metals
Characteristics are owed to non-localized electrons (metallic
bond between atoms) i.e. electrons are not bound to a
particular atom.
They are characterized by their high thermal and electrical
conductivities.
They are opaque, can be polished to high luster. The opacity
and reflectivity of a metal arise from the response of the
unbound electrons to electromagnetic vibrations at light
frequencies.
Relatively heavier, strong, yet deformable.
E.g.: Steel, Aluminium, Brass, Bronze, Lead, Titanium, etc.

Ceramics
They contain both metallic and nonmetallic elements.
Characterized by their higher resistance to high temperatures
and harsh environments than metals and polymers.
Typically good insulators to passage of both heat and
electricity.
Less dense than most metals and alloys.
They are harder and stiffer, but brittle in nature.
They are mostly oxides, nitrides, and carbides of metals.
Wide range: traditional (clay, silicate glass, cement) to
advanced (carbides, pure oxides, non-silicate glasses).
E.g.: Glass, Porcelain, Minerals, etc.

Polymers
Commercially called plastics; noted for their low density,
flexibility and use as insulators.
Mostly are of organic compounds i.e. based on carbon,
oxygen and other nonmetallic elements.
Consists large molecular structures bonded by covalent and
vander Waals forces.
They decompose at relatively moderate temperatures (100-
400 C).
Application: packaging, textiles, biomedical devices, optical
devices, ceramics household items, toys, etc.
E.g.: Nylon, Teflon, Rubber, Polyester, etc.

Composites
Consist more than one kind of material; tailor made to
benefit from combination of best characteristics of each
constituent.
Available over a very wide range: natural (wood) to
synthetic (fiberglass).
Many are composed of two phases; one is matrix – which is
continuous and surrounds the other, dispersed phase.
Classified into many groups: (1) depending on orientation of
phases; such as particle reinforced, fiber reinforced, etc. (2)
depending on matrix; metal matrix, polymer matrix, ceramic
matrix.
E.g.: Cement concrete, Fiberglass, special purpose
refractory bricks, plywood, etc.

Semiconductors
Their electrical properties are intermediate when compared
with electrical conductors and electrical insulators.
These electrical characteristics are extremely sensitive to the
presence of minute amounts of foreign atoms.
Found very many applications in electronic devices over
decades through integrated circuits. In can be said that
semiconductors revolutionized the electronic industry for
last few decades.

Biomaterials
Those used for replacement of damaged or diseased body
parts.
Primary requirements: must be biocompatible with body
tissues, must not produce toxic substances.
Important materials factors: ability to support the forces, low
friction and wear, density, reproducibility and cost.
All the above materials can be used depending on the
application.
A classic example: hip joint.
E.g.: Stainless steel, Co-28Cr-6Mo, Ti-6Al-4V, ultra high
molecular weight polyethylene, high purity dense Al-oxide,
etc.

Advanced Materials
Can be defined as materials used in high-tech devices i.e.
which operates based on relatively intricate and
sophisticated principles (e.g. computers, air/space-crafts,
electronic gadgets, etc.).
These are either traditional materials with enhanced
properties or newly developed materials with high-
performance capabilities. Thus, these are relatively
expensive.
Typical applications: integrated circuits, lasers, LCDs, fiber
optics, thermal protection for space shuttle, etc.
E.g.: Metallic foams, inter-metallic compounds, multi-
component alloys, magnetic alloys, special ceramics and
high temperature materials, etc.

Future Materials - 1
Group of new and state-of-the-art materials now being
developed, and expected to have significant influence on
present-day technologies, especially in the fields of
medicine, manufacturing and defense.
Smart/Intelligent material system consists some type of
sensor (detects an input) and an actuator (performs
responsive and adaptive function).
Actuators may be called upon to change shape, position,
natural frequency, mechanical characteristics in response to
changes in temperature, electric/magnetic fields, moisture,
pH, etc.

Four types of materials used as actuators:
Shape memory alloys
Piezoelectric ceramics
Magnetostrictive materials
Electro-/Magneto-rheologic fluids
Materials / Devices used as sensors:
Optical fibers
Piezoelectric materials
Micro-electro-mechanical systems (MEMS)- etc.

Typical applications:
1. By incorporating sensors, actuators and chip processors into
system, researchers are able to stimulate biological human-
like behavior.
2. Fibers for bridges, buildings, and wood utility poles.
3. They also help in fast moving and accurate robot parts, high
speed helicopter rotor blades.
4. Actuators that control chatter in precision machine tools.
5. Small microelectronic circuits in machines ranging from
computers to photolithography prints.
6. Health monitoring detecting the success or failure of a
product.

Modern Materials’ Needs
Engine efficiency increases at high temperatures; requires
high temperature structural materials.
Use of nuclear energy requires solving problems with residue,
or advance in nuclear waste processing.
Hypersonic flight requires materials that are light, strong and
resist high temperatures.
Optical communications require optical fibers that absorb
light negligibly.
Civil construction – materials for unbreakable windows.
Structures: materials that are strong like metals and resist
corrosion like plastics.

Material Science/Atomic Structure, Inter atomic bonding Learning Material
and structure of crystalline solids and atomic bonding in solids
Atomic Structure and atomic Bonding in solids
Atomic Structure:
Atoms are composed of electrons, protons, and neutrons. Electron and protons are
negative and positive charges of the same magnitude, 1.6 × 10-19
Coulombs.
The mass of the electron is negligible with respect to those of the proton and the neutron,
which form the nucleus of the atom. The unit of mass is an atomic mass unit (amu) =
1.66 × 10-27
kg, and equals 1/12 the mass of a carbon atom. The Carbon nucleus has Z=6,
and A=6, where Z is the number of protons, and A the number of neutrons. Neutrons and
protons have very similar masses, roughly equal to 1 amu. A neutral atom has the same
number of electrons and protons, Z.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu
of the atoms. Thus, a mole of carbon has a mass of 12 grams. The number of atoms in a
mole is called the Avogadro number, Nav = 6.023 × 1023
. Note that Nav = 1 gram/1 amu.
Calculating n, the number of atoms per cm3
in a piece of material of density δ (g/cm3
).
n = Nav × δ / M
where M is the atomic mass in amu (grams per mol). Thus, for graphite (carbon) with a
density δ = 1.8 g/cm3
, M =12, we get 6 × 1023
atoms/mol × 1.8 g/cm3
/ 12 g/mol) = 9 ×
1022
C/cm3
.
For a molecular solid like ice, one uses the molecular mass, M(H2O) = 18. With a density
of 1 g/cm3
, one obtains n = 3.3 × 1022
H2O/cm3
. Note that since the water molecule
contains 3 atoms, this is equivalent to 9.9 × 1022
atoms/cm3
.
Most solids have atomic densities around 6 × 1022
atoms/cm3
. The cube root of that
number gives the number of atoms per centimeter, about 39 million. The mean distance
between atoms is the inverse of that, or 0.25 nm. This is an important number that gives
the scale of atomic structures in solids.

Atomic bonding in solids:
Primary Interatomic Bonds
Ionic Bonding
This is the bond when one of the atoms is negative (has an extra electron) and another is
positive (has lost an electron). Then there is a strong, direct Coulomb attraction. An
example is NaCl. In the molecule, there are more electrons around Cl, forming Cl-
and
less around Na, forming Na+
. Ionic bonds are the strongest bonds. In real solids, ionic
bonding is usually combined with covalent bonding.
Covalent Bonding
In covalent bonding, electrons are shared between the molecules, to saturate the valency.
The simplest example is the H2 molecule, where the electrons spend more time in
between the nuclei than outside, thus producing bonding.
Metallic Bonding
In metals, the atoms are ionized, loosing some electrons from the valence band. Those
electrons form an electron sea, which binds the charged nuclei in place, in a similar way
that the electrons in between the H atoms in the H2 molecule bind the protons.
Secondary Bonding (Van der Waals)
Fluctuating Induced Dipole Bonds
Since the electrons may be on one side of the atom or the other, a dipole is formed: the +
nucleus at the center, and the electron outside. Since the electron moves, the dipole
fluctuates. This fluctuation in atom A produces a fluctuating electric field that is felt by
the electrons of an adjacent atom, B. Atom B then polarizes so that its outer electrons are
on the side of the atom closest to the + side (or opposite to the – side) of the dipole in A.
This bond is called van der Waals bonding.
Polar Molecule-Induced Dipole Bonds
A polar molecule like H2O (Hs are partially +, O is partially – ), will induce a dipole in a
nearby atom, leading to bonding.
Permanent Dipole Bonds
This is the case of the hydrogen bond in ice. The H end of the molecule is positively
charged and can bond to the negative side of another dipolar molecule, like the O side of
the H2O dipole

Crystal Structures:
Atoms self-organize in crystals, most of the time. The crystalline lattice is a periodic
array of the atoms. When the solid is not crystalline, it is called amorphous. Examples of
crystalline solids are metals, diamond and other precious stones, ice, graphite. Examples
of amorphous solids are glass, amorphous carbon (a-C), amorphous Si, most plastics
To discuss crystalline structures it is useful to consider atoms as being hard spheres, with
well-defined radii. In this scheme, the shortest distance between two like atoms is one
diameter.
Metallic Crystal Structures
Important properties of the unit cells are
• The type of atoms and their radii R.
• Cell dimensions (side a in cubic cells, side of base a and height c in HCP) in
terms of R.
• n, number of atoms per unit cell. For an atom that is shared with m adjacent unit
cells, we only count a fraction of the atom, 1/m.
• CN, the coordination number, which is the number of closest neighbors to which
an atom is bonded.
• APF, the atomic packing factor, which is the fraction of the volume of the cell
actually occupied by the hard spheres. APF = Sum of atomic volumes/Volume of
cell.
Unit Cell n CN a/R APF
SC 1 6 2 0.52
BCC 2 8 4√ 3 0.68
FCC 4 12 2√ 2 0.74
HCP 6 12 0.74

Crystalline and Non-crystalline materials:
Single Crystals
Crystals can be single crystals where the whole solid is one crystal. Then it has a regular
geometric structure with flat faces.
Polycrystalline Materials
A solid can be composed of many crystalline grains, not aligned with each other. It is
called polycrystalline. The grains can be more or less aligned with respect to each other.
Where they meet is called a grain boundary.
Non-Crystalline Solids
In amorphous solids, there is no long-range order. But amorphous does not mean random,
since the distance between atoms cannot be smaller than the size of the hard spheres.
Also, in many cases there is some form of short-range order. For instance, the tetragonal
order of crystalline SiO2 (quartz) is still apparent in amorphous SiO2 (silica glass.)

Miller Indices:
Rules for Miller Indices:
• Determine the intercepts of the face along the crystallographic axes, in terms of
unit cell dimensions.
• Take the reciprocals
• Clear fractions
• Reduce to lowest terms
For example, if the x-, y-, and z- intercepts are 2, 1, and 3, the Miller indices are
calculated as:
• Take reciprocals: 1/2, 1/1, 1/3
• Clear fractions (multiply by 6): 3, 6, 2
• Reduce to lowest terms (already there)
Thus, the Miller indices are 3,6,2. If a plane is parallel to an axis, its intercept is at
infinity and its Miller index is zero. A generic Miller index is denoted by (hkl).
If a plane has negative intercept, the negative number is denoted by a bar above the
number. Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get
1,1,1. This implies symmetry that the crystal may not have!

Some General Principles
• If a Miller index is zero, the plane is parallel to that axis.
• The smaller a Miller index, the more nearly parallel the plane is to the axis.
• The larger a Miller index, the more nearly perpendicular a plane is to that axis.
• Multiplying or dividing a Miller index by a constant has no effect on the
orientation of the plane
• Miller indices are almost always small.
Why Miller Indices?
• Using reciprocals spares us the complication of infinite intercepts.
• Formulas involving Miller indices are very similar to related formulas from
analytical geometry.
• Specifying dimensions in unit cell terms means that the same label can be applied
to any face with a similar stacking pattern, regardless of the crystal class of the
crystal. Face 111 always steps the same way regardless of crystal system.
Anisotropy
Different directions in the crystal have different packing. For instance, atoms along the
edge FCC crystals are more separated than along the face diagonal. This causes
anisotropy in the properties of crystals; for instance, the deformation depends on the
direction in which a stress is applied.
Elastic Behavior of Composites:
The idea is that by combining two or more distinct materials one can engineer a new
material with the desired combination of properties (e.g., light, strong, corrosion
resistant). The idea that a better combination of properties can be achieved is called the
principle of combined action.
A type of composite that has been discussed is perlitic steel, which combines hard, brittle
cementite with soft, ductile ferrite to get a superior material.
Natural composites: wood (polymer-polymer), bones (polymer-ceramics).
Usual composites have just two phases:

• matrix (continuous)
• dispersed phase (particulates, fibers)
Properties of composites depend on
• Properties of phases
• Geometry of dispersed phase (particle size, distribution, orientation)
• Amount of phase
Classification of composites: three main categories:
• Particle-reinforced (large-particle and dispersion-strengthened)
• Fiber-reinforced (continuous (aligned) and short fibers (aligned or random)
• Structural (laminates and sandwich panels)
In many applications, like in aircraft parts, there is a need for high strength per unit
weight (specific strength). This can be achieved by composites consisting of a low-
density (and soft) matrix reinforced with stiff fibers.
The strength depends on the fiber length and its orientation with respect to the stress
direction.
The efficiency of load transfer between matrix and fiber depends on the interfacial bond.

Structure and properties of polymers:
Polymers are common in nature, in the form of wood, rubber, cotton, leather, wood, silk,
proteins, enzymes, starches, cellulose. Artificial polymers are made mostly from oil.
Their use has grown exponentially, especially after WW2. The key factor is the very low
production cost and useful properties (e.g., combination of transparency and flexibility,
long elongation).
Hydrocarbon Molecules
Most polymers are organic, and formed from hydrocarbon molecules. These molecules
can have single, double, or triple carbon bonds. A saturated hydrocarbon is one where
all bonds are single, that is, the number of atoms is maximum (or saturated). Among this
type are the paraffin compounds, CnH2n+2 (Table 15.1). In contrast, non-saturated
hydrocarbons contain some double and triple bonds.
Isomers are molecules that contain the same molecules but in a different arrangement.
An example is butane and isobutane.
Polymer molecules are huge, macromolecules that have internal covalent bonds. For most
polymers, these molecules form very long chains. The backbone is a string of carbon
atoms, often single bonded.
Polymers are composed of basic structures called mer units. A molecule with just one
mer is a monomer.
The Chemistry of Polymer Molecules
Examples of polymers are polyvinyl chloride (PVC), poly-tetra-chloro-ethylene (PTFE or
Teflon), polypropylene, nylon and polystyrene. Chains are represented straight but in
practice they have a three-dimensional, zig-zag structure (Fig. 15.1b).
When all the mers are the same, the molecule is called a homopolymer. When there is
more than one type of mer present, the molecule is a copolymer.
Molecular Weight
The mass of a polymer is not fixed, but is distributed around a mean value, since polymer
molecules have different lengths. The average molecular weight can be obtained by
averaging the masses with the fraction of times they appear (number-average) or with the
mass fraction of the molecules (called, improperly, a weight fraction).

The degree of polymerization is the average number of mer units, and is obtained by
dividing the average mass of the polymer by the mass of a mer unit.
Polymers of low mass are liquid or gases, those of very high mass (called high-polymers,
are solid). Waxes, paraffins and resins have intermediate masses.
Molecular Shape
Polymers are usually not linear; bending and rotations can occur around single C-C bonds
(double and triple bonds are very rigid) (Fig. 15.5). Random kings and coils lead to
entanglement, like in the spaghetti structure shown in Fig. 15.6.
Molecular Structure
Typical structures are :
• linear (end-to-end, flexible, like PVC, nylon)
• branched
• cross-linked (due to radiation, vulcanization, etc.)
• network (similar to highly cross-linked structures).
Molecular Configurations
The regularity and symmetry of the side-groups can affect strongly the properties of
polymers. Side groups are atoms or molecules with free bonds, called free-radicals, like
H, O, methyl, etc.
If the radicals are linked in the same order, the configuration is called isostatic
In a stereoisomer in a syndiotactic configuration, the radical groups alternative sides in
the chain.
In the atactic configuration, the radical groups are positioned at random.
Copolymers
Copolymers, polymers with at least two different types of mers can differ in the way the
mers are arranged. Fig. 15.9 shows different arrangements: random, alternating, block,
and graft.
Polymer Crystallinity

Crystallinity in polymers is more complex than in metals (fig. 15.10). Polymer molecules
are often partially crystalline (semicrystalline), with crystalline regions dispersed within
amorphous material. .
Chain disorder or misalignment, which is common, leads to amorphous material since
twisting, kinking and coiling prevent strict ordering required in the crystalline state.
Thus, linear polymers with small side groups, which are not too long form crystalline
regions easier than branched, network, random copolymers, or polymers with bulky side
groups.
Crystalline polymers are denser than amorphous polymers, so the degree of crystallinity
can be obtained from the measurement of density.
Polymer Crystals
Different models have been proposed to describe the arrangement of molecules in
semicrytalline polymers. In the fringed-micelle model, the crystallites (micelles) are
embedded in an amorphous matrix (Fig.15.11). Polymer single crystals grown are shaped
in regular platelets (lamellae) (Fig. 15.12). Spherulites (Fig. 15.4) are chain-folded
crystallites in an amorphous matrix that grow radially in spherical shape “grains”.

Structure and properties of ceramics:
Ceramics are inorganic and non-metallic materials that are commonly electrical and
thermal insulators, brittle and composed of more than one element (e.g., two in Al2O3)
Ceramic Structures
Ceramic bonds are mixed, ionic and covalent, with a proportion that depends on the
particular ceramics. The ionic character is given by the difference of electronegativity
between the cations (+) and anions (-). Covalent bonds involve sharing of valence
electrons. Very ionic crystals usually involve cations which are alkalis or alkaline-earths
(first two columns of the periodic table) and oxygen or halogens as anions.
The building criteria for the crystal structure are two:
• maintain neutrality
• charge balance dictates chemical formula
• achieve closest packing
the condition for minimum energy implies maximum attraction and minimum repulsion.
This leads to contact, configurations where anions have the highest number of cation
neighbors and viceversa.
Silicate Ceramics
Oxygen and Silicon are the most abundant elements in Earth’s crust. Their combination
(silicates) occur in rocks, soils, clays and sand. The bond is weekly ionic, with Si4+
as the
cation and O2-
as the anion. rSi = 0.04 nm, rO.= 0.14 nm, so rC/rA = 0.286.
The tetrahedron is charged: Si4+
+ 4 O2-
⇒ (Si O4)4-
. Silicates differ on how the
tetrahedra are arranged. In silica, (SiO2), every oxygen atom is shared by adjacent
tetrahedra. Silica can be crystalline (e.g., quartz) or amorphous, as in glass.
Soda glasses melt at lower temperature than amorphous SiO2 because the addition of
Na2O (soda) breaks the tetrahedral network. A lower melting point makes it easy to form
glass to make, for instance, bottles.
Carbon

Carbon is not really a ceramic, but an allotropic form, diamond, may be thought as a type
of ceramic. Diamond has very interesting and even unusual properties:
• diamond-cubic structure (like Si, Ge)
• covalent C-C bonds
• highest hardness of any material known
• very high thermal conductivity (unlike ceramics)
• transparent in the visible and infrared, with high index of refraction
• semiconductor (can be doped to make electronic devices)
• metastable (transforms to carbon when heated)
Synthetic diamonds are made by application of high temperatures and pressures or by
chemical vapor deposition. Future applications of this latter, cheaper production method
include hard coatings for metal tools, ultra-low friction coatings for space applications,
and microelectronics.
Graphite has a layered structure with very strong hexagonal bonding within the planar
layers (using 3 of the 3 bonding electrons) and weak, van der Waals bonding between
layers using the fourth electron. This leads to easy interplanar cleavage and applications
as a lubricant and for writing (pencils). Graphite is a good electrical conductor and
chemically stable even at high temperatures. Applications include furnaces, rocket
nozzles, electrodes in batteries.
A recently (1985) discovered formed of carbon is the C60 molecule, also known as
fullerene or bucky-ball (after the architect Buckminster Fuller who designed the geodesic
structure that C60 resembles.) Fullerenes and related structures like bucky-onions amd
nanotubes are exceptionally strong. Future applications are as a structural material and
possibly in microelectronics, due to the unusual properties that result when fullerenes are
doped with other atoms.
Imperfections in Ceramics
Imperfections include point defects and impurities. Their formation is strongly affected
by the condition of charge neutrality (creation of unbalanced charges requires the
expenditure of a large amount of energy.
Non-stoichiometry refers to a change in composition so that the elements in the ceramic
are not in the proportion appropriate for the compound (condition known as
stoichiometry). To minimize energy, the effect of non-stoichiometry is a redistribution of
the atomic charges (Fig. 13.1).

Charge neutral defects include the Frenkel and Schottky defects. A Frenkel-defect is a
vacancy- interstitial pair of cations (placing large anions in an interstitial position requires
a lot of energy in lattice distortion). A Schottky-defect is the a pair of nearby cation and
anion vacancies.
Introduction of impurity atoms in the lattice is likely in conditions where the charge is
maintained. This is the case of electronegative impurities that substitute a lattice anions
or electropositive substitutional impurities. This is more likely for similar ionic radii
since this minimizes the energy required for lattice distortion. Defects will appear if the
charge of the impurities is not balanced.
Brittle Fracture of Ceramics
The brittle fracture of ceramics limits applications. It occurs due to the unavoidable
presence of microscopic flaws (micro-cracks, internal pores, and atmospheric
contaminants) that result during cooling from the melt. The flaws need to crack
formation, and crack propagation (perpendicular to the applied stress) is usually
transgranular, along cleavage planes. The flaws cannot be closely controlled in
manufacturing; this leads to a large variability (scatter) in the fracture strength of ceramic
materials.
The compressive strength is typically ten times the tensile strength. This makes ceramics
good structural materials under compression (e.g., bricks in houses, stone blocks in the
pyramids), but not in conditions of tensile stress, such as under flexure.
Plastic deformation in crystalline ceramics is by slip, which is difficult due to the
structure and the strong local (electrostatic) potentials. There is very little plastic
deformation before fracture.
Non-crystalline ceramics, like common glass deform by viscous flow (like very high-
density liquids). Viscosity decreases strongly with increases temperature.

Atomic Structures, Interatomic Bonding and Structure
of Crystalline Solids
Module 2

1. Atomic Structure and Atomic bonding in solids
2. Crystal structures, Crystalline and Non-crystalline materials
3. Miller indices, Anisotropic elasticity and Elastic behavior
of Composites
4. Structure and properties of polymers
5. Structure and properties of ceramics
Contents

Atomic Structure -1
Every atom consists of a small nucleus composed of
protons and neutrons, which is encircled by moving
electrons in their orbitals, specific energy levels.
The top most ortibal electrons, valence electrons, affect
most material properties that are of interest to engineer.
E.g.: chemical properties, nature of bonding, size of atom,
optical/magnetic/electrical properties.
Electrons and protons are negative and positive charges of
the same magnitude being 1.60x10-19 coulombs.
Neutrons are electrically neutral.
Protons and neutrons have approximately the mass,
1.67x10-27 kg, which is larger than that of an electron,
9.11x10-31 kg.

Atomic number (Z) - is the number of protons per atoms.
Atomic mass (A) - is the sum of the masses of protons
and neutrons within the nucleus.
Atomic mass is measured in atomic mass unit (amu)
where 1amu=(112) the mass of most common isotope of
carbon atom, measured in grams.
A ≅ Z+N, where N is number of neutrons.
Isotopes - atoms with same atomic number but different
atomic masses.
A mole is the amount of matter that has a mass in grams
equal to the atomic mass in amu of the atoms. Thus a
mole of carbon has a mass of 12 grams.
Atomic Structure -2

The number of atoms or molecules in a mole of substance is
called the Avogadro’s number, Nay. Nay=1gram/1amu =
6.023x1023.
E.g.: Calculating the number of atoms per cm3, n, in a piece
of material of density d (g/cm3)
n = Nav × d / M, where M is the atomic mass in amu.
Thus, for graphite (carbon) with a density d = 1.8 g/cm3 and
M =12, n = 6.023 × 1023 atoms/mol × 1.8 g/cm3 / 12 g/mol)
= 9 × 1022 atoms/cm3.
Most solid materials will have atomic density in the order of
6x1022, that’s about 39 million atoms per centimeter.
Mean distance between atoms is in the range of 0.25 nm. It
gives an idea about scale of atomic structures in solids.
Atomic Structure -3

Atomic Bonding In Solids
Two questions need to be answered: why the atoms are
clustered together?, and how they are arranged?
Bonds are two kinds – Primary, and Secondary
Primary bonds – relatively stronger. Exists in almost all solid
materials.
E.g.: Ionic, Covalent, and Metallic bonds.
Secondary bonds – relatively weaker bonds. Exists in many
substances like water along with primary bonds.
E.g.: Hydrogen, and Vander Waals forces.

Atomic bonding
Primary bonding
Secondary bonding
ionic covalent metallic
Fluctuating
induced
Polar
induced
permanent
Atomic Bond In Solids

Primary Inter-Atomic Bonds
These bonds invariably involves valence electrons.
Nature of bond depends on electron arrangement in
respective atoms.
Atoms tend to acquire stable electron arrangement in their
valence orbitals by transferring (ionic), sharing (covalent,
and metallic) valence electrons. This leads to formation of
bonds.
Bond energies are in order of 1000 kJ/mol.

Ionic Bond
This primary bond exists between two atoms when transfer
of electron(s) results in one of the atoms to become negative
(has an extra electron) and another positive (has lost an
electron).
This bond is a direct consequence of strong Coulomb
attraction between charged atoms.
Basically ionic bonds are non-directional in nature.
In real solids, ionic bonding is usually exists along with
covalent bonding.
E.g.: NaCl. In the molecule, there are more electrons around
Cl, forming Cl- and fewer electrons around Na, forming Na+.

Covalent Bond
This bond comes into existence if valence electrons are
shared between a pair of atoms, thus acquire stability by
saturating the valence configuration.
Covalent bonds are stereo specific i.e. each bond is between
a specific pair of atoms, which share a pair of electrons (of
opposite magnetic spins).
Typically, covalent bonds are very strong, and directional in
nature.
E.g.: H2 molecule, where an electron from each of the atom
shared by the other atom, thus producing the covalent bond.

Metallic Bond
This bond comes into existence if valence electrons are
shared between number of atoms, i.e. arranged positive
nucleuses are surrounded by electron pool.
Shared electrons are not specific to a pair of atoms, in
contrast to Covalent bond, i.e. electrons are delocalized.
As shared electrons are delocalized, metallic bonds are non-
directional.
Very characteristic properties of metals like high thermal and
electrical conductivities are result of presence of delocalized
electron pool.

Secondary Inter-Atomic Bonds - 1
These bonds involves atomic or molecular dipoles.
Bonds can exists between induced and permanent dipoles
(polar molecules).
Bond comes into existence because of Columbic attraction
between positive end of one dipole and negative end of
another dipole.
Bond energies are in order of 10 kJ/mol

Secondary Inter-Atomic Bonds - 2
Existence of these depends on three kinds of dipoles –
fluctuating dipoles, Polar-molecule dipoles and Permanent
dipoles.
Permanent dipole bonds are also called Hydrogen bonds as
covalently bonded hydrogen atoms – for example C-H, O-H,
F-H – share single electron becomes positively charged
proton that is capable of strong attractive force with the
negative end of an adjacent molecule.
Hydrogen bonds is responsible for water t exist in liquid state
at room temperature.

Crystal Structures
All solid materials are made of atoms/molecules, which are
arranged in specific order in some materials, called
crystalline solids. Otherwise non-crystalline or amorphous
solids.
Groups of atoms/molecules specifically arranged – crystal.
Lattice is used to represent a three-dimensional periodic
array of points coinciding with atom positions.
Unit cell is smallest repeatable entity that can be used to
completely represent a crystal structure. It is the building
block of crystal structure.

Unit Cell
It is characterized by:
Type of atom and their radii, R
Cell dimensions, a and c (for hexagonal structures)
Number of atoms per unit cell, n
Coordination number (CN)– closest neighbors to an atom
Atomic packing factor, APF
Most common unit cells – Face-centered cubic, Body-
centered cubic and Hexagonal.

Common Crystal Structures
0.74126Hexagonal Close Packed
0.744/Ö 2124Face-Centered Cubic
0.684/Ö 382Body-Centered Cubic
0.524/Ö 461Simple Cubic
APFa/RCNnUnit Cell

Schematic Unit Cells

Miller Indices
A system of notation is required to identify particular
direction(s) or plane(s) to characterize the arrangement of
atoms in a unit cell
Formulas involving Miller indices are very similar to related
formulas from analytical geometry – simple to use
Use of reciprocals avoids the complication of infinite
intercepts
Specifying dimensions in unit cell terms means that the same
label can be applied to any plane with a similar stacking
pattern, regardless of the crystal class of the crystal. Plane
(111) always steps the same way regardless of crystal system

Miller Indices - Direction
A vector of convenient length is placed parallel to the
required direction
The length of the vector projection on each of three axes are
measured in terms of unit cell dimensions
These three numbers are made to smallest integer values,
known as indices, by multiplying or dividing by a common
factor
The three indices are enclosed in square brackets, [uvw].
A family of directions is represented by <uvw>

Miller Indices - Plane
Determine the intercepts of the plane along the
crystallographic axes, in terms of unit cell dimensions. If
plane is passing through origin, there is a need to construct a
plane parallel to original plane
Take the reciprocals of these intercept numbers
Clear fractions
Reduce to set of smallest integers
The three indices are enclosed in parenthesis, (hkl).
A family of planes is represented by {hkl}

Miller Indices - Examples

Miller Indices – Useful Conventions
If a plane is parallel to an axis, its intercept is at infinity and
its Miller index will be zero
Never alter negative numbers. This implies symmetry that
the crystal may not have! Use bar over the number to
represent negative numbers.
A plane or direction of family is not necessarily parallel to
other planes or directions in the same family
The smaller the Miller index, more nearly parallel the plane
to that axis, and vice versa
Multiplying or dividing a Miller index by constant has no
effect on the orientation of the plane
When the integers used in the Miller indices contain more
than one digit, the indices must be separated by commas.
E.g.: (3,10,13)

Useful Conventions For Cubic Crystals
[uvw] is normal to (hkl) if u = h, v = k, and w = l. E.g.: (111)
┴ [111]
[uvw] is parallel to (hkl) if hu + kv + lw = 0
Two planes (h1k1l1) and (h2k2l2) are normal if h1h2 + k1k2
+ l1l2=0
Two directions (u1v1w1) and (u2v2w2) are normal if u1u2 +
v1v2 + w1w2=0
Inter-planar distance between family of planes {hkl} is given
by:
Angle between two planes is given by:
222
}{
lkh
a
d hkl
++
=
2
2
2
2
2
2
2
1
2
1
2
1
212121
cos
lkhlkh
llkkhh
++++
++
=θ

Miller-Bravis Indices
Miller indices can describe all possible planes/directions in
any crystal.
However, Miller-Bravis indices are used in hexagonal
systems as they can reveal hexagonal symmetry more clearly
Indices are based on four axes – three are coplanar on basal
plane at 120˚ apart, fourth axis is perpendicular to basal
plane
Both for planes/directions, extra index is given by
t = -(u+v), i = -(h+k)
where plane is represented as [uvtw], and a direction is
represented by (hkil)
E.g.: Basal plane – (0001), Prismatic plane – (10ֿ10)

Polymers - Definition
Polymers are made of basic units called mers
These are usually Hydrocarbons – where major constituent
atoms are Hydrogen and Carbon
When structure consists of only one mer, it is monomer. If it
contains more than one mer, it is called polymer
Isomers are molecules those contain same number of similar
mers but arrangement will be different
E.g.: Butene and Isobutene
When a polumer has ONE kind of mers in its structure, it is
called homopolymer
Polymer made with more than one kind of mers is called
copolymer

Polymer Structures
Linear, where mer units are joined together end to end in
single chains. E.g.: PVC, nylon.
Branched, where side-branch chains are connected to main
ones. Branching of polymers lowers polymer density because
of lower packing efficiency
Cross-linked, where chains are joined one to another at
various positions by covalent bonds. This cross-linking is
usually achieved at elevated temperatures by additive atoms.
E.g.: vulcanization of rubber
Network, trifunctional mer units with 3-D networks comes
under this category. E.g.: epoxies, phenol-formaldehyde.

Polymer Structures
Schematic presentation of polymer structures.
Individual mers are represented by solid circles.

Thermo-Sets – Thermo-Plasts
Polymers mechanical response at elevated temperatures
strongly depends their chain configuration
Based on this response polymers are grouped in to two -
thermo-sets and thermo-plasts
Thermo-sets: become permanently hard when heated, and do
not soften during next heat cycle. During first heating
covalent bonds forms thus extensive cross-linking takes
place. Stronger and harder than thermo-plasts.
E.g.: Vulcanized rubber, epoxies, some polyester resins
Thermo-plasts: softens at high temperatures, and becomes
hard at ambient temperatures. The process is reversible.
Usually made of linear and branched structures.
E.g.: Polystyrene, Acrylics, Cellulosics, Vinyls

Polymer Crystallinity
Crystallinity in polymers is more complex than in metals
Polymer crystallinity range from almost crystalline to
amorphous in nature
It depends on cooling path and on chain configuration
Crystalline polymers are more denser than amorphous
polymers
Many semicrystalline polymers form spherulites. Each
spherulite consists of collection of ribbon like chain folded
lamellar crystallites.
E.g.: PVC (Poly Vinyl Chloride)

Polymer Properties

Ceramics
Ceramics are inorganic and non-metallic materials
Atomic bonds in ceramics are mixed – covalent + ionic
Proportion of bonds is specific for a ceramic
Ionic bonds exists between alkalis/alkaline-earth metals and
oxygen/halogens.
Mostly oxides, carbides, nitrides of metals are ceramics
E.g.: Sand, Glass, Bricks, Marbles

Ceramic Structures
Building criteria for ceramic structures:
- maintain neutrality
- closest packing
Packing efficiency can be characterized by coordination
number which depends on cation-anion radius ratio (rc/ra)
1286432
Coordination
number
>
1.00
0
0.732
–
1.000
0.414 –
0.732
0.225 –
0.414
0.155 –
0.225
<
0.15
5
Cation-anion
radius ratio
(rc/ra)

Ion Arrangement – Coordination Numbers

Ceramic Crystal Structures
AX-type: most common in ceramics. They assume different
structures of varying coordination number (CN).
Rock salt structure – CN=6. E.g.: NaCl, FeO
Cesium Chloride structure – CN=8 E.g.: CsCl
Zinc Blende structure – CN=4 E.g.: ZnS, SiC
AmXp-type: number of anions and cations are different (m≠p).
One unit cell is made of eight cubes.
E.g.: CaF2, ThO2
AmBnXp-type: when ceramic contains more then one kind of
cations. Also called perovskite crystal structure.
E.g.: BaTiO3

Silicates - 1
Most common ceramic in nature – Silicates, as constituent
elements – silicon and oxygen – are most abundant in earth’s
crust.
Bond between Si4+ and O2- is weak ionic and very strong
covalent in nature. Thus, basic unit of silicates is SiO4
4-
tetrahedron.

Silicates - 2
In Silica (SiO2), every oxygen atom the corner of the
tetrahedron is shared by the adjacent tetrahedron.
Silica can be both crystalline (quartz) and amorphous (glass)
Crystalline forms of silica are complicated, and
comparatively open…thus low in density compared with
amorphous glasses
Addition of network modifiers (Na2O) and intermediates
(Al2O3, TiO2)lowers the melting point…thus it is easy to
form. E.g.: Bottles.
In complicated silicates, corner oxygen is shared by other
tetrahedra….thus consists SiO4
4-, Si2O7
6-, Si3O9
6- groups
Clays comprises 2-D sheet layered structures made of Si2O5
2-

Carbon
Carbon is not a ceramic, but its allotropic form - Diamond is
Diamond:
C-C covalent bonds, highest known hardness,
Semiconductor, high thermal conductivity, meta-stable
Graphite - another allotropic form of carbon layered
structure - hexagonal bonding within planar layers, good
electrical conductor, solid lubricant
Another allotropic form - C60 - also called Fullerene / Bucky
ball. Structure resembles hallow ball made of 20 hexagons
and 12 pentagons where no two pentagons share a common
edge.
Fullerenes and related nanotubes are very strong, ductile -
could be one of the important future engineering materials

Imperfections In Ceramics
Imperfections in ceramics – point defects, and impurities.
Their formation is strongly affected by charge neutrality
Frenkel-defect is a vacancy-interstitial pair of cations
Schottky-defect is a pair of nearby cation and anion vacancies
Impurities:
Introduction of impurity atoms in the lattice is likely in
conditions where the charge is maintained.
E.g.:electronegative impurities that substitute lattice anions
or electropositive substitutional impurities

Mechanical Response Of Ceramics
1Engineering applications of ceramics are limited because of
presence of microscopic flaws – generated during cooling
stage of processing.
However, as ceramics are high with hardness, ceramics are
good structural materials under compressive loads.
Plastic deformation of crystalline ceramics is limited by
strong inter-atomic forces. Little plastic strain is
accomplished by process of slip.
Non-crystalline ceramics deform by viscous flow.
Characteristic parameter of viscous flow – viscosity.
Viscosity decreases with increasing temperature. However,
at room temperature, viscosity of non-crystalline ceramics is
very high.

Mechanical Response Of Ceramics - 2
Hardness – one best mechanical property of ceramics which
is utilized in many application such as abrasives, grinding
media
Hardest materials known are ceramics
Ceramics having Knoop hardness about 1000 or greater are
used for their abrasive characteristics
Creep – Ceramics experience creep deformation as a result
of exposure to stresses at elevated temperatures.
Modulus of elasticity, E, as a function of volume fraction of
porosity, P: E = E0 (1-1.9 P + 0.9 P2)
Porosity is deleterious to the flexural strength for two
reasons:
- reduces the cross-sectional area across where load is
applied
- act as stress concentrations

Material Science/Imperfections in Solids Lecture Notes
Satish Kailash Vasu/IISc, Bangalore M3/L1/V1/dec2004/1
Chapter 3. Imperfections in Solids
3.1 Point Defects
Vacancies and Self-Interstitials
A vacancy is a lattice position that is vacant because the atom is missing. It is created
when the solid is formed. There are other ways of making a vacancy, but they also occur
naturally as a result of thermal vibrations.
An interstitial is an atom that occupies a place outside the normal lattice position. It may
be the same type of atom as the others (self interstitial) or an impurity atom.
In the case of vacancies and interstitials, there is a change in the coordination of atoms
around the defect. This means that the forces are not balanced in the same way as for
other atoms in the solid, which results in lattice distortion around the defect.
The number of vacancies formed by thermal agitation follows the law:
NV = NA × exp(-QV/kT)
where NA is the total number of atoms in the solid, QV is the energy required to form a
vacancy, k is Boltzmann constant, and T the temperature in Kelvin (note, not in o
C or o
F).
When QV is given in joules, k = 1.38 × 10-23
J/atom-K. When using eV as the unit of
energy, k = 8.62 × 10-5
eV/atom-K.
Note that kT(300 K) = 0.025 eV (room temperature) is much smaller than typical
vacancy formation energies. For instance, QV(Cu) = 0.9 eV/atom. This means that NV/NA
at room temperature is exp(-36) = 2.3 × 10-16
, an insignificant number. Thus, a high
temperature is needed to have a high thermal concentration of vacancies. Even so, NV/NA
is typically only about 0.0001 at the melting point.
3.2 Theoretical yield point:
Theoretical yield is the maximum quantity of a product that could be formed in a
chemical reaction if all the limiting reactant reacted to form products (distinguished from
actual yield).
3.3 Dislocations—Linear Defects :
Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation
line) in the solid. They occur in high density and are very important in mechanical
properties of material. They are characterized by the Burgers vector, found by doing a
loop around the dislocation line and noticing the extra interatomic spacing needed to
close the loop. The Burgers vector in metals points in a close packed direction.

Material Science/Imperfections in Solids Lecture Notes
Edge dislocations occur when an extra plane is inserted. The dislocation line is at the end
of the plane. In an edge dislocation, the Burgers vector is perpendicular to the dislocation
line.
Screw dislocations result when displacing planes relative to each other through shear. In
this case, the Burgers vector is parallel to the dislocation line.

3.4 Interfacial Defects :
The environment of an atom at a surface differs from that of an atom in the bulk, in that
the number of neighbors (coordination) decreases. This introduces unbalanced forces
which result in relaxation (the lattice spacing is decreased) or reconstruction (the crystal
structure changes).
The density of atoms in the region including the grain boundary is smaller than the bulk
value, since void space occurs in the interface.
Surfaces and interfaces are very reactive and it is usual that impurities segregate there.
Since energy is required to form a surface, grains tend to grow in size at the expense of
smaller grains to minimize energy. This occurs by diffusion, which is accelerated at high
temperatures.
3.5 Bulk or Volume Defects :
Other defects exist in all solid materials that are much larger than those heretofore
discussed. A typical volume defect is porosity, often introduced in the solid during
processing. A common example is snow, which is highly porous ice.
3.6 Atomic Vibrations :
Atomic vibrations occur, even at zero temperature (a quantum mechanical effect) and
increase in amplitude with temperature. Vibrations displace transiently atoms from their
regular lattice site, which destroys the perfect periodicity .In a sense, these atomic
vibrations may be thought of as imperfections or defects. At room temperature, a typical
vibrational frequency of atoms is of the order of 10^13 vibrations per second, whereas the
amplitude is a few thousandths of a nanometer.

Imperfections in Solids
Module-3

1. Theoretical yield strength, Point defects and Line defects
or Dislocations
2. Interfacial defects, Bulk or Volume defects and Atomic
vibrations
Contents

Theoretical Yield Strength - 1
Ideal solids are made of atoms arranged in orderly way.

Theoretical Yield Strength – 2
Using a sin function to represent the variation in shear stress
b
x
m
Π
=
2
sinττ
b
x
m
Π
≈
2
ττ
a
Gx
G == γτ
a
bG
m
Π
=
2
τ
Π
=
2
G
mτ
(Hooke’s law)
If b≈a
G ≈ 20-150 GPa
Shear strength ≈ 3-30 GPa
(ideal)
Real strength values ≈ 0.5-10 MPa

Theoretical Yield Strength - 3
Theoretical strength of solids shall possess an ideal value
in the range of 3-30 GPa.
Real values observed in practice are 0.5-10 MPa.
The assumption of perfectly arranged atoms in a solid
may not valid…..i.e. atomic order must have been
disturbed.
Disordered atomic region is called defect or imperfection.
Based on geometry, defects are: Point defects (zero-D),
Line defects (1-D) or Dislocations, Interfacial defects (2-
D) and Bulk or Volume defects (3-D).

Point Defects - 1
Point defects are of zero-dimensional i.e. atomic disorder
is restricted to point-like regions.
Thermodynamically stable compared with other kind of
defects.

Point Defects - 2
Fraction of vacancy sites can be given as follows:
In ionic crystals, defects can form on the condition of
charge neutrality.
Two possibilities are:
kT
Q
e
N
n −
=

Line Defects
Line defects or Dislocations are abrupt change in atomic
order along a line.
They occur if an incomplete plane inserted between
perfect planes of atoms or when vacancies are aligned in a
line.
A dislocation is the defect responsible for the
phenomenon of slip, by which most metals deform
plastically.
Dislocations occur in high densities (108-1010 m-2 ), and
are intimately connected to almost all mechanical
properties which are in fact structure-sensitive.
Dislocation form during plastic deformation,
solidification or due to thermal stresses arising from rapid
cooling.

Line Defects – Burger’s Vector
A dislocation in characterized by Burger’s vector, b.
It is unique to a dislocation, and usually have the direction
of close packed lattice direction. It is also the slip
direction of a dislocation.
It represents the magnitude and direction of distortion
associated with that particular dislocation.
Two limiting cases of dislocations, edge and screw, are
characterized by Burger’s vector perpendicular to the
dislocation line (t) and Burger’s vector parallel to the
dislocation line respectively. Ordinary dislocation is of
mixed character of edge and screw type.

Line Defects – Edge Dislocation
It is also called as Taylor-Orowan dislocation.
It will have regions of compressive and tensile stresses on
either side of the plane containing dislocation.

Line Defects – Screw Dislocation
It is also called as Burger’s dislocation.
It will have regions of shear stress around the dislocation
line
For positive screw dislocation, dislocation line direction is
parallel to Burger’s vector, and vice versa.
A negative
dislocation

Line Defects – Dislocation Motion
Dislocations move under applied stresses, and thus causes
plastic deformation in solids.
Dislocations can move in three ways – glide/slip, cross-
slip and climb – depending on their character. Slip is
conservative in nature, while the climb is non-
conservative, and is diffusion-controlled.
Any dislocation can slip, but in the direction of its
burger’s vector.
Edge dislocation moves by slip and climb.
Screw dislocation moves by slip / cross-slip. Possibility
for cross-slip arises as screw dislocation does not have a
preferred slip plane as edge dislocation have.

Line Defect – Dislocation Characteristics
A dislocation line cannot end at abruptly inside a crystal.
It can close-on itself as a loop, either end at a node or
surface.
Burger’s vector for a dislocation line is invariant i.e. it
will have same magnitude and direction all along the
dislocation line.
Energy associated with a dislocation because of presence
of stresses is proportional to square of Burger’s vector
length. Thus dislocations, at least of same nature, tend to
stay away from each other.
Dislocations are, thus, two types – full and partial
dislocations. For full dislocation, Burger’s vector is
integral multiple of inter-atomic distance while for partial
dislocation, it is fraction of lattice translation.

Interfacial Defects - 1
An interfacial defect is a 2-D imperfection in crystalline
solids, and have different crystallographic orientations on
either side of it.
Region of distortion is about few atomic distances.
They usually arise from clustering of line defects into a
plane.
These imperfections are not thermodynamically stable,
but meta-stable in nature.
E.g.: External surface, Grain boundaries, Stacking faults,
Twin boundaries, Phase boundaries.

Interfacial Defects - 2
Grain boundaries

Bulk or Volume Defects
Volume defects are three-dimensional in nature.
These defects are introduced, usually, during processing
and fabrication operations like casting, forming etc.
E.g.: Pores, Cracks, Foreign particles
These defects act like stress raisers, thus deleterious to
mechanical properties of parent solids.
In some instances, foreign particles are added to
strengthen the solid – dispersion hardening. Particles
added are hindrances to movement of dislocations which
have to cut through or bypass the particles thus increasing
the strength.

Atomic Vibrations
Atoms are orderly arranged, but they are expected to
vibrate about their positions where the amplitude of
vibration increases with the temperature.
After reaching certain temperature, vibrations are
vigorous enough to rupture the inter-atomic forces casing
melting of solids.
Average amplitude of vibration at room temperature is
about 10-12m i.e. thousandth of a nanometer.
Frequency of vibrations is the range of 1013 Hz.
Temperature of a solid body is actually a measure of
vibrational activity of atoms and/or molecules.

Material Science/Mechanical Properties of Metals Lecture Notes
Chapter 4. Mechanical Properties of Metals
4.1 Elastic deformation:
When the stress is removed, the material returns to the dimension it had before the load
was applied. Valid for small strains (except the case of rubbers).
Deformation is reversible, non permanent
4.2 Plastic deformation:
When the stress is removed, the material does not return to its previous dimension but
there is a permanent, irreversible deformation.
In tensile tests, if the deformation is elastic, the stress-strain relationship is called Hooke's
law:
σ = E ε
That is, E is the slope of the stress-strain curve. E is Young's modulus or modulus of
elasticity. In some cases, the relationship is not linear so that E can be defined
alternatively as the local slope:
E = dσ/dε
Shear stresses produce strains according to:
τ = G γ
where G is the shear modulus.Elastic moduli measure the stiffness of the material. They
are related to the second derivative of the interatomic potential, or the first derivative of
the force vs. internuclear distance (Fig. 6.6). By examining these curves we can tell
which material has a higher modulus. Due to thermal vibrations the elastic modulus
decreases with temperature. E is large for ceramics (stronger ionic bond) and small for
polymers (weak covalent bond). Since the interatomic distances depend on direction in
the crystal, E depends on direction (i.e., it is anisotropic) for single crystals. For randomly
oriented policrystals, E is isotropic.
4.4 Yielding under multiaxial stress-strain curves
4.5 Yield criteria and macroscopic aspects of plastic deformation
Gross plastic deformation of a polycrystalline specimen corresponds to the comparable
distortion of the individual grains by means of slip. During deformation, mechanical
integrity and coherency are maintained along the grain boundaries; that is, the grain
boundaries is constrained, to some degree, in the shape it may assume by its neighboring

grains. Before deformation the grains are equiaxed, or have approximately the same
dimension in all directions. For this particular deformation, the grains become elongated
along the directions. For this particular deformation, the grains become elongated along
the direction in which the specimen was extended.
4.6 Property variability and design factors
To take into account variability of properties, designers use, instead of an average value
of, say, the tensile strength, the probability that the yield strength is above the minimum
value tolerable. This leads to the use of a safety factor N > 1. Thus, a working value for
the tensile strength would be σW = σTS / N.
Utilization of design stress is usually preferred since it is based on the anticipated
maximum applied stress instead of the yield strength of the material. The choice of an
appropriate value of N is necessary. If N is too large, then component over design will
result; that is , either too much material or an alloy having a higher than necessary
strength will be used. Values normally range between 1.2 and 4.0. Selection of N will
depend on a number of factors, including economics, previous experience, the accuracy
with which mechanical forces and material properties may be determined and most
important, the consequences of failure in terms of loss of life or property damage.

4.3 Interpretation of tensile stress-strain curves:
Tensile Properties
Yield point. If the stress is too large, the strain deviates from being proportional to the
stress. The point at which this happens is the yield point because there the material yields,
deforming permanently (plastically).
Yield stress. Hooke's law is not valid beyond the yield point. The stress at the yield point
is called yield stress, and is an important measure of the mechanical properties of
materials. In practice, the yield stress is chosen as that causing a permanent strain of
0.002
The yield stress measures the resistance to plastic deformation.
The reason for plastic deformation, in normal materials, is not that the atomic bond is
stretched beyond repair, but the motion of dislocations, which involves breaking and
reforming bonds.
Plastic deformation is caused by the motion of dislocations.
Tensile strength. When stress continues in the plastic regime, the stress-strain passes
through a maximum, called the tensile strength (σTS) , and then falls as the material starts
to develop a neck and it finally breaks at the fracture point .
For structural applications, the yield stress is usually a more important property than the
tensile strength, since once the it is passed, the structure has deformed beyond acceptable
limits.
Ductility. The ability to deform before braking. It is the opposite of brittleness. Ductility
can be given either as percent maximum elongation εmax or maximum area reduction.
%EL = εmax x 100 %
%AR = (A0 - Af)/A0
These are measured after fracture (repositioning the two pieces back together).
Resilience. Capacity to absorb energy elastically. The energy per unit volume is the
area under the strain-stress curve in the elastic region.
Toughness. Ability to absorb energy up to fracture. The energy per unit volume is the
total area under the strain-stress curve. It is measured by an impact test .

True Stress and Strain
When one applies a constant tensile force the material will break after reaching the tensile
strength. The material starts necking (the transverse area decreases) but the stress cannot
increase beyond σTS. The ratio of the force to the initial area, what we normally do, is
called the engineering stress. If the ratio is to the actual area (that changes with stress)
one obtains the true stress.

4.4 Yielding under multiaxial stress-strain curves
4.5 Yield criteria and macroscopic aspects of plastic deformation
Gross plastic deformation of a polycrystalline specimen corresponds to the comparable
distortion of the individual grains by means of slip. During deformation, mechanical
integrity and coherency are maintained along the grain boundaries; that is, the grain
boundaries is constrained, to some degree, in the shape it may assume by its neighboring
grains. Before deformation the grains are equiaxed, or have approximately the same
dimension in all directions. For this particular deformation, the grains become elongated
along the directions. For this particular deformation, the grains become elongated along
the direction in which the specimen was extended.
4.6 Property variability and design factors
To take into account variability of properties, designers use, instead of an average value
of, say, the tensile strength, the probability that the yield strength is above the minimum
value tolerable. This leads to the use of a safety factor N > 1. Thus, a working value for
the tensile strength would be σW = σTS / N.
Utilization of design stress is usually preferred since it is based on the anticipated
maximum applied stress instead of the yield strength of the material. The choice of an
appropriate value of N is necessary. If N is too large, then component over design will
result; that is , either too much material or an alloy having a higher than necessary
strength will be used. Values normally range between 1.2 and 4.0. Selection of N will
depend on a number of factors, including economics, previous experience, the accuracy
with which mechanical forces and material properties may be determined and most
important, the consequences of failure in terms of loss of life or property damage.

Mechanical Properties Of Metals
Module - 4

1. Elastic deformation and Plastic deformation
2. Interpretation of tensile stress-strain curves
3. Yielding under multi-axial stress, Yield criteria,
Macroscopic aspects of plastic deformation and Property
variability & Design considerations
Contents

Mechanical Loads - Deformation
Object
External load
translation rotation deformation
distortion – change in shape
dilatation – change in size

Temporary / recoverable Permanent
time independent – elastic
time dependent – anelastic (under
load),
elastic aftereffect (after removal
of load)
Deformation – Function Of Time?
time independent – plastic
time dependent –creep
(under load),
combination of recoverable and permanent, but time
dependent – visco-elastic

Engineering Stress – Engineering Strain
Load applied acts over an area.
Parameter that characterizes the load effect is given as
load divided by original area over which the load acts. It
is called conventional stress or engineering stress or
simply stress. It is denoted by s.
Corresponding change in length of the object is
characterized using parameter – given as per cent change
in the length – known as strain. It is denoted by e.
As object changes its dimensions under applied load,
engineering stress and strain are not be the true
representatives.
0
0
0
,
L
LL
e
A
P
s
−
==

True Stress – True Strain
True or Natural stress and strain are defined to give true
picture of the instantaneous conditions.
True strain:
True stress:
∑ +
−
+
−
+
−
= ...
2
23
1
12
0
01
L
LL
L
LL
L
LL
ε
0
ln
0
L
L
L
dL
L
L
== ∫ε
)1(0
0
+=== es
A
A
A
P
A
P
σ

Different Loads – Strains

Elastic Deformation - 1
A material under goes elastic deformation first followed
by plastic deformation. The transition is not sharp in
many instances.
For most of the engineering materials, complete elastic
deformation is characterized by strain proportional to
stress. Proportionality constant is called elastic modulus
or Young’s modulus, E.
Non-linear stress-strain relation is applicable for
materials. E.g.: rubber.
εσ ∝ εσ E=

For materials without linear stress-strain portion, either tangent
or secant modulus is used in design calculations.
The tangent modulus is
taken as the slope of
stress-strain curve at
some specified level.
Secant module
represents the slope of
secant drawn from the
origin to some given
point of the σ-ε curve.

Theoretical basis for elastic deformation – reversible
displacements of atoms from their equilibrium positions
– stretching of atomic bonds.
Elastic moduli measures stiffness of material. It can also
be a measure of resistance to separation of adjacent
atoms.
Elastic modulus = fn (inter-atomic forces)
= fn (inter-atomic distance)
= fn (crystal structure, orientation)
=> For single crystal elastic moduli are not isotropic.
For a polycrystalline material, it is considered as
isotropic.
Elastic moduli slightly changes with temperature
(decreases with increase in temperature).

Linear strain is always accompanied by lateral strain, to
maintain volume constant.
The ratio of lateral to linear strain is called Poisson’s ratio
(ν).
Shear stresses and strains are related as τ = Gγ, where G is
shear modulus or elastic modulus in shear.
Bulk modulus or volumetric modulus of elasticity is
defined as ratio between mean stress to volumetric strain.
K = σm/∆
All moduli are related through Poisson’s ratio.
)1(2 ν+
=
E
G
)21(3 ν
σ
−
=
∆
=
E
K m

Plastic Deformation - 1
Following the elastic deformation, material undergoes
plastic deformation.
Also characterized by relation between stress and strain at
constant strain rate and temperature.
Microscopically…it involves breaking atomic bonds,
moving atoms, then restoration of bonds.
Stress-Strain relation here is complex because of atomic
plane movement, dislocation movement, and the obstacles
they encounter.
Crystalline solids deform by processes – slip and twinning
in particular directions.
Amorphous solids deform by viscous flow mechanism
without any directionality.

Because of the complexity involved, theory of plasticity
neglects the following effects:
- Anelastic strain, which is time dependent recoverable
strain.
- Hysteresis behavior resulting from loading and un-
loading of material.
- Bauschinger effect – dependence of yield stress on
loading path and direction.
Equations relating stress and strain are called constitutive
equations.
A true stress-strain curve is called flow curve as it gives
the stress required to cause the material to flow plastically
to certain strain.

Because of the complexity involved, there have been
many stress-strain relations proposed.
),,,( turemicrostrucTfn εεσ &=
n
Kεσ =
m
Kεσ &=
n
K )( 0 εεσ +=
n
o Kεσσ +=
Strain hardening exponent, n = 0.1-0.5
Strain-rate sensitivity, m = 0.4-0.9
Yield strength – σ0
Strain from previous work – ε0

Tensile Stress-Strain Curve - 1
A – Starting point E– Tensile strength
E’ – Corresponding to E on flow curve
F – Fracture point I – Fracture strain

A – Starting point B – Proportional limit
C – Elastic limit D – Yield limit
G – 0.2% offset strain H – Yield strain

Apart from different strains and strength points, two other
important parameters can be deduced from the curve are –
resilience and toughness.
Resilience (Ur) – ability to absorb energy under elastic
deformation
Toughness (Ut) – ability to absorb energy under loading
involving plastic deformation. Represents combination of
both strength and ductility.
E
s
E
s
sesUr
22
1
2
1 2
00
000 ===
f
u
fut e
ss
esU
2
0 +
≈≈ fut esU
3
2
≈
area ADH
area AEFI (for brittle
materials)

Yielding Under Multi-Axial Stress
With on-set of necking, uni-axial stress condition turns
into tri-axial stress as geometry changes tales place. Thus
flow curve need to be corrected from a point
corresponding to tensile strength. Correction has been
proposed by Bridgman.
[ ])2/1ln()/21(
)(
RaaR
avgx
++
=
σ
σ
where
(σx)avg measured stress in the axial direction,
a – smallest radius in the neck region,
R – radius of the curvature of neck

Yield Criteria - 1
Von Mises or Distortion energy criterion:
yielding occurs once second invariant of stress deviator
(J2) reaches a critical value. In other terms, yield starts
once the distortion energy reaches a critical value.
2
2 kJ = [ ]2
13
2
32
2
212 )()()(
6
1
σσσσσσ −+−+−=J
Under uni-axial tension, σ1 = σ0, and σ2= σ3= 0
[ ] 2
1
2
13
2
32
2
210
0
22
0
2
0
)()()(
2
1
3)(
6
1
σσσσσσσ
σσσ
−+−+−=⇒
=⇒=+ kk
00 577.0
3
1
σσ ==k where k – yield stress under shear

Yield Criteria - 2
Tresca or Maximum shear stress criterion
yielding occurs once the maximum shear stress of the
stress system equals shear stress under uni-axial stress.
2
31
max
σσ
τ
−
=
Under uni-axial tension, σ1 = σ0, and σ2= σ3= 0
031
0
0
31
max
22
σσσ
σ
τ
σσ
τ =−⇒==
−
=
0
31
2
1
2
σ
σσ
=
−
=k
Under pure shear stress conditions (σ1 =- σ3 = k, σ2 = 0)

Macroscopic Aspects – Plastic
Deformation - 1
As a result of plastic deformation (Dislocation generation,
movement and (re-)arrangement ), following observations
can be made at macroscopic level:
dimensional changes
change in grain shape
formation of cell structure in a grain

Macroscopic Aspects – Plastic
Deformation- 2

n
x
x
n
i
i∑=
= 1
21
1
2
1
)(
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
=
∑=
n
xx
s
n
i
i
Property Variability
Scatter in measured properties of engineering materials is
inevitable because of number of factors such as:
test method
specimen fabrication procedure
operator bias
apparatus calibration, etc.
Average value of x over n
samples.
Property variability measure –
Standard deviation
Scatter limits:
x - s, +sx

Design Consideration - 1
To account for property variability and unexpected
failure, designers need to consider tailored property
values. Parameters for tailoring: safety factor (N) and
design factor (N’). Both parameters take values greater
than unity only.
E.g.: Yield strength
σw = σy / N σd = N’σc
where σw – working stress
σy – yield strength
σd – design stress
σc – calculated stress

Design Consideration - 2
Values for N ranges around: 1.2 to 4.0.
Higher the value of N, lesser will the design efficiency i.e.
either too much material or a material having a higher
than necessary strength will be used.
Selection of N will depend on a number of factors:
Economics.
Previous experience
The accuracy with which mechanical forces
Material properties
The consequences of failure in terms of loss of life or
property damage.

Material Science/Diffusion Lecture Notes
Chapter 5. Diffusion
5.1 Diffusion Mechanisms
Atom diffusion can occur by the motion of vacancies (vacancy diffusion) or impurities
(impurity diffusion). The energy barrier is that due to nearby atoms which need to move
to let the atoms go by. This is more easily achieved when the atoms vibrate strongly, that
is, at high temperatures.
There is a difference between diffusion and net diffusion. In a homogeneous material,
atoms also diffuse but this motion is hard to detect. This is because atoms move randomly
and there will be an equal number of atoms moving in one direction than in another. In
inhomogeneous materials, the effect of diffusion is readily seen by a change in
concentration with time. In this case there is a net diffusion. Net diffusion occurs
because, although all atoms are moving randomly, there are more atoms moving in
regions where their concentration is higher.
5.2 Steady-State Diffusion
The flux of diffusing atoms, J, is expressed either in number of atoms per unit area and
per unit time (e.g., atoms/m2
-second) or in terms of mass flux (e.g., kg/m2
-second).
Steady state diffusion means that J does not depend on time. In this case, Fick’s first law
holds that the flux along direction x is:
J = – D dC/dx
Where dC/dx is the gradient of the concentration C, and D is the diffusion constant. The
concentration gradient is often called the driving force in diffusion (but it is not a force in
the mechanistic sense). The minus sign in the equation means that diffusion is down the
concentration gradient.
5.3 Nonsteady-State Diffusion
This is the case when the diffusion flux depends on time, which means that a type of
atoms accumulates in a region or that it is depleted from a region (which may cause them
to accumulate in another region).

Material Science/Diffusion Lecture Notes
5.4 Factors that influence diffusion
As stated above, there is a barrier to diffusion created by neighboring atoms that need to
move to let the diffusing atom pass. Thus, atomic vibrations created by temperature assist
diffusion. Also, smaller atoms diffuse more readily than big ones, and diffusion is faster
in open lattices or in open directions. Similar to the case of vacancy formation, the effect
of temperature in diffusion is given by a Boltzmann factor: D = D0 × exp(–Qd/kT).
5.5 Non-equilibrium transformation and microstructure:
Non-equilibrium solidification
Conditions of equilibrium solidification and the development of microstructures are
realized only for extremely slow cooling rates. The reason for that is that with changes in
temperature, there must be readjustments in the compositions of liquids and solid phases
in accordance with the phase diagram. These readjustments are accomplished by
diffusional processes- that is, diffusion in both solid and liquid phases and also across the
solid-liquid interface.
Non-equilibrium cooling
During cooling metastable equilibrium have been continuously maintained, that is
sufficient time has been allowed to each new temperature for any necessary adjustment in
phase compositions and relative amounts as predicted from iron-iron carbide phase
diagram. In most situations these cooling rates are impractically slow and really
unnecessary; in fact, on many occasions non-equilibrium conditions are desirable. Two
non equilibrium effects of practical importance are (1) the occurrence of phase changes
or transformations at temperatures other than those predicted by phase boundary lines on
the phase diagram, and (2) the existence at room temperature of non-equilibrium phases
that do not appear on the phase diagram.

1. Diffusion mechanisms and steady-state & non-steady-state
diffusion
2. Factors that influence diffusion and non-equilibrium
transformation & microstructure
Contents

Diffusion Phenomenon
Definition – Diffusion is the process of mass flow in
which atoms change their positions relative to neighbors
in a given phase under the influence of thermal and a
gradient.
The gradient can be a compositional gradient, an electric
or magnetic gradient, or stress gradient.
Many reactions in solids and liquids are diffusion
dependent.
Diffusion is very important in many industrial and
domestic applications.
E.g.: Carburizing the steel, annealing homogenization
after solidification, coffee mixing, etc.

Diffusion Mechanisms - 1
From an atomic perceptive, diffusion is a step wise
migration of atoms from one lattice position to another.
Migration of atoms in metals/alloys can occur in many
ways, and thus corresponding diffusion mechanism is
defined.

Most energetically favorable diffusion mechanism is
vacancy mechanism. Other important mechanism is
interstitial mechanism by which
hydrogen/nitrogen/oxygen diffuse into many metals.
In ionic crystal, Schottky and Frankel defects assist the
diffusion process.
When Frenkel defects dominate in an ionic crystal, the
cation interstitial of the Frenkel defect carries the
diffusion flux. If Schottky defects dominate, the cation
vacancy carries the diffusion flux.
In thermal equilibrium, in addition to above defects, ionic
crystal may have defects generated by impurities and by
deviation from stochiometry.

Diffusion that occurs over a region is volume diffusion.
Diffusion can occur with aid of linear/surface defects,
which are termed as short-circuit paths. These enhances
the diffusivity.
However, diffusion by short-circuit paths
(E.g.:dislocaions, grain boundaries) is small because the
effective cross-sectional area over which these are
operative is small.
Diffusion can occur even in pure metals that is not
noticeable. Diffusion that occurs in alloys which is
noticeable called net diffusion as there occurs a noticeable

Diffusion – Time Function? - 1
Steady-state and Non-steady-state diffusion processes are
distinguished by the parameter – diffusion flux, J.
Flux is defined as number of atoms crossing a unit area
perpendicular to a given direction per unit time.
Thus flux has units of atoms/m2.sec or moles/m2.sec.
If the flux is independent of time, then the diffusion
process is called steady-state diffusion. On the other hand,
for non-steady-state diffusion process, flux is dependent
on time.

Diffusion – Time Function? - 2

Steady-State Diffusion
Steady-state diffusion processes is characterized by Fick’s
first law, which states that diffusion flux is proportional to
The proportionality constant, D, is called diffusion
coefficient or diffusivity. It has units as m2/sec.
For one-dimensional case, it can be written as
where D is the diffusion constant, dc/dx is the gradient of
the concentration c, dn/dt is the number atoms crossing per
unit time a cross-sectional plane of area A.
E.g.: Hydrogen gas purification using palladium metal
sheet.
dt
dn
Adx
dc
DJx
1
=−= ),( txfJx ≠

Non-Steady-State Diffusion 1
Most interesting industrial applications are non-steady-state
diffusion in nature.
Non-steady-state diffusion is characterized by Fick’s second
law, which can be expressed as
where dc/dt is the time rate of change of concentration at a
particular position, x.
A meaningful solution can be obtained for the above
second-order partial equation if proper boundary conditions
can be defined.
⎟
⎠
⎞
⎜
⎝
⎛
=−=
dx
dc
D
dx
d
dx
dJ
dt
dc
2
2
dx
cd
D
dt
dc
=

Non-Steady-State Diffusion 2
One common set of boundary conditions and the solution is:
For t = 0, C = C0 at
For t > 0, C = Cs at x=0
C = C0 at
The solution is
where Cx represents the concentration at depth x after time t.
The term erf stands for Gaussian error function, whose
values can be obtained from standard mathematical tables.
E.g.: Carburization and decarburization of steel, corrosion
resistance of duralumin, doping of semi-conductors, etc.
∞=x
∞≤≤ x0
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
−
−
Dt
x
erf
CC
CC
s
x
2
1
0
0

Influencing Factors For Diffusion 1
Diffusing species: Interstitial atoms diffuse easily than
substitution atoms. Again substitution atoms with small
difference in atomic radius with parent atoms diffuse
with ease than atoms with larger diameter.
Temperature: It is the most influencing factor. Their
relations can be given by the following Arrhenius
equation
where D0 is a pre-exponential constant, Q is the
activation energy for diffusion, R is gas constant
(Boltzmann’s constant) and T is absolute temperature.
⎟
⎠
⎞
⎜
⎝
⎛
−=
RT
Q
DD exp0

Influencing Factors For Diffusion - 2
From the temperature dependence of diffusivity, it is
experimentally possible to find the values of Q and D0.
Lattice structure: Diffusivity is high for open lattice structure
and in open lattice directions.
Presence of defects: The other important influencing factor of
diffusivity is presence of defects. Many atomic/volume
diffusion processes are influenced by point defects like
vacancies, interstitials.
Apart from these, dislocations and grain boundaries, i.e.
short-circuit paths as they famously known, greatly
enhances the diffusivity.

Non-Equilibrium Transformation &
Microstructure 1
Non-equilibrium transformation occurs, usually, during
many of the cooling processes like casting process.
Equilibrium transformation requires extremely large time
which is in most of the cases impractical and not
necessary.
Alloy solidification process involves diffusion in liquid
phase, solid phase, and also across the interface between
liquid and solid.
As diffusion is very sluggish in solid, and time available
for it is less, compositional gradients develop in cast
components.
These are two kinds: coring and segregation.

Microstructure 2
Coring: It is defined as gradual compositional changes
across individual grains.
Coring is predominantly observed in alloys having a
marked difference between liquidus and solidus
temperatures.
It is often being removed by subsequent annealing and/or
hot-working.
It is exploited in zone-refining technique to produce high-
purity metals.
Segregation: It is defined as concentration of particular,
usually impurity elements, along places like grain
boundaries, and entrapments.
Segregation is also useful in zone refining, and also in the
production of rimming steel.

Microstructure 3
Micro-segregation is used to describe the differences in
composition across a crystal or between neighboring crystals.
Micro-segregation can often be removed by prolonged
annealing or by hot-working.
Macro-segregation is used to describe more massive
heterogeneities which may result from entrapment of liquid
pockets between growing solidifying zones.
Macro-segregation persists through normal heating and
working operations.
Two non equilibrium effects of practical importance:(1) the
occurrence of phase changes or transformations at temperatures
other than those predicted by phase boundary lines on the phase
diagram, and (2) the existence of non-equilibrium phases at
room temperature that do not appear on the phase diagram.

Material Science/Dislocations and Strengthening Mechanisms Lecture Notes
Chapter 6. Dislocations and Strengthening Mechanisms
6.1 Basic Concept of dislocation
Dislocations can be edge dislocations, screw dislocations and exist in combination of the
two. Their motion (slip) occurs by sequential bond breaking and bond reforming . The
number of dislocations per unit volume is the dislocation density, in a plane they are
measured per unit area.
Characteristics of Dislocations
There is strain around a dislocation which influences how they interact with other
dislocations, impurities, etc. There is compression near the extra plane (higher atomic
density) and tension following the dislocation line.
Dislocations interact among themselves. When they are in the same plane, they repel if
they have the same sign and annihilate if they have opposite signs (leaving behind a
perfect crystal). In general, when dislocations are close and their strain fields add to a
larger value, they repel, because being close increases the potential energy (it takes
energy to strain a region of the material).
The number of dislocations increases dramatically during plastic deformation.
Dislocations spawn from existing dislocations, and from defects, grain boundaries and
surface irregularities.
Plastic Deformation
Slip directions vary from crystal to crystal. When plastic deformation occurs in a grain, it
will be constrained by its neighbors, which may be less favorably oriented. As a result,
polycrystalline metals are stronger than single crystals (the exception is the perfect
single crystal, as in whiskers.)
6.2 Mechanisms of Strengthening in Metals
General principles. Ability to deform plastically depends on ability of dislocations to
move. Strengthening consists in hindering dislocation motion. We discuss the methods of
grain-size reduction, solid-solution alloying and strain hardening. These are for single-
phase metals. We discuss others when treating alloys. Ordinarily, strengthening reduces
ductility.

Strengthening by Grain Size Reduction
This is based on the fact that it is difficult for a dislocation to pass into another grain,
especially if it is very misaligned. Atomic disorder at the boundary causes discontinuity
in slip planes. For high-angle grain boundaries, stress at end of slip plane may trigger
new dislocations in adjacent grains. Small angle grain boundaries are not effective in
blocking dislocations.
The finer the grains, the larger the area of grain boundaries that impedes dislocation
motion. Grain-size reduction usually improves toughness as well. Usually, the yield
strength varies with grain size d according to:
σy = σ0 + ky / d1/2
Grain size can be controlled by the rate of solidification and by plastic deformation.
Solid-Solution Strengthening
Adding another element that goes into interstitial or substitutional positions in a solution
increases strength. The impurity atoms cause lattice strain (Figs. 7.17 and 7.18) which
can "anchor" dislocations. This occurs when the strain caused by the alloying element
compensates that of the dislocation, thus achieving a state of low potential energy. It
costs strain energy for the dislocation to move away from this state (which is like a
potential well). The scarcity of energy at low temperatures is why slip is hindered.
Pure metals are almost always softer than their alloys.
Strain Hardening
Ductile metals become stronger when they are deformed plastically at temperatures well
below the melting point (cold working). (This is different from hot working is the
shaping of materials at high temperatures where large deformation is possible.) Strain
hardening (work hardening) is the reason for the elastic recovery discussed in Ch. 6.8.
The reason for strain hardening is that the dislocation density increases with plastic
deformation (cold work) due to multiplication. The average distance between dislocations
then decreases and dislocations start blocking the motion of each one.
The measure of strain hardening is the percent cold work (%CW), given by the relative
reduction of the original area, A0 to the final value Ad :
%CW = 100 (A0–Ad)/A0

6.3 Recovery, recrystallization and Grain Growth
Plastic deformation causes 1) change in grain size, 2) strain hardening, 3) increase in the
dislocation density. Restoration to the state before cold-work is done by heating through
two processes: recovery and recrystallization. These may be followed by grain growth.
Recovery
Heating increased diffusion enhanced dislocation motion relieves internal strain
energy and reduces the number of dislocation. The electrical and thermal conductivity are
restored to the values existing before cold working.
Recrystallization
Strained grains of cold-worked metal are replaced, upon heating, by more regularly-
spaced grains. This occurs through short-range diffusion enabled by the high temperature.
Since recrystallization occurs by diffusion, the important parameters are both temperature
and time.
Recrystallization temperature: is that at which the process is complete in one hour. It is
typically 1/3 to 1/2 of the melting temperature. It falls as the %CW is increased. Below a
"critical deformation", recrystallization does not occur.
Grain Growth
The growth of grain size with temperature can occur in all polycrystalline
materials. It occurs by migration of atoms at grain boundaries by
diffusion, thus grain growth is faster at higher temperatures. The "driving
force" is the reduction of energy, which is proportional to the total area.
Big grains grow at the expense of the small ones.

Dislocations And Strengthening Mechanisms
Module-6

1. Dislocations & Plastic deformation and Mechanisms of plastic
deformation in metals
2. Strengthening mechanisms in metals
3. Recovery, Recrystallization and Grain growth
Contents

Plastic Deformation – Dislocations
Permanent plastic deformation is due to shear process –
atoms change their neighbors.
Inter-atomic forces and crystal structure plays an important
role during plastic deformation.
Cumulative movement of dislocations leads to gross plastic
deformation.
Edge dislocation move by slip and climb, while screw
dislocation move by slip and cross-slip.
During their movement, dislocations tend to interact. The
interaction is very complex because of number of
dislocations moving over many slip systems in different
directions.

Plastic Deformation – Dislocations
Dislocations moving on parallel planes may annihilate each
other, resulting in either vacancies or interstitials.
Dislocations moving on non-parallel planes hinder each
other’s movement by producing sharp breaks – jog (break
out of slip plane), kink (break in slip plane)
Other hindrances to dislocation motion – interstitial and
substitutional atoms, foreign particles, grain boundaries,
external grain surface, and change in structure due to phase
change.
Material strength can be increased by arresting dislocation
motion.

Plastic Deformation Mechanisms – Slip
1
Mainly two kinds: slip and twinning.
Slip is prominent among the two. It involves sliding of
blocks of crystal over other along slip planes.
Slip occurs when shear stress applied exceeds a critical
value.
Slip occurs most readily in specific directions (slip
directions) on certain crystallographic planes.
Feasible combination of a slip plane together with a slip
direction is considered as a slip system.
During slip each atom usually moves same integral number
of atomic distances along the slip plane.

Plastic Deformation Mechanisms – Slip
2
Extent of slip depends on many factors - external load and
the corresponding value of shear stress produced by it,
crystal structure, orientation of active slip planes with the
direction of shearing stresses generated.
Slip occurs when shear stress applied exceeds a critical
value.
For single crystal, Schmid defined critical shear stress as
λφ
λφσλφ
φ
λ
τ
coscos
coscoscoscos
cos
cos
=⇒
===
m
A
P
A
P
R

Plastic Deformation Mechanisms - Slip
3
In a polycrystalline aggregate, individual grains provide a
mutual geometrical constraint on one other, and this
precludes plastic deformation at low applied stresses.
Slip in polycrystalline material involves generation,
movement and (re-)arrangement of dislocations.
During deformation, mechanical integrity and coherency
are maintained along the grain boundaries.
A minimum of five independent slip systems must be
operative for a polycrystalline solid to exhibit ductility and
maintain grain boundary integrity – von Mises.
On the other hand, crystal deform by twinning.

<110>{110}NaCl
Close packed
directions
Basal plane
Prismatic & Pyramidal
planes
More common
Less common
HCP
<111>{110}
{112},{123}
More common
Less common
BCC
<110>{111}FCC
Slip
directions
Slip planesOccurrenceCrystal
Slip Systems

Plastic Deformation Mechanisms -
Twinning
It results when a portion of crystal takes up an orientation
that is related to the orientation of the rest of the untwined
lattice in a definite, symmetrical way.
The important role of twinning in plastic deformation is
that it causes changes in plane orientation so that further
slip can occur.
Twinning also occurs in a definite direction on a specific
plane for each crystal structure.
[¯1011](10¯12)Zn, Cd, Mg, TiHCP
[111](112)α-Fe, TaBCC
[112](111)Ag, Au, CuFCC
Twin
direction
Twin planeExampleCrystal

Slip Vs. Twinning
On a particular plane
for each crystal
On many slip systems
simultaneouslyOccurrence
Micro secondsMilli secondsTime required
Every plane of
region involvedWidely spread planesOccurs on
FractionsMultiples
Size (in terms of
inter-atomic
distance)
Differ across the
twin plane
Same above and
below the slip plane
Crystal
orientation
during/in twinningduring/in slip

Strengthening Mechanisms
Material can be increased by hindering dislocation, which
is responsible for plastic deformation.
Different ways to hinder dislocation motion / Strengthening
mechanisms:
in single-phase materials
- Grain size reduction
- Solid solution strengthening
- Strain hardening
in multi-phase materials
- Precipitation strengthening
- Dispersion strengthening
- Fiber strengthening
- Martensite strengthening

Strengthening By Grain Size Reduction
1
It is based on the fact that dislocations will experience
hindrances while trying to move from a grain into the next
because of abrupt change in orientation of planes.
Hindrances can be two types: forcible change of slip
direction, and discontinuous slip plane.
Smaller the grain size, often a dislocation encounters a
hindrance. Yield strength of material will be increased.
Yield strength is related to grain size (diameter, d) as Hall-
Petch relation:
Grain size can be tailored by controlled cooling or by
plastic deformation followed by appropriate heat treatment.
21−
+= kdiy σσ

Strengthening By Grain Size Reduction
2Grain size reduction improves not only strength, but also the
toughness of many alloys.
If d is average grain diameter, Sv is grain boundary area per unit
volume, NL is mean number of intercepts of grain boundaries
per unit length of test line, NA is number of grains per unit area
on a polished surface:
Grain size can also be measured by comparing the grains at a
fixed magnification with standard grain size charts.
Other method: Use of ASTM grain size number (Z). It is
related to grain diameter, D (in mm) as follows:
Lv NS 2=
Lv NS
d
2
33
==
AN
d
π
6
=
1
2
645
100
1
−
= G
D

Solid Solution Strengthening
Impure foreign atoms in a single phase material produces
lattice strains which can anchor the dislocations.
Effectiveness of this strengthening depends on two factors
– size difference and volume fraction of solute.
Solute atoms interact with dislocations in many ways:
- elastic interaction
- modulus interaction
- stacking-fault interaction
- electrical interaction
- short-range order interaction
- long-range order interaction
Elastic, modulus, and long-range order interactions are of
long-range i.e. they are relatively insensitive to temperature
and continue to act about 0.6 Tm.

Yield Point Phenomenon - 1
Localized, heterogeneous
type of transition from
elastic to plastic
deformation marked by
abrupt elastic-plastic
transition – Yield point
phenomenon.
It characterizes that
material needs higher
stress to initiate plastic
flow than to continue it.

Yield Point Phenomenon - 2
The bands are called Lüders bands / Hartmann lines /
stretcher stains, and generally are approximately 45 to the
tensile axis.
Occurrence of yield point is associated with presence of
small amounts of interstitial or substitutional impurities.
It’s been found that either unlocking of dislocations by a
high stress for the case of strong pinning or generation of
new dislocations are the reasons for yield-point
phenomenon.
Magnitude of yield-point effect will depend on energy of
interaction between solute atoms and dislocations and on
the concentration of solute atoms at the dislocations.

Strain Hardening - 1
Phenomenon where ductile metals become stronger and
harder when they are deformed plastically is called strain
hardening or work hardening.
Increasing temperature lowers the rate of strain hardening.
Hence materials are strain hardened at low temperatures,
thus also called cold working.
During plastic deformation, dislocation density increases.
And thus their interaction with each other resulting in
increase in yield stress.
Dislocation density (ρ) and shear stress (τ) are related as
follows:
ρττ A+= 0

Strain Hardening - 2
During strain hardening, in addition to mechanical properties
physical properties also changes:
- a small decrease in density
- an appreciable decrease in electrical conductivity
- small increase in thermal coefficient of expansion
- increased chemical reactivity (decrease in corrosion
resistance).
Deleterious effects of cold work can be removed by heating the
material to suitable temperatures – Annealing. It restores the
original properties into material. It consists of three stages –
recovery, recrystallization and grain growth.
In industry, alternate cycles of strain hardening and annealing
are used to deform most metals to a very great extent.

Precipitation & Dispersion Hardening
1
Foreign particles can also obstructs movement of dislocations
i.e. increases the strength of the material.
Foreign particles can be introduced in two ways –
precipitation and mixing-and-consolidation technique.
Precipitation hardening is also called age hardening because
strength increases with time.
Requisite for precipitation hardening is that second phase
must be soluble at an elevated temperature but precipitates
upon quenching and aging at a lower temperature.
E.g.: Al-alloys, Cu-Be alloys, Mg-Al alloys, Cu-Sn alloys
If aging occurs at room temperature – Natural aging
If material need to be heated during aging – Artificial aging.

2
In dispersion hardening, fine second particles are mixed with
matrix powder, consolidated, and pressed in powder
metallurgy techniques.
For dispersion hardening, second phase need to have very low
solubility at all temperatures.
E.g.: oxides, carbides, nitrides, borides, etc.
Dislocation moving through matrix embedded with foreign
particles can either cut through the particles or bend around
and bypass them.
Cutting of particles is easier for small particles which can be
considered as segregated solute atoms. Effective strengthening
is achieved in the bending process, when the particles are
submicroscopic in size.

3
Stress (τ) required to bend a dislocation is inversely
proportional to the average interspacing (λ) of particles:
Interspacing (λ) of spherical particles:
where r - particle radius, f - volume fraction
Optimum strengthening occurs during aging once the right
interspacing of particles is achieved.
- Smaller the particles, dislocations can cut through them at
lower stresses
- larger the particles they will be distributed at wider
distances.
λτ Gb=
f
rf
3
)1(4 −
=λ

Fiber Strengthening - 1
Second phase can be introduced into matrix in fiber form too.
Requisite for fiber strengthening:
Fiber material – high strength and high modulus
Matrix material – ductile and non-reactive with fiber material
E.g.: fiber material – Al2O3, boron, graphite, metal, glass, etc.
matrix material – metals, polymers.
Mechanism of strengthening is different from other methods.
Higher modulus fibers carry load, ductile matrix distributes
load to fibers. Interface between matrix and fibers thus plays
an important role.
Strengthening analysis involves application of continuum, not
dislocation concepts as in other methods of strengthening.

Fiber Strengthening - 2
To achieve any benefit from presence of fibers, critical fiber
volume which must be exceeded for fiber strengthening to
occur:
where σmu – strength of strain hardened matrix, σ’m – flow
stress of matrix at a strain equal to fiber breaking stress, σfu –
ultimate tensile strength of the fiber.
Minimum volume fraction of fiber which must be exceeded to
have real reinforcement:
'
'
mfu
mmu
criticalf
σσ
σσ
−
−
=
'
'
min
mmufu
mmu
f
σσσ
σσ
−+
−
=

Martensite Strengthening - 1
This strengthening method is based on formation of martensitic
phase from the retained high temperature phase at temperatures
lower then the equilibrium invariant transformation
temperature.
Martensite forms as a result of shearing of lattices.
Martensite platelets assumes characteristic lenticular shape that
minimizes the elastic distortion in the matrix. These platelets
divide and subdivide the grains of the parent phase. Always
touching but never crossing one another.
Martensite platelets grow at very high speeds (1/3rd of sound
speed) i.e. activation energy for growth is less. Thus volume
fraction of martensite exist is controlled by its nucleation rate.

Martensite Strengthening - 2
Martensite platelets attain their shape by two successive shear
displacements - first displacement is a homogeneous shear
throughout the plate which occurs parallel to a specific plane in
the parent phase known as the habit plane, second
displacement, the lesser of the two, can take place by one of
two mechanisms: slip as in Fe-C Martensite or twinning as in
Fe-Ni Martensite.
Martensite formation occurs in many systems.
E.g.: Fe-C, Fe-Ni, Fe-Ni-C, Cu-Zn, Au-Cd, and even in pure
metals like Li, Zr and Co. However, only the alloys based on
Fe and C show a pronounced strengthening effect.
High strength of Martensite is attributed to its characteristic
twin structure and to high dislocation density. In Fe-C system,
carbon atoms are also involved in strengthening.

Recovery
Annealing relieves the stresses from cold working – three
stages: recovery, recrystallization and grain growth.
Recovery involves annihilation of point defects.
Driving force for recovery is decrease in stored energy from
cold work.
During recovery, physical properties of the cold-worked
material are restored without any observable change in
microstructure.
Recovery is first stage of annealing which takes place at low
temperatures of annealing.
There is some reduction, though not substantial, in dislocation
density as well apart from formation of dislocation
configurations with low strain energies.

Recrystallization
This follows recovery during annealing of cold worked
material. Driving force is stored energy during cold work.
It involves replacement of cold-worked structure by a new set
of strain-free, approximately equi-axed grains to replace all
the deformed crystals.
This is process is characterized by recrystallization
temperature which is defined as the temperature at which 50%
of material recrystallizes in one hour time.
The recrystallization temperature is strongly dependent on the
purity of a material.
Pure materials may recrystallizes around 0.3 Tm, while impure
materials may recrystallizes around 0.5-0.7 Tm, where Tm is
absolute melting temperature of the material.

Recrystallization Laws
A minimum amount of deformation is needed to cause
recrystallization (Rx).
Smaller the degree of deformation, higher will be the Rx
temperature.
The finer is the initial grain size; lower will be the Rx
temperature.
The larger the initial grain size, the greater degree of
deformation is required to produce an equivalent Rx
temperature.
Greater the degree of deformation and lower the annealing
temperature, the smaller will be the recrystallized grain size.
The higher is the temperature of cold working, the less is the
strain energy stored and thus Rx temperature is correspondingly
higher.
The Rx rate increases exponentially with temperature.

Grain Growth
Grain growth follows complete crystallization if the material
is left at elevated temperatures.
Grain growth does not need to be preceded by recovery and
recrystallization; it may occur in all polycrystalline materials.
In contrary to recovery and recrystallization, driving force for
this process is reduction in grain boundary energy.
Tendency for larger grains to grow at the expense of smaller
grains is based on physics.
In practical applications, grain growth is not desirable.
Incorporation of impurity atoms and insoluble second phase
particles are effective in retarding grain growth.
Grain growth is very strongly dependent on temperature.

Material Science/Phase Diagrams Lecture Notes
Chapter 7. Phase Diagrams
7.1 Equilibrium Phase Diagrams
Give the relationship of composition of a solution as a function of temperatures and the
quantities of phases in equilibrium. These diagrams do not indicate the dynamics when
one phase transforms into another. Sometimes diagrams are given with pressure as one of
the variables. In the phase diagrams we will discuss, pressure is assumed to be constant at
one atmosphere.
Binary Isomorphous Systems
This very simple case is one complete liquid and solid solubility, an isomorphous
system. The example is the Cu-Ni alloy of Fig. 9.2a. The complete solubility
occurs because both Cu and Ni have the same crystal structure (FCC), near the
same radii, electronegativity and valence.
The liquidus line separates the liquid phase from solid or solid + liquid phases.
That is, the solution is liquid above the liquidus line.
The solidus line is that below which the solution is completely solid (does not
contain a liquid phase.)
Interpretation of phase diagrams
Concentrations: Tie-line method
a. locate composition and temperature in diagram
b. In two phase region draw tie line or isotherm
c. note intersection with phase boundaries. Read compositions.
Fractions: lever rule
a. construct tie line (isotherm)
b. obtain ratios of line segments lengths.
Development of microstructure in isomorphous alloys
a) Equilibrium cooling
Solidification in the solid + liquid phase occurs gradually upon cooling from the
liquidus line. The composition of the solid and the liquid change gradually during
cooling (as can be determined by the tie-line method.) Nuclei of the solid phase
form and they grow to consume all the liquid at the solidus line.

b) Non-equilibrium cooling
Solidification in the solid + liquid phase also occurs gradually. The composition
of the liquid phase evolves by diffusion, following the equilibrium values that can
be derived from the tie-line method. However, diffusion in the solid state is very
slow. Hence, the new layers that solidify on top of the grains have the equilibrium
composition at that temperature but once they are solid their composition does not
change. This lead to the formation of layered (cored) grains (Fig. 9.14) and to the
invalidity of the tie-line method to determine the composition of the solid phase
(it still works for the liquid phase, where diffusion is fast.)
Binary Eutectic Systems
Interpretation: Obtain phases present, concentration of phases and their fraction
(%).
Solvus line: limit of solubility
Eutectic or invariant point. Liquid and two solid phases exist in equilibrium at the
eutectic composition and the eutectic temperature.
Note:
• the melting point of the eutectic alloy is lower than that of the
components (eutectic = easy to melt in Greek).
• At most two phases can be in equilibrium within a phase field.
• Single-phase regions are separated by 2-phase regions.
Development of microstructure in eutectic alloys
Case of lead-tin alloys, figures 9.9–9.14. A layered, eutectic structure develops
when cooling below the eutectic temperature. Alloys which are to the left of the
eutectic concentration (hipoeutectic) or to the right (hypereutectic) form a
proeutectic phase before reaching the eutectic temperature, while in the solid +
liquid region. The eutectic structure then adds when the remaining liquid is
solidified when cooling further. The eutectic microstructure is lamellar (layered)
due to the reduced diffusion distances in the solid state.
To obtain the concentration of the eutectic microstructure in the final solid
solution, one draws a vertical line at the eutectic concentration and applies the
lever rule treating the eutectic as a separate phase .

Equilibrium Diagrams Having Intermediate Phases or Compounds
A terminal phase or terminal solution is one that exists in the extremes of concentration
(0 and 100%) of the phase diagram. One that exists in the middle, separated from the
extremes, is called an intermediate phase or solid solution.
An important phase is the intermetallic compound, that has a precise chemical
compositions. When using the lever rules, intermetallic compounds are treated like any
other phase, except they appear not as a wide region but as a vertical line.
Eutectoid and Peritectic Reactions
The eutectoid (eutectic-like) reaction is similar to the eutectic reaction but occurs from
one solid phase to two new solid phases. It also shows as V on top of a horizontal line in
the phase diagram. There are associated eutectoid temperature (or temperature), eutectoid
phase, eutectoid and proeutectoid microstructures.
Solid Phase 1 Solid Phase 2 + Solid Phase 3
The peritectic reaction also involves three solid in equilibrium, the transition is from a
solid + liquid phase to a different solid phase when cooling. The inverse reaction occurs
when heating.
Solid Phase 1 + liquid Solid Phase 2
Congruent Phase Transformations
Another classification scheme. Congruent transformation is one where there is no change
in composition, like allotropic transformations (e.g., α−Fe to γ-Fe) or melting transitions
in pure solids.
7.2 Particle strengthening by precipitation
The strength and hardness of some metal and alloys may be enhanced by the formation of
extremely small uniformly dispersed particles of a second phase within the original phase
matrix; this must be accomplished by phase transformations that are induced by
appropriate heat treatments. The process is called precipitation hardening because the
small particles of the new phase are termed “precipitates”. Precipitation hardening and
the treating of steel to form tempered matrensite are totally different phenomena, even
though the heat treatment procedures are similar.
7.3 Precipitation reactions
A precipitation reaction is a reaction in which soluble ions in separate solutions are mixed
together to form an insoluble compound that settles out of solution as a solid. That
insoluble compound is called a precipitate

7.4 Kinetics of nucleation and growth
From a micro structural standpoint, the first process to accompany a phase transformation
is nucleation- the formation of very small particles or nuclei, of the new phase which are
capable of growing. The second stage is growth, in which the nuclei increase in size;
during this process, some volume of the parent phase disappears. The transformation
reaches completion if growth of these new phase particles is allowed to proceed until the
equilibrium fraction is attained.
As would be expected, the time dependence of the transformations rate (which is often
termed the kinetics of a transformation) is an important consideration in the heat
treatment of materials. With many investigations, the fraction of reaction that has
occurred is measured as a function of time, while the temperature is maintained constant.
Transformation progress is usually ascertained by either microscopic examination or
measurement of some physical property. Data are plotted as the fraction of transformed
material versus the logarithm of time; an S-shaped curve, represents the typical kinetic
behavior for most solid state reactions.

7.5 The Iron–Carbon Diagram
The Iron–Iron Carbide (Fe–Fe3C) Phase Diagram
This is one of the most important alloys for structural applications. The
diagram Fe—C is simplified at low carbon concentrations by assuming it
is the Fe—Fe3C diagram. Concentrations are usually given in weight
percent. The possible phases are:
• α-ferrite (BCC) Fe-C solution
• γ-austenite (FCC) Fe-C solution
• δ-ferrite (BCC) Fe-C solution
• liquid Fe-C solution
• Fe3C (iron carbide) or cementite. An intermetallic compound.
The maximum solubility of C in α- ferrite is 0.022 wt%. δ−ferrite is only stable at
high temperatures. It is not important in practice. Austenite has a maximum C
concentration of 2.14 wt %. It is not stable below the eutectic temperature (727 C)
unless cooled rapidly (Chapter 10). Cementite is in reality metastable,
decomposing into α-Fe and C when heated for several years between 650 and 770
C.
For their role in mechanical properties of the alloy, it is important to note that:
Ferrite is soft and ductile
Cementite is hard and brittle
Thus, combining these two phases in solution an alloy can be obtained with
intermediate properties. (Mechanical properties also depend on the
microstructure, that is, how ferrite and cementite are mixed.)
Development of Microstructures in Iron—Carbon Alloys
The eutectoid composition of austenite is 0.76 wt %. When it cools slowly it forms
perlite, a lamellar or layered structure of two phases: α-ferrite and cementite (Fe3C).
Hypoeutectoid alloys contain proeutectoid ferrite plus the eutectoid perlite.
Hypereutectoid alloys contain proeutectoid cementite plus perlite.
Since reactions below the eutectoid temperature are in the solid phase, the equilibrium is
not achieved by usual cooling from austenite. The new microstructures that form are
discussed in Ch. 10.
The Influence of Other Alloying Elements

Alloying strengthens metals by hindering the motion of dislocations. Thus, the
strength of Fe–C alloys increase with C content and also with the addition of other
elements.

7.7 Transformation rate effects and TTT diagrams:
There are two main types of transformation diagram that are helpful in selecting the
optimum steel and processing route to achieve a given set of properties. These are time-
temperature transformation (TTT) and continuous cooling transformation (CCT)
diagrams. CCT diagrams are generally more appropriate for engineering applications as
components are cooled (air cooled, furnace cooled, quenched etc.) from a processing
temperature as this is more economic than transferring to a separate furnace for an
isothermal treatment.
Time-temperature transformation (TTT) diagrams measure the rate of transformation
at a constant temperature. In other words a sample is austenitised and then cooled rapidly
to a lower temperature and held at that temperature whilst the rate of transformation is
measured, for example by dilatometry. Obviously a large number of experiments is
required to build up a complete TTT diagram.
Continuous cooling transformation (CCT) diagrams measure the extent of
transformation as a function of time for a continuously decreasing temperature. In other
words a sample is austenitised and then cooled at a predetermined rate and the degree of
transformation is measured, for example by dilatometry. Obviously a large number of
experiments is required to build up a complete CCT diagram
• An increase in carbon content shifts the CCT and TTT curves to the right (this
corresponds to an increase in hardenability as it increases the ease of forming
martensite - i.e. the cooling rate required to attain martensite is less severe).
• An increase in carbon content decreases the martensite start temperature.
• An increase in Mo content shifts the CCT and TTT curves to the right and also
separates the ferrite + pearlite region from the bainite region making the attainment of
a bainitic structure more controllable.
7.8 Microstructure and Property Changes in Fe-C Alloys
Isothermal Transformation Diagrams
We use as an example the cooling of an eutectoid alloy (0.76 wt% C) from the austenite
(γ- phase) to pearlite, that contains ferrite (α) plus cementite (Fe3C or iron carbide). When
cooling proceeds below the eutectoid temperature (727 o
C) nucleation of pearlite starts.
The S-shaped curves (fraction of pearlite vs. log. time, fig. 10.3) are displaced to longer
times at higher temperatures showing that the transformation is dominated by nucleation
(the nucleation period is longer at higher temperatures) and not by diffusion (which
occurs faster at higher temperatures).
The family of S-shaped curves at different temperatures can be used to construct the TTT
(Time-Temperature-Transformation) diagrams (e.g., fig. 10.4.) For these diagrams to
apply, one needs to cool the material quickly to a given temperature To before the
transformation occurs, and keep it at that temperature over time. The horizontal line that
indicates constant temperature To intercepts the TTT curves on the left (beginning of the
transformation) and the right (end of the transformation); thus one can read from the

diagrams when the transformation occurs. The formation of pearlite shown in fig. 10.4
also indicates that the transformation occurs sooner at low temperatures, which is an
indication that it is controlled by the rate of nucleation. At low temperatures, nucleation
occurs fast and grain growth is reduced (since it occurs by diffusion, which is hindered at
low temperatures). This reduced grain growth leads to fine-grained microstructure (fine
pearlite). At higher temperatures, diffusion allows for larger grain growth, thus leading to
coarse pearlite.
At lower temperatures nucleation starts to become slower, and a new phase is formed,
bainite. Since diffusion is low at low temperatures, this phase has a very fine
(microscopic) microstructure.
Spheroidite is a coarse phase that forms at temperatures close to the eutectoid
temperature. The relatively high temperatures caused a slow nucleation but enhances the
growth of the nuclei leading to large grains.
A very important structure is martensite, which forms when cooling austenite very fast
(quenching) to below a maximum temperature that is required for the transformation. It
forms nearly instantaneously when the required low temperature is reached; since no
thermal activation is needed, this is called an athermal transformation. Martensite is a
different phase, a body-centered tetragonal (BCT) structure with interstitial C atoms.
Martensite is metastable and decomposes into ferrite and pearlite but this is extremely
slow (and not noticeable) at room temperature.
In the examples, we used an eutectoid composition. For hypo- and hypereutectoid alloys,
the analysis is the same, but the proeutectoid phase that forms before cooling through the
eutectoid temperature is also part of the final microstructure.

1. Equilibrium phase diagrams, Particle strengthening by
precipitation and precipitation reactions
2. Kinetics of nucleation and growth
3. The iron-carbon system, phase transformations
4. Transformation rate effects and TTT diagrams, Microstructure
and property changes in iron-carbon system
Contents

Mixtures – Solutions – Phases - 1
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.

Mixtures – Solutions – Phases - 2
When two phases are present in a system, it is not
necessary that there be a difference in both physical and
chemical properties; a disparity in one or the other set of
properties is sufficient.
A solution (liquid or solid) is phase with more than one
component; a mixture is a material with more than one
phase.
Solute (minor component of two in a solution) does not
change the structural pattern of the solvent, and the
composition of any solution can be varied.
In mixtures, there are different phases, each with its own
atomic arrangement. It is possible to have a mixture of two
different solutions!

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:
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:
2+=+ CFP 1+=+ CFP

Equilibrium Phase Diagram
A diagram that depicts 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.
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.
Useful terminology related to phase diagrams: liquidus,
solidus, solvus, terminal solid solution, invariant reaction,
intermediate solid solution, inter-metallic compound, etc.
Phase diagrams are classified according to the number of
component present in a particular system.

Phase Diagram – Useful Information
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.

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.

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.
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.
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.
For isomorphous system - E.g.: Cu-Ni, Ag-Au, Ge-Si,
Al2O3-Cr2O3.

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 electro-
negativities of the two elements.
- Elements should have the same valence.

Isomorphous Binary System
An isomorphous system – phase diagram and corresponding
microstructural changes.

Tie Line – Lever Rule - 1
At a point in a phase diagram, phases present and their
composition (tie-line method) along with relative fraction
of phases (lever rule) can be computed.
Procedure to find equilibrium concentrations of phases
(refer to the figure in previous slide):
- A tie-line or isotherm (UV) is drawn across two-phase
region to intersect the boundaries of the region.
- Perpendiculars are dropped from these intersections to
the composition axis, represented by U’ and V’, from
which each of each phase is read. U’ represents
composition of liquid phase and V’ represents composition
of solid phase as intersection U meets liquidus line and V
meets solidus line.

Tie Line – Lever Rule - 2
Procedure to find equilibrium relative amounts of phases
(lever rule):
- A tie-line is constructed across the two phase region at
the temperature of the alloy to intersect the region
boundaries.
- The relative amount of a phase is computed by taking
the length of tie line from overall composition to the phase
boundary for the other phase, and dividing by the total tie-
line length. In previous figure, relative amount of liquid
and solid phases is given respectively by:
UV
cV
CL =
UV
Uc
CS = 1=+ SL CC

Eutectic Binary System
Many of the binary systems with limited solubility are of
eutectic type – eutectic alloy of eutectic composition
solidifies at the end of solidification at eutectic
temperature.
E.g.: Cu-Ag, Pb-Sn

EutecticSystem–Cooling Curve -
Microstructure - 1

Eutectic System–Cooling Curve –
Microstructure - 2

Eutectic system – Cooling curve –
Microstructure - 3

Eutectic system – Cooling curve –
Microstructure - 4

Invariant Reactions - 1
Observed triple point in unary phase diagram for water?
How about eutectic point in binary phase diagram?
These points are specific in the sense that they occur only
at that particular conditions of concentration, temperature,
pressure etc.
Try changing any of the variable, it does not exist i.e.
phases are not equilibrium any more!
Hence they are known as invariant points, and represents
invariant reactions.
In binary systems, we will come across many number of
invariant reactions!

Invariant Reactions - 2

Intermediate Phases
Invariant reactions result in different product phases –
terminal phases and intermediate phases.
Intermediate phases are either of varying composition
(intermediate solid solution) or fixed composition (inter-
metallic compound).
Occurrence of intermediate phases cannot be readily
predicted from the nature of the pure components!
Inter-metallic compounds differ from other chemical
compounds in that the bonding is primarily metallic rather
than ionic or covalent.
E.g.: Fe3C is metallic, whereas MgO is covalent.
When using the lever rules, inter-metallic compounds are
treated like any other phase.

Congruent, Incongruent Transformations
Phase transformations are two kinds – congruent and
incongruent.
Congruent transformation involves no compositional
changes. It usually occurs at a temperature.
E.g.: Allotropic transformations, melting of pure a
substance.
During incongruent transformations, at least one phase will
undergo compositional change.
E.g.: All invariant reactions, melting of isomorphous alloy.
Intermediate phases are sometimes classified on the basis
of whether they melt congruently or incongruently.
E.g.: MgNi2, for example, melts congruently whereas
Mg2Ni melts incongruently since it undergoes peritectic
decomposition.

Precipitation – Strengthening – Reactions
1
A material can be strengthened by obstructing movement
of dislocations. Second phase particles are effective.
Second phase particles are introduced mainly by two
means – direct mixing and consolidation, or by
precipitation.
Most important pre-requisite for precipitation
strengthening: there must be a terminal solid solution
which has a decreasing solid solubility as the temperature
decreases.
E.g.: Au-Cu in which maximum solid solubility of Cu in
Al is 5.65% at 548ْ C that decreases with decreasing
temperature.
Three basic steps in precipitation strengthening:
solutionizing, quenching and aging.

2
Solutionizing (solution heat treatment), where the alloy is
heated to a temperature between solvus and solidus
temperatures and kept there till a uniform solid-solution
structure is produced.
Quenching, where the sample is rapidly cooled to a lower
temperature (room temperature). Resultant product –
supersaturated solid solution.
Aging is the last but critical step. During this heat treatment
step finely dispersed precipitate particle will form. Aging
the alloy at room temperature is called natural aging,
whereas at elevated temperatures is called artificial aging.
Most alloys require artificial aging, and aging temperature
is usually between 15-25% of temperature difference
between room temperature and solution heat treatment
temperature.

3
Al-4%Cu alloy is used to explain the mechanism of
precipitation strengthening.

4Al-4%Cu alloy when cooled slowly from solutionizing
temperature, produces coarse grains – moderate
strengthening.
For precipitation strengthening, it is quenched, and aged!
Following sequential reactions takes place during aging:
Supersaturated α → GP1 zones → GP2 zones (θ” phase)
→ θ’ phase → θ phase (CuAl2)

Nucleation And Growth
Structural changes / Phase transformations takes place by
nucleation followed by growth.
Temperature changes are important among variables (like
pressure, composition) causing phase transformations as
diffusion plays an important role.
Two other factors that affect transformation rate along with
temperature – 1. diffusion controlled rearrangement of
atoms because of compositional and/or crystal structural
differences; 2. difficulty encountered in nucleating small
particles via change in surface energy associated with the
interface.
Just nucleated particle has to overcome the +ve energy
associated with new interface formed to survive and grow
further. It does by reaching a critical size.

Homogeneous Nucleation – Kinetics
1
Homogeneous nucleation – nucleation occurs within parent
phase. All sites are of equal probability for nucleation.
It requires considerable under-cooling (cooling a material
below the equilibrium temperature for a given
transformation without the transformation occurring).
Free energy change associated with formation of new
particle
where r is the radius of the particle, ∆g is the Gibbs free
energy change per unit volume and γ is the surface energy
of the interface.
γππ 23
4
3
4
rgrf +∆=∆

Homogeneous Nucleation – Kinetics
2Critical value of particle size (which reduces with under-
cooling) is given by
or
where Tm – freezing temperature (in K), ∆Hf – latent heat
of fusion, ∆T – amount of under-cooling at which nucleus
is formed.
g
r
∆
−=
γ2*
TH
T
r
f
m
∆∆
=
γ2*

Heterogeneous Nucleation – Kinetics
1
In heterogeneous nucleation, the probability of nucleation
occurring at certain preferred sites is much greater than that
at other sites.
E.g.: During solidification - inclusions of foreign particles
(inoculants), walls of container holding the liquid
In solid-solid transformation - foreign inclusions, grain
boundaries, interfaces, stacking faults and dislocations.
Considering, force equilibrium during second phase
formation:
βδαβαδ γθγγ += cos

Heterogeneous Nucleation – Kinetics
2
When product particle makes only a point contact with the
foreign surface, i.e. θ = 180ْ, the foreign particle does not
play any role in the nucleation process →
If the product particle completely wets the foreign surface,
i.e. θ = 0ْ, there is no barrier for heterogeneous nucleation →
In intermediate conditions such as where the product
particle attains hemispherical shape, θ = 0ْ→
4
coscos32
)coscos32(
)(3
4 3
*
hom
3
2
3
* θθ
θθ
πγαβ +−
∆=+−
∆
=∆ f
g
fhet
*
hom
*
ffhet ∆=∆
0*
=∆ hetf
*
hom
*
2
1
ffhet ∆=∆

Growth Kinetics - 1
After formation of stable nuclei, growth of it occurs until
equilibrium phase is being formed.
Growth occurs in two methods – thermal activated diffusion
controlled individual atom movement, or athermal collective
movement of atoms. First one is more common than the
other.
Temperature dependence of nucleation rate (U), growth rate
(I) and overall transformation rate (dX/dt) that is a function
of both nucleation rate and growth rate i.e. dX/dt= fn (U, I):

Growth Kinetics - 2
Time required for a transformation to completion has a
reciprocal relationship to the overall transformation rate, C-
curve (time-temperature-transformation or TTT diagram).
Transformation data are plotted as characteristic S-curve.
At small degrees of supercooling, where slow nucleation and
rapid growth prevail, relatively coarse particles appear; at
larger degrees of supercooling, relatively fine particles result.

Martensitic Growth Kinetics
Diffusion-less, athermal collective movement of atoms can
also result in growth – Martensitic transformation.
Takes place at a rate approaching the speed of sound. It
involves congruent transformation.
E.g.: FCC structure of Co transforms into HCP-Co or FCC-
austenite into BCT-Martensite.
Because of its crystallographic nature, a martensitic
transformation only occurs in the solid state.
Consequently, Ms and Mf are presented as horizontal lines on
a TTT diagram. Ms is temperature where transformation
starts, and Mf is temperature where transformation
completes.
Martensitic transformations in Fe-C alloys and Ti are of great
technological importance.

Fe-C Binary System – Phase
Transformations - 1

Fe-C Binary System – Phase
Transformations - 2
Fe-Fe3C phase diagram is characterized by five individual
phases,: α–ferrite (BCC) Fe-C solid solution, γ-austenite
(FCC) Fe-C solid solution, δ-ferrite (BCC) Fe-C solid
solution, Fe3C (iron carbide) or cementite - an inter-metallic
compound and liquid Fe-C solution and four invariant
reactions:
- peritectic reaction at 1495 ْC and 0.16%C, δ-ferrite + L
↔ γ-iron (austenite)
- monotectic reaction 1495 ْC and 0.51%C, L ↔ L + γ-iron
(austenite)
- eutectic reaction at 1147 ْC and 4.3 %C, L ↔ γ-iron +
Fe3C (cementite) [ledeburite]
- eutectoid reaction at 723 ْC and 0.8%C, γ-iron ↔ α–
ferrite + Fe3C (cementite) [pearlite]

Fe-C Alloy Classification
Fe-C alloys are classified according to wt.% C present in the
alloy for technological convenience as follows:
Commercial pure irons % C < 0.008
Low-carbon/mild steels 0.008 - %C - 0.3
Medium carbon steels 0.3 - %C - 0.8
High-carbon steels 0.8- %C - 2.11
Cast irons 2.11 < %C
Cast irons that were slowly cooled to room temperature
consists of cementite, look whitish – white cast iron. If it
contains graphite, look grayish – gray cast iron. It is heat
treated to have graphite in form of nodules – malleable cast
iron. If inoculants are used in liquid state to have graphite
nodules – spheroidal graphite (SG) cast iron.

TTT Diagram For Eutectoid
Transformation In Fe-C System

Transformations Involving Austenite For
Fe-C System

CCT Diagram For Fe-C System - 1
TTT diagram though gives very useful information, they are
of less practical importance since an alloy has to be cooled
rapidly and then kept at a temperature to allow for respective
transformation to take place.
Usually materials are cooled continuously, thus Continuous
Cooling Transformation diagrams are appropriate.
For continuous cooling, the time required for a reaction to
begin and end is delayed, thus the isothermal curves are
shifted to longer times and lower temperatures.
Main difference between TTT and CCT diagrams: no space
for bainite in CCT diagram as continuous cooling always
results in formation of pearlite.

CCT Diagram For Fe-C System - 2

Material Science/Failure Lecture Notes
Chapter 8. Failure
8.1 Fundamentals of Fracture
Fracture is a form of failure where the material separates in pieces due to stress, at
temperatures below the melting point. The fracture is termed ductile or brittle
depending on whether the elongation is large or small.
Steps in fracture (response to stress):
• Track formation
• Track propagation
Ductile vs. brittle fracture
Ductile Brittle
Deformation Extensive Little
Track propagation Slow, needs stress Fast
Type of materials Most metals (not too cold) Ceramics, ice, cold metals
Warning Permanent elongation None
Strain energy Higher Lower
Fractured surface Rough Smoother
Necking Yes No
8.2 Ductile Fracture
Stages of ductile fracture
• Initial necking
• Small cavity formation (microvoids)
• Void growth (ellipsoid) by coalescence into a crack
• Fast crack propagation around neck. Shear strain at
45o
• Final shear fracture (cup and cone)

The interior surface is fibrous, irregular, which signify plastic
deformation.
Brittle Fracture
There is no appreciable deformation, and crack propagation is very fast. In
most brittle materials, crack propagation (by bond breaking) is along
specific crystallographic planes (cleavage planes). This type of fracture is
transgranular (through grains) producing grainy texture (or faceted
texture) when cleavage direction changes from grain to grain. In some
materials, fracture is intergranular.

8.3 Fracture Mechanics
Fracture occurs due to stress concentration at flaws, like surface scratches, voids, etc. If a
is the length of the void and ρ the radius of curvature, the enhanced stress near the flaw
is:
σm ≈ 2 σ0 (a/ρ)1/2
where σ0 is the applied macroscopic stress. Note that a is 1/2 the length of the flaw, not
the full length for an internal flaw, but the full length for a surface flaw. The stress
concentration factor is:
Kt = σm/σ0 ≈ 2 (a/ρ)1/2
Because of this enhancement, flaws with small radius of curvature are called stress
raisers.

8.4 Impact Fracture:
Impact fractures can best be described as a flute or strip of material that was cleanly
sheared from a projectile point. The most common type of impact fracture starts at the tip
of a point and runs down one blade edge possibly reaching the shoulder of a point. Some
points were reworked into a useable point after having been damaged by an impact
fracture.
Normalized tests, like the Charpoy and Izod tests measure the impact
energy required to fracture a notched specimen with a hammer mounted
on a pendulum. The energy is measured by the change in potential energy
(height) of the pendulum. This energy is called notch toughness.
8.5 Ductile brittle transition :
Ductile to brittle transition occurs in materials when the temperature is
dropped below a transition temperature. Alloying usually increases the
ductile-brittle transition temperature, for ceramics, this type of transition
occurs at much higher temperatures than for metals.

8.6 Fatigue:
Fatigue is the catastrophic failure due to dynamic (fluctuating) stresses. It
can happen in bridges, airplanes, machine components, etc. The
characteristics are:
• long period of cyclic strain
• the most usual (90%) of metallic failures (happens
also in ceramics and polymers)
• is brittle-like even in ductile metals, with little
plastic deformation
• it occurs in stages involving the initiation and
propagation of cracks.
Cyclic Stresses
These are characterized by maximum, minimum and mean stress, the stress amplitude,
and the stress ratio.
8.7 Crack Initiation and Propagation
Stages is fatigue failure:
I. crack initiation at high stress points (stress
raisers)
II. propagation (incremental in each cycle)
III. final failure by fracture
Nfinal = Ninitiation + Npropagation
Stage I - propagation
• slow
• along crystallographic planes of high shear stress
• flat and featureless fatigue surface
Stage II - propagation
Crack propagates by repetitive plastic blunting and sharpening of the
crack tip.

8.8 Crack propagation rate
Crack propagation life is computed based on a crack-growth model such as Paris,
Forman, Walker, Elber or Collipriest, depending on the material and type of loading. The
first two models are used for constant amplitude loading, while the latter three correspond
to variable amplitude loading and include crack-growth retardation/ acceleration effects.
Threshold cracks are also incorporated. K vs. relations are available for standard crack
configurations. For other cases, values of K vs. a are generated from fracture analysis.
Crack growth is computed using either the cycle-by-cycle or segment-by-segment
approach. While the first method is accurate, it requires considerable computational time.
The latter approach provides a fast approximation. Accordingly, crack growth is divided
into a finite number of segments and number of cycles required for each segment is
obtained, which is then cumulated.

8.9 Creep
Creep is the time-varying plastic deformation of a material stressed at high
temperatures. Examples: turbine blades, steam generators. Keys are the
time dependence of the strain and the high temperature.
8.10 Generalized Creep Behavior
At a constant stress, the strain increases initially fast with time (primary or
transient deformation), then increases more slowly in the secondary region
at a steady rate (creep rate). Finally the strain increases fast and leads to
failure in the tertiary region. Characteristics:
• Creep rate: dε/dt
• Time to failure.
8.11 Stress and Temperature Effects:
Both temperature and the level of the applied stress influence the creep characteristics.
The results of creep rupture tests are most commonly presented as the logarithm of stress
versus the logarithm of rupture lifetime.
Creep becomes more pronounced at higher temperatures. There is essentially no creep at
temperatures below 40% of the melting point.
Creep increases at higher applied stresses.
The behavior can be characterized by the following expression, where K, n and Qc are
constants for a given material:
dε/dt = K σn
exp(-Qc/RT)

1. Fracture, ductile and brittle fracture
2. Fracture mechanics
3. Impact fracture, ductile-to-brittle transition
4. Fatigue, crack initiation and propagation, crack propagation
rate
5. Creep, generalized creep behavior, stress and temperature
effects
Contents

Failure – Classification
Failure of a material component is the loss of ability to
function normally or to perform the intended job!
Three general ways failure:
Excessive elastic deformation, E.g.: buckling. Controlled
by design and elastic modulus of the material.
Excessive plastic deformation, Controlled by yield strength
of the material. E.g.: loss of shape, creep and/ or stress-
rupture at elevated temperatures.
Fracture, involves complete disruption of continuity of a
component – under static load: brittle or ductile, under
fluctuating/cyclic load: fatigue, mode in which most
machine parts fail in service.

Fracture
Fracture defined as the separation or fragmentation of a
solid body into two or more parts under the action of stress.
Fracture is classified based on several characteristic
features:
Through grains
Along grain
boundaries
Crack propagation
Granular and
bright
Fibrous and grayAppearance
CleavageShearCrystallographic mode
BrittleDuctileStrain to fracture
Terms UsedCharacteristic

Fracture Modes
Ductile and Brittle are relative terms.
Most of the fractures belong to one of the following modes:
(a) rupture, (b) cup-&-cone and (c) brittle.

Ceramics, Glasses,
Ice
Most metals (not too
cold)
Type of materials
Smooth and brightRough and dullFractured surface
NoYesNecking
LittleExtensiveDeformation
NonePlastic deformationWarning sign
FastSlowCrack propagation
ConstantIncreasing
Stress, during
cracking
LowerHigher
Strain energy
required
Brittle fractureDuctile fractureParameter
Ductile Fracture Vs Brittle Fracture

Ductile Fracture - 1
Ductile fracture in tension occurs after appreciable plastic
deformation.
It is usually preceded by necking.
It exhibits three stages - (1) formation of cavities (2)
growth of cavities (3) final failure involving rapid crack
propagation at about 45ْto the tensile axis.
Fractography of ductile fracture reveals numerous spherical
dimples separated by thin walls on the fractured surface.
McClintock’s strain to ductile fracture, εf,
[ ])32()()1(sinh
)2ln()1( 00
σσσ
ε
ba
f
n
bln
+−
−
=

Ductile Fracture - 2
Stages of void nucleation, void growth, crack initiation and
eventual fracture under ductile fracture mode:

Brittle Fracture
Brittle fracture intakes place with little or no preceding
plastic deformation.
It occurs, often at unpredictable levels of stress, by rapid
crack propagation.
Crack propagates nearly perpendicular to the direction of
applied tensile stress, and hence called cleavage fracture.
Most often brittle fracture occurs through grains i.e.
transgranular.
Three stages of brittle fracture - (1) plastic deformation that
causes dislocation pile-ups at obstacles, (2) micro-crack
nucleation as a result of build-up of shear stresses, (3)
eventual crack propagation under applied stress aided by
stored elastic energy.

Brittle Fracture – Griffith Theory
Nominal fracture stress that causes brittle fracture in
presence of cracks (length of interior crack=2c), the stress
raisers,
Griffith’s criteria: a crack will propagate when the
decrease in elastic energy is at least equal to the energy
required to create the new crack surface. Thus for thin
plates:
For thick plates:
When plastic energy is also taken into account (Orowan’s
modification):
21
2
⎟
⎠
⎞
⎜
⎝
⎛
=
π
γ
σ
c
E
21
2
)1(
2
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−
=
πν
γ
σ
c
E
2121
)(2
⎟
⎠
⎞
⎜
⎝
⎛
≈⎟
⎠
⎞
⎜
⎝
⎛ +
=
c
Ep
c
pE
π
γ
σ
21
4
⎟
⎠
⎞
⎜
⎝
⎛
≈
c
E
f
γ
σ

Fracture Mechanics - 1
Relatively new field of mechanics, that deals with
possibility whether a crack of given length in a material
with known toughness is dangerous at a given stress level or
not!
Fracture resistance of a material in the presence of cracks,
known as fracture toughness, is expressed in two forms.
(1) Strain-energy release rate, G:
(2) Stress concentration factor, K:
Both parameters are related as:
For plane stress conditions i.e. thin plates:
For plane strain conditions i.e. thick plates:
E
c
G
2
πσ
=
πασ cK =
GEK =2
)1( 22
ν−= GEK

Fracture Mechanics - 2
K depends on many factors, the most influential of which
are temperature, strain rate, microstructure and orientation
of fracture. The value of K decreases with increasing strain
rate, grain size and/or decreasing temperature.
Depending on the orientation of fracture, three modes of
fracture are identified as shown in the figure:

Notch-Impact Testing - 1
Ductile and Brittle are terms used to distinguish two
extremes of fractures modes based on plastic deformation
involved before fracture occurs.
Three factors that aid transition from ductile to brittle-
cleavage type of fracture are: 1. tri-axial state of stress
2. low temperature, and 3. rapid rate of loading.
Since brittle fracture is most unpredictable, its been extend
at a greater extent. Usually a notch will be introduced to
simulate the conditions.
A notch increases the tendency for brittle fracture by four
means: a) by producing high local stresses, b) by
introducing a tri-axial state of stress, c) by producing high
local strain hardening and cracking, and d) by producing a
local magnification to the strain rate.

Notch-Impact Testing - 2
A material’s susceptibility to different kinds of fracture is
measured using notched specimen subjected to impact
load. Further study involves examining the fracture
surfaces, and calculation of ductility.
Two kind of specimen configurations & loading directions:

Ductile-To-Brittle Transition
Energy absorbed during the notch-impact is plotted as a
function of temperature to know at what temperature range
(DBTT) material fracture in a particular mode.
In metals DBTT is around 0.1-0.2 Tm while in ceramics it is
about 0.5-0.7 Tm, where Tm represents absolute melting
temperature.

Fatigue Failure - 1
Failure that occurs under fluctuating/cyclic loads – Fatigue.
Fatigue occurs at stresses that considerable smaller than
yield/tensile stress of the material.
These failures are dangerous because they occur without
any warning. Typical machine components subjected to
fatigue are automobile crank-shaft, bridges, aircraft landing
gear, etc.
Fatigue failures occur in both metallic and non-metallic
materials, and are responsible for a large number fraction
of identifiable service failures of metals.
Fatigue fracture surface is perpendicular to the direction of
an applied stress.

Fatigue Failure - 2
Fatigue failure can be recognized from the appearance of
the fracture surface:
Any point with stress concentration such as sharp corner or
notch or metallurgical inclusion can act as point of
initiation of fatigue crack.

Fatigue Failure - 3
Three basic requisites for occurrence of fatigue fracture
are: a) a maximum tensile stress of sufficiently high value
b) a large enough variation or fluctuation in the applied
stress and c) a sufficiently large number of cycles of
applied stress.
Stress cycles that can cause fatigue failure are
characterized using the following parameters:
Range of stress, σr = σmax – σmin
Alternating stress, σa = σr/2 = (σmax – σmin)/2
Mean stress, σm = (σmax + σmin)/2
Stress ratio, R= σmin / σmax
Amplitude ratio, A= σa / σm = (1-R) / (1+R)

Fatigue Testing – Data Presentation
Fatigue test, usually, involves applying fluctuating load
cyclically.
A specimen of rotating beam type is often used because of
its simplicity.
Fatigue data is usually presented by plotting maximum
stress (S) against number of cycles to fracture (N), using a
logarithmic scale for the latter variable.
S-N curve can be
represented by the
Basquin equation:
CN p
a =σ

Fatigue Parameters
Material fails under fatigue mode at higher number of
stress cycles if stress applied is lower.
After a limiting stress, ferrous materials won’t fail for any
number of stress cycles. This limiting stress is called –
fatigue limit / endurance limit.
For non-ferrous materials, there is no particular limiting
stress i.e. as stress reduces, number of cycles to failure
keep increasing. Hence stress corresponding to 107 cycles
is considered as characteristic of material, and known as
fatigue strength. Number of cycles is called fatigue life.
Endurance ratio – ratio of fatigue stress to tensile stress of
a material. For most materials it is in the range of 0.4-0.5.

The Goodman diagram presents the dependence of
allowable stress ranges on mean stress for a material.
Allowable stress range increases with increasing
compressive mean stress i.e. compressive stress increases
the fatigue limit.
Fatigue Data Presentation – Goodman
Diagram - 1

An alternative method of presenting mean stress data is by
using Heig-Soderberg diagram. The following equation
summarizes the diagram:
x=1 for Goodman line, x=2 for the Gerber
parabola.
Fatigue Data Presentation - 2
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
−=
x
u
m
ea
σ
σ
σσ 1

Fatigue failure consists of four stages:
(a) crack initiation – includes the early development of
fatigue damage that can be removed by suitable thermal
anneal
(b) slip-band crack growth – involves the deepening of
initial crack on planes of high shear stress (stage-I crack
growth)
(c) crack growth on planes of high tensile stress – involves
growth of crack in direction normal to maximum tensile
stress (stage-II crack growth)
(d) final ductile failure – occurs when the crack reaches a
size so that the remaining cross-section cannot support the
applied load.
Stage-I is secondary to stage-II crack growth in importance
because very low crack propagation rates involved during
the stage.
Fatigue – Crack Initiation &
Propagation

Not necessaryRequired
Necessity of
diffusion
Very highLess
Vacancy
concentration
Some grainsAll grainsGrains involved
Extrusions &
Intrusions
ContourDeformation feature
1-101000Slip (nm)
Cyclic loadStatic loadFeature
Static Load Vs Cyclic Load - 1

Static Load Vs Cyclic Load - 2

Fatigue Crack Growth: Stage-I Vs
Stage-II
StriationsFeature lessFeature
Multiple slip planesSingle slip planeSlip on
High (µm/cycle)Low (nm/cycle)Crack propagation rate
NoYes
Crystallographic
orientation
TensileShearStresses involved
Stage-IIStage-IParameter

Fatigue Crack Propagation Rate
nm
a aCafn
dN
da
σσ == ),(
p
KA
dN
da
)(∆=
Studies of fatigue crack propagation rate attained much
importance because it can be used as fail-safe design
consideration.
Paris law:
p= 3 for steels, 3-4 for
Al alloys

Deformation that occurs under constant load/stress and
elevated temperatures which is time-dependent is known as
creep.
Creep deformation (constant stress) is possible at all
temperatures above absolute zero. However, it is extremely
sensitive to temperature.
Hence, creep in usually considered important at elevated
temperatures (temperatures greater than 0.4 Tm, Tm is
absolute melting temperature).
Creep test data is presented as a plot between time and
strain known as creep curve.
The slope of the creep curve is designated as creep rate.
Creep Failure

Creep Curve - 1

Creep Curve - 2
Creep curve is considered to be consists of three portions.
After initial rapid elongation, ε0, the creep rate decreases
continuously with time, and is known as primary or
transient creep.
Primary creep is followed by secondary or steady-state or
viscous creep, which is characterized by constant creep
rate. This stage of creep is often the longest duration of
the three modes.
Finally, a third stage of creep known as, tertiary creep
occurs that is characterized by increase in creep rate.
Andrade creep equation:
Garofalo creep equation:
kt
et )1( 31
0 βεε +=
te s
rt
t εεεε &+−+= −
)1(0

Creep In Different Stages
First stage creep is associated with strain hardening of the
sample.
Constant creep rate during secondary creep is believed to
be due to balance between the competing processes of
strain hardening and recovery. Creep rate during the
secondary creep is called the minimum creep rate.
Third stage creep occurs in constant load tests at high
stresses at high temperatures. This stage is greatly delayed
in constant stress tests. Tertiary creep is believed to occur
because of either reduction in cross-sectional area due to
necking or internal void formation. Third stage is often
associated with metallurgical changes such as coarsening
of precipitate particles, recrystallization, or diffusional
changes in the phases that are present.

Creep Rate – Stress & Temperature
Effects
Two most important parameter that influence creep rate
are: stress and temperature.
With increase in either stress or temperature (a)
instantaneous elastic strain increases (b) steady state creep
rate increases and (c) rupture lifetime decreases.
RT
Q
n
s
c
eK
−
= σε 2
&

Material Science/Applications and Processing of Metals and Alloys Lecture Notes
Satish Kailash Vasu/IISc, Bangalore M9/L1/V1/feb2005/1
Chapter 9 Applications and Processing of Metals and Alloys
9.1 Types of metals and alloys:
Ferrous alloys:
Ferrous alloys are those in which iron is the prime constituent. They are especially
important as engineering construction materials. The principal disadvantage of many
ferrous alloys is their susceptibility to corrosion. Different alloys of iron are given below:
Alloys of iron
• Steel (carbon)
o Stainless steel (chromium, nickel)
Surgical stainless steel (chromium, molybdenum, nickel)
o Silicon steel (silicon)
o Tool steel (tungsten or manganese)
• Cast iron (carbon)
• Spiegeleisen (manganese, carbon, silicon)
Nonferrous alloys:
Alloys of cobalt
• Stellite (chromium, tungsten, carbon)
o Talonite
Alloys of nickel
• Mu-metal (iron)
• Monel metal (copper, iron, manganese)
• Nichrome (chromium, iron)
Alloys of copper
• Brass (zinc)
• Prince's metal (zinc)
• Gilding metal (zinc)
• Bronze (tin, aluminium or any other element)
o Phosphor bronze (tin and phosphorus)
• Bell metal (tin)
• Beryllium copper (beryllium)
• Cupronickel (nickel)

• Nickel silver (nickel)
• Billon (silver)
• Nordic gold (aluminium, zinc, tin)
Alloys of silver
• Sterling silver (copper)
Alloys of tin
• Pewter (lead, copper)
• Solder (lead)
Alloys of gold
• Electrum (silver, copper)
Alloys of mercury
• Amalgam
Alloys of lead
• Solder
• Type metal
Alloys of bismuth
• Wood's metal
9.2 Fabrication of Metals and Composite Materials:
The fabrication of metals and composite materials can be conducted on a variety of
processing equipment. Alloys can be produced by arc melting or induction melting in a
vacuum or in a controlled atmosphere, and can be shaped using a variety of equipment.
The facility includes various sizes of rolling mills, draw benches, tubing reducers,
welding equipment (including electron-beam), 1/2 in. steel capacity shear, swaging
machines, straightening equipment, and hydraulic presses. Laboratory-sized extrusions
can also be produced. Furnaces up to 24 in. x 24 in. x 72 in. in size and with temperatures
up to 2400°C with controlled or vacuum atmospheres are available for heat treating. An
area for cleaning and chemical etching with exhaust systems is also located at the facility.
In addition, specialty equipment such as a hot isostatic press and a high-energy impact

mill are available. Complete metallographic facilities to study the microstructure of the
materials processed are also located at the facility.
Forming operations
Forming operations are those in which the shape of a metal piece is changed by plastic
deformation; for example, forging, rolling, extrusion and drawing are common forming
techniques. When deformation is achived at a temperature above that at which
recrystallization occurs, the process is termed hot working, otherwise it is cold working.
Forging
Forging is mechanically working or deforming a single piece of a normally hot metal;
this may be accomplished by the application of successive blows or by continuous
squeezing.
Rolling
Rolling, the most widely used deformation process consists of passing a piece of metal
between two rolls, a reduction in thickness results from compressive stresses exerted by
the rolls.
Extrusion
For extrusion, a bar of metal piece through a die orifice by a compressive force that is
applied to a ram; the extruded piece that emerges has the desired shape and a reduced
cross sectional area.
Drawing
Drawing is the pulling of a metal pice through a die having a tapered bore by means of a
tensile force that is applied on the exit side. A reduction in cross section results, with a
corresponding increase in length.
Casting:
Casting is a fabrication process whereby a totally molten metal is poured into a mold
cavity having the desired shape; upon solidification, the metal assumes the shape of the
mold but experiences some shrinkages. Different types of casting techniques which are
commonly employed are: sand , die, investment and continuous casting.

Miscellaneous Techniques:
Powder Metallurgy
This is another fabrication technique which involoves the compaction of powdered metal,
followed by a heat treatment to produce a more dense piece. Diffusional processes during
the heat treatment are central to the development of these properties. This method is
especially suitable for metals having low ductilities, since only small plastic deformation
of the powder particles need occur.
Welding
In welding, two or more metal parts are joined to form a single piece when one part
fabrication is expensive or inconvenient. Both similar and non similar metals can be
joined by welding. The joining bond is metallurgical rather than juts mechanical. During
arc and gas welding, the work pieces to be joined and the filler material are heated to a
sufficiently high temperature to cause both to melt; upon solidification, the filler material
forms a fusion joint between the work pieces.
9.3 Thermal Processing of metals
Annealing Processes
Annealing is a heat treatment where the material is taken to a high temperature, kept there
for some time and then cooled. High temperatures allow diffusion processes to occur
fast. The time at the high temperature (soaking time) is long enough to allow the desired
transformation to occur. Cooling is done slowly to avoid the distortion (warping) of the
metal piece, or even cracking, caused by stresses induced by differential contraction due
to thermal inhomogeneities. Benefits of annealing are:
• relieve stresses
• increase softness, ductility and toughness
• produce a specific microstructure

9.4 Heat Treatments
Precipitation hardening is achieved by:
a) solution heat treatment where all the solute atoms are dissolved to form
a single-phase solution.
b) rapid cooling across the solvus line to exceed the solubility limit. This
leads to a supersaturated solid solution that remains stable (metastable)
due to the low temperatures, which prevent diffusion.
c) precipitation heat treatment where the supersaturated solution is heated
to an intermediate temperature to induce precipitation and kept there for
some time (aging).
If the process is continued for a very long time, eventually the hardness decreases. This
is called overaging.
The requirements for precipitation hardening are:
• appreciable maximum solubility
• solubility curve that falls fast with temperature
• composition of the alloy that is less than the maximum solubility
9.5 Precipitation Hardening
Hardening can be enhanced by extremely small precipitates that hinder dislocation
motion. The precipitates form when the solubility limit is exceeded. Precipitation
hardening is also called age hardening because it involves the hardening of the material
over a prolonged time.

Applications and Processing of Metals and Alloys
Module-09

1. Types of metals and alloys
2. Fabrication of metals
3. Thermal processing of metals
Contents

Materials – Classification
Materials are classified into three basic groups based on
their mechanical and physical nature as – metals, ceramics
and polymers.
For an engineer, especially, metals are more important
owing to ability to carry loads and ease of manufacturing.
Metallic materials are again classified for ease of selection
and/or based on their tonnage of usage broadly into two
classes – ferrous and non-ferrous.
Ferrous materials – chief constituent is iron (Fe). E.g.:
steel, cast iron.
Metallic materials those are not ferrous are termed as non-
ferrous materials. E.g.: Brass, Silver, Aluminium,
Titanium.

Ferrous Materials - Introduction
In engineering applications, lion share is served by ferrous
materials.
Factors account for it are:
- availability of abundant raw materials combined with
economical extraction
- ease of forming
- their versatile mechanical and physical properties.
There are some drawbacks about ferrous materials:
- poor corrosion resistance
- high density i.e. low specific strength
- low thermal and electrical conductivities

Ferrous Materials - Classification
There are two classes – steels and cast irons – categorized
based on carbon content.
Steels: %C is up to 2.14%
Cast irons: %C is above 2.14%
Cast irons are called so because they are usually
manufactured through casting technique owing to their
brittle nature due to presence of iron carbide.
Steels are serving major part of present engineering
applications.
However, cast irons mostly serve as structural components.
E.g.: automobile motor casings, lathe bed, sliding guides in
machinery.

Steels - 1
In steels, C atoms occupies interstitial sites of Fe.
Steels are classified based on their C content/alloying
additions which in turn dictates their applications: plain
carbon steels and alloying steels.
Low-carbon steels: % wt of C < 0.3
Medium carbon steels: 0.3 <% wt of C < 0.6
High-carbon steels: % wt of C > 0.6
Low carbon steels:
- Carbon present is not enough to strengthen them by heat
treatment, hence are strengthened by cold work.
- They are easily weldable and machinable.
- Typical applications: tin cans, automotive body
components, structural shapes, etc.

Steels - 2
Medium carbon steels:
- They are less ductile and stronger than low carbon steels.
- Heat treatable (austenitizing, quenching and tempering).
- Hardenability is increased by adding Ni, Cr, Mo.
- Used in various tempered conditions.
- Typical applications: gears, railway tracks, machine parts.
High carbon steels:
- They are strongest and hardest of carbon steels.
- Heat treatable. Used in tempered or hardened conditions.
- Alloying additions – Cr, V, W, Mo
- Typical applications: Knives, razors, hacksaw blades, etc
where high wear resistance is the prime requirement.

HSLA And Stainless Steels - 1
HSLA (high strength low alloy) steels:
- They can be strengthened by heat treatment.
- Ductile and formable.
- Alloying addition – Cu, V, W, Ni, Cr, Mo, etc.
- Typical applications: support columns, pressure vessels,
bridge beams.
Stainless steels:
- They typical consists min.12% Cr along with other
alloying elements, thus highly corrosion resistant owing to
presence of chromium oxide.
- Three kinds - ferritic & hardenable Cr steels, austenitic
and precipitation hardenable (martensitic, semi-austenitic)
– based on presence of prominent microstructural
constituent.

Stainless Steels - 2
Stainless steels:
- Typical applications – cutlery, surgical knives, storage
tanks, domestic items
- Ferritic steels are principally Fe-Cr-C alloys with 12-14%
Cr. And small additions of Mo, V, Nb, Ni.
- Austenitic steels contain 18% Cr and 8% Ni plus minor
alloying elements. Ni stabilizes the austenitic phase assisted
by C and N.
- For, martensitic steels Ms is made to be above the room
temperature. These alloys are heat treatable. Major alloying
elements are: Cr, Mn and Mo.
- Ferritic and austenitic steels are hardened and strengthened
by cold work because they are not heat treatable.
- Austenitic steels are non-magnetic as against ferritic and
martensitic steels, which are magnetic.

Cast Irons - 1
Grey cast iron
- Cementite decomposes during solidification to form carbon
flakes. Thus they are brittle.
- Fractured surface looks grey because of presence of
graphite, hence the name.
- Possess good damping properties.
- Typical applications – base structures, machine beds
White cast iron
- Cooled fast so that cementite does not decompose.
- Fractures surface looks whitish because of cementite, hence
the name.
- They are brittle and extremely difficult to machine.
- Used as source materials for producing malleable iron.

Cast Irons - 2
Nodular cast iron
- Alloying addition of Mg/Ce to grey cast iron melt results in
graphite to form as modules.
- They are stronger and ductile than grey cast iron.
- Typical applications – pump bodies, crank shafts, automotive
components, etc.
Malleable cast iron
- Formed by heat treating white cast iron. Heat treatment
involves heating to 800-900C, keep it there for long hours,
then cooling to room temperature.
- Cementite decomposes to form graphite and ferrite.
- Typical applications – railroad, connecting rods, marine and
other heavy-duty services.

Non-Ferrous Materials
Typical advantages of non-ferrous materials over ferrous
materials:
- high specific strength.
- low density.
- high electrical and thermal conductivities.
- distinct properties thus used for specific purposes.
- can be formed with ease.
E.g.: Al-alloys
Cu-alloys (brass, bronze)
Mg-alloys
Ti-alloys
Noble metals (E.g.: Ag, Au, Pt, Pa)
Refractory metals (E.g.: Nb, Mo, W and Ta)

Fabrication Of Metals And Alloys
Four basic manufacturing processes:
Casting – to give a shape by pouring in liquid metal into a
mold that holds the required shape, and letting harden the
metal without external pressure.
Forming – to give shape in solid state by applying pressure.
Machining – in which material is removed in order to give
it the required shape.
Joining – where different parts are joined by various
means.
Other important technique is powder metallurgy.

Metal Casting – Metal Forming
Four important casting techniques are:
Sand casting
Die casting
Investment casting
Continuous casting
Four important forming techniques are:
Forging
Rolling
Extrusion
Drawing

Metal Forming Techniques

Thermal Processing
Two main kinds of metal processing methods – mechanical
and thermal.
Thermal processing is also known as heat treatment.
Purpose of heat treatment:
- improvement in ductility
- relieving internal stresses
- grain size refinement
- increase of strength
- improvement in machinability and toughness
Thermal processing factors – temperature up to which
material is heated, length of time that the material is held at
the elevated temperature, rate of cooling, and the
surrounding atmosphere under the thermal treatment.

Thermal Processing Methods
Two kinds heat treating methods are – annealing and
quenching & tempering.
These differ in the way material is cooled from an elevated
temperature.
Annealing involves cooling the material slowly, allowing
phase changes.
Quenching (also known as hardening) means cooling the
material at a rapid rate to arrest the equilibrium phase
transformations.
During annealing, material is cooled in air and/or heating
furnace itself.
For quenching, material is immersed in water / oil quench
bath.

Annealing Techniques
Process annealing – applied to cold worked materials to
negate effects of cold work. Commonly sandwiched
between two cold work operations. Improves ductility.
Stress relief – purpose of it is to remove stresses.
Temperatures are low such that cold work effects are not
affected.
Full annealing – used for products that are to be machined
later-on. Cooling is done in furnace itself. Hardness and
strength are restored by additional heat treatments after
machining.
Normalizing – used to refine the grains and produce a more
uniform and desirable size distribution. It involves heating
the component to attain single phase (e.g.: austenite in
steels), then cooling in open air atmosphere.

Quenching & Tempering
Quenching operation is usually followed by tempering.
Tempering involves heating martensitic steel at a
temperature below the eutectoid transformation
temperature to make it softer and more ductile. Here
Martensite transforms to ferrite embedded with carbide
particles.
Martempering is used to minimize distortion and cracking.
It involves cooling the austenized steel to temperature just
above Ms temperature, holding it there until temperature is
uniform, followed by cooling at a moderate rate to room
temperature before austenite-to-bainite transformation
begins. The final structure of martempered steel is
tempered Martensite.
Austempering involves austenite-to-bainite transformation.
Thus, the final structure of austempered steel is bainite.

Material Science/Applications and Processing of Ceramics Lecture Notes
Chapter 10. Applications and Processing of Ceramics
10.1 Types and applications of ceramics:
Ceramics offer a high temperature range. However, ceramics are not very strong.
To compensate for their lack of strength ceramics are usually combined with
some other material to form a ceramic composite.
1) Glasses and glass ceramics- The glasses are a familiar group of ceramics;
containers, windows, lenses and fiberglass represent typical applications. The
properties of standard vitrified products are insufficient for architectural
applications and structural building components, insulation or other specialized
applications. Yet there is an effective way to improve these properties without
major alterations to the process itself - the introduction of a controlled
crystallization process through a subsequent heat treatment, i.e. by forming a
glass-ceramic.
Production of Glass-Ceramics
Glass-ceramic articles may be produced by three routes:
· The heat treatment of solid glass (the traditional route)
· The controlled cooling of a molten glass, known as the petrurgic method
· The sintering and crystallisation of glass powders.
In the latter case, the powders are densified at relatively low temperatures by exploiting a
viscous flow sintering mechanism. After densification, the material is subjected to a
crystallisation heat-treatment to obtain the required glass-ceramic microstructure.
Alternatively, both densification and crystallisation may take place during a single
sintering step.
Along with the economic advantage of using relatively low processing temperatures, the
powder technology route is suitable for the production of a range of advanced materials,
including glass-ceramics with specified porosities and glass-ceramic matrix composites.
Using the petrurgic method, the slow cooling from the molten state causes nucleation and
growth of certain crystalline phases. Therefore, the final microstructure, and hence the
properties, depends mainly on the composition and the cooling rate.
Glass-Ceramics Based on Coal Ash
The very high iron oxide content of coal ash, table 1, indicates the potential for
developing magnetic phases using appropriate processing - this was the aim of our work.
We calcined the as-received ash at 800°C for two hours to remove any volatile

compounds, including sulfur and carbon. The powder and petrurgic methods were
explored, and gave us products with different phases and microstructures. For the
sintering experiments, we mixed calcined ash powder with various amounts (10-50wt%)
of borosilicate (Pyrex) glass. The powder mixtures were uniaxial cold pressed to a
cylindrical shape and sintered in air at temperatures in the range of 1,000-1,500°C for
periods of up to 15 hours. Using the petrurgic method, coal ash was mixed with soda-
lime glass powder. The mixture was melted at 1,500°C and cooled to room temperature
at rates of between 1-10°C per minute.
Glass-Ceramic Composites
Work to date has largely concentrated on composites with a matrix of the slag-based
Silceram glass-ceramic (a glass-ceramic for floor and wall tiles and wear components).
We have investigated both particulate- (SiC and TiC) and fibre-reinforcement (SiC).
Properties measured include the fundamental mechanical properties but also more
complex properties such as thermal shock resistance and erosion resistance. As
mentioned previously, the thermal shock resistance of glass-ceramics is superior to the
parent glasses, and the shock resistance is further improved by particulate reinforcement.
For example, monolithic Silceram has a thermal shock critical temperature of 180°C,
whereas a 20wt%SiC composite has a value of 270°C. Erosion resistance may also be
improved by particulate reinforcement, e.g., for TiC reinforced Silceram - the larger the
reinforcement particle size and the greater the volume fraction, the lower the erosion rate.
Results indicate a way for transforming vitrified silicate residues into useful products
with broad application potential. The glass-ceramics obtained are candidate materials for
applications in floors of industrial buildings and in construction, and for outside and
inside facing walls. We are currently addressing issues associated with the effect of
environmental influences on the chemical durability and toxic potential of the materials,
which may be compromised by the presence of heavy metals incorporated in the glass or
crystalline phases. Public acceptance of the use and exploitation of glass-ceramic-based
materials in such applications will strongly depend on a satisfactory consideration of
these issues.
2) Refractories -Refractories are materials needed for handling high temperature liquids,
gases and solids, e.g., for industrial processing. Applications include solar furnaces,
casting molds for molten materials, heat exchangers, and aerobraking heat shields.
Industrial refractory needs can be satisfied by sintered calcia (CaO), silica (SiO2),
magnesia (MgO), alumina (Al2O3) and titania (TiO2), with the desired porosity. Of
course, these stable materials are commonly used on Earth for the same purposes, due to
their great resistance to heat, oxidation (they are already fully oxidized), corrosion and
abrasion. Minerals such as olivine [(MgFe)2SiO4] and anorthite (CaAl2Si2O8) are also
useful for making refractory bricks and ceramics. Some refractories and their ceramics
have low expansion due to heat and are attractive for space environments where a wide
range of temperatures are experienced.

Production of ceramics and refractories in space from lunar materials has been discussed
in a number of papers, including Poisl and Fabes, as well as Shirley et al., and Mackenzie
and Claridge, among others.
One particular application of refractories is in transportation for returning cargoes to low
Earth orbit by aerobraking with the upper atmosphere, and perhaps slowing down some
incoming asteroid payloads by aerobraking. Of course, this is the method used by
spacecraft to return to Earth, including the reusable Space Shuttle. The Space Shuttle's
tiles are made from silica (SiO2) (with a thin borosilicate coating to provide a smooth,
aerodynamic surface for a smooth landing).
Aerobraking tiles are produced from amorphous silica fibers which are pressed and
sintered, with the resulting tile having as much as 93% porosity (i.e., very lightweight)
and low thermal expansion, low thermal conductivity, and good thermal shock properties.
This process can be readily performed in space when we can produce silica of the
required purity.
Cheaper materials besides silica fibers can be used. Silica fibers are used on the Space
Shuttle in order to keep its weight down, thereby increasing cargo weight capacity. For
resources already in space, we don't have this economic need. A number of other
materials can be used for heat shields, e.g., alumina (Al2O3) or anorthite (CaAl2Si2O8).
3) Abrasives- Abrasive cements are used to wear, grind or cut away other material, which
necessarily is softer. Therefor, the prime requisite for this group of materials is hardness
or wear resistancr; in addition, a hig degree of toughness is essential to ensure that the
abrasive particles do not easily fracture. Furthermore, high temperatures may be
produced from abrasive frictional forces, so some refractoriness is also desirable.
Diamonds, both natural and synthetic, are utilized as abrasives; however, they are
relatively expensive. The more common ceramic abrasives include silicon carbide,
tungsten carbide(WC), aluminium oxide and silica sand. Abrasives are used in several
forms-bonded to grinding wheels, as coated abrasives and as loose grains. Coated
abrasives are those in which an abrasive powder is coated on some type of paper or cloth
material; sandpaper is probably the mostly familiar example. Wood, metals, ceramics and
plastics are all frequently ground and polished using this form of abrasive.Grinding,
lapping and polishing wheels often employ loose abrasive grains that are delivered in
some type of oil or water based vehicle. Diamonds, corundum,silicon carbide and rouge
are used in loose form over a variety of grain size ranges.
4) Cements:
Several familiar ceramic materials are classified as inorganic cements:cements,
plaster of paris, and lime, which as a group are produced in extremely large
quantities. The characteristic feature of these materials is that when mixed with
water, they form a paste that subsequently sets and hardens. This trait is especially
useful in that solid and rigid structures having just about any shape may be
expeditiously formed.

Portland Cement
Portland cement is a closely controlled chemical combination of calcium, silicon,
aluminum, iron and small amounts of other compounds, to which gypsum is added in the
final grinding process to regulate the setting time of the concrete. Some of the raw
materials used to manufacture cement are limestone, shells, and chalk or marl, combined
with shale, clay, slate or blast furnace slag, silica sand, and iron ore. Lime and silica
make up approximately 85 percent of the mass (1).
The term "Portland" in Portland cement originated in 1824 when an English mason
obtained a patent for his product, which he named Portland Cement. This was because his
cement blend produced concrete that resembled the color of the natural limestone
quarried on the Isle of Portland in the English Channel.
Different types of Portland cement are manufactured to meet different physical and
chemical requirements for specific purposes. The American Society for Testing and
Materials (ASTM) Designation C 150 provides for eight types of Portland cement:
(reference).Portland Cement is a type of cement, not a brand name. Many cement
manufacturers make Portland Cement. Variuos types of Portland cements are:
Type 1
normal portland cement. Type 1 is a general use cement.
Type 2
is used for structures in water or soil containing moderate amounts of sulfate, or when
heat build-up is a concern.
Type 3
high early strength. Used when high strength are desired at very early periods.
Type 4
low heat portland cement. Used where the amount and rate of heat generation must be
kept to a minimum.
Type 5
Sulfate resistant portland cement. Used where the water or soil is high in alkali.
Types IA, IIA and IIIA are cements used to make air-entrained concrete. They have the
same properties as types I, II, and III, except that they have small quantities of air-
entrained materials combined with them.
These are very short descriptions of the basic types of cement. There are other types for
various purposes such as architectural concrete and masonry cements, just to name two
examples

5) Advanced Ceramics:
Advanced Cerametrics Inc. (ACI) has evolved over its 56 year history
from a small, family owned manufacturer of ceramic wear parts for the
textile industry, to a prominent, high-tech company developing and
manufacturing advanced materials. In recent years ACI has been the
recipient of numerous R & D grants from the Defense Department,
NASA and the Department of Energy.
ACI serves the aerospace, military, industrial, medical, textile,
consumer, electronic, and automotive industries with three main product
lines — traditional ceramics, including thread guides, insulators and
thermally resistant parts; an advanced line of thick walled and complex
injection molded ceramics; and ceramic fiber. Visit the pages below for
further information on services and products.
ACI Products - photographs and technical details of ceramic
components, finishes, capabilities, and processes. Includes a material
selection and property chart.
ACI Technology - information on applications of ACI materials, and
current research and development projects.
Contact Advanced Cerametrics for product details, new materials
research information, and all other inquiries.
Ceramic Fiber
ACI has developed a line of piezoelectric fiber materials using its
patented VSSP manufacturing process to make actively controlled
structures. This fiber technology has been incorporated in the newest
generation of active, smart sporting goods. Head Sport introduced their
new line of Intellifiber and Intellichip active fiber composite tennis
rackets and skis with energy harvesting actuators made from ACI's
patented PZT fiber. These self-powered products actively dampen the
vibration created during a ball strike or edge chatter from a ski turn and
use the energy to create electrical force to control the shape of the ski or
racket, using ACI’s PZT fiber's electrical and mechanical properties to
counteract the forces. This active structural control adds up to 15% more
power to a ball hit and about 6% more functional edge on a ski. This
technology has opened the doors to many new sporting goods
ACI's fiber works extremely well as an acoustic transducer. As an
integral component for the ultrasonic equipment market, the ability of a
transducer to provide clear signals directly impacts the quality of the
images produced. Using ACI's fiber transducers to replace the bulk

ceramic transducers, which are currently used in commercial ultrasound
testing equipment, has yielded excellent results with no lateral wave
interference. Acoustic applications include ultrasound imaging for
medical and non-destructive testing, hearing aids, music, voice
reproduction, recreational and commercial fish finders, and military
systems.
Other products using this fiber include smart, actively controlled
automotive suspensions, vibration damping in military and industrial
systems and energy harvesting footwear.
Energy Harvesting: ACI's PZT materials have demonstrated the
capability for use as a renewable energy source by incorporating it's
patented PZT technology into flexible, motion sensitive (vibration,
compression or flexure), active fiber composite shapes that can be placed
in shoes, boots, and clothing or any location where there is a source of
waste energy or mechanical deflexion. These flexible composites
generate power from the scavenged energy and harness it using
microprocessor controls developed specifically for this purpose. Projects
currently under development with major manufacturers include self-
heated boots for hiking, skiing, and military applications (also for battery
charging
Industry of Ceramic Segments
Industry Segment Common Examples
Structural clay products Brick, sewer pipe, roofing tile, clay floor and
wall tile (i.e., quarry tile), flue linings
Whitewares Dinnerware, floor and wall tile, sanitaryware,
electrical porcelain, decorative ceramics
Refractories Brick and monolithic products are used in
iron and steel, non-ferrous metals, glass,
cements, ceramics, energy conversion,
petroleum, and chemicals industries
Glasses Flat glass (windows), container glass
(bottles), pressed and blown glass
(dinnerware), glass fibers (home insulation),
and advanced/specialty glass (optical fibers)
Abrasives Natural (garnet, diamond, etc.) and synthetic
(silicon carbide, diamond, fused alumina,
etc.) abrasives are used for grinding, cutting,

polishing, lapping, or pressure blasting of
materials
Cements Used to produce concrete roads, bridges,
buildings, dams, and the like
Advanced ceramics
Structural Wear parts, bioceramics,
cutting tools, and engine
components
Electrical Capacitors, insulators,
substrates, integrated circuit
packages, piezoelectrics,
magnets and superconductors
Coatings Engine components, cutting
tools, and industrial wear parts
Chemical
and
environmen
tal
Filters, membranes, catalysts,
and catalyst supports
10.2 Fabrication and processing of ceramics:
Ceramic Synthesis: Our expertise and capabilities in synthesizing ceramics are based on
chemical solution techniques. Chemical solution or sol-gel approaches have been
developed to fabricate powders, films, and porous bodies. Materials of interest range
from silica to complex, multicomponent electronic ceramics. The complexity inherent in
fabricating materials with structured nanoporosity or complex chemistries requires a
fundamental understanding of these chemical solution approaches. Fabrication of unique
precursors for complex oxides is being done with novel metal alkoxide chemistry to
produce powders and thin-film materials with carefully controlled properties. Our ability
to synthesize materials with complex structures, chemistries, or both, is at the heart of
numerous research and development efforts at Sandia.
Ceramic Processing: Sandia's fabrication of ceramic components and devices is based
on a strong ceramic-processing capability. We recently have demonstrated the ability to
characterize and model the powder-compaction process in detail, and to address and
control density gradients in powder compacts that cause shape distortion and differential
shrinkage. Proprietary 3D, finite-element code packing and compaction models, and
process-control tools are now available to improve the production of ceramic
components. Sandia has capabilities in the areas of hydrostatic and triaxial compaction
testing to characterize materials properties, and x-ray radiography, ultrasound, and
computed tomography for density characterization. In addition, expertise in slurry

processing has enabled the development of direct-fabrication processes. Furthermore, we
are developing phenomenological sintering models to enhance both ceramic component
design and manufacturing capability.
Ceramic Synthesis and Processing Research Briefs:
Constrained Sintering of Multi-Material Systems
Development of A Predictive Model for Ceramic Powder Compaction
ESP (Engineered Stress Profile) Glass - Unique Opportunities for Performance
and Reliability
Molecular Dynamics Simulations of Reactive Wetting in Ceramic-Metal Systems
PZT 95/5 Material Development for Neuron Generator Applications
Precursor's Structure Effects on Thin-Film Densification of TiO2
Relationship between Interfacial Interactions and Fracture Stress for Adhesive
Joints in Mode II Loading
Robocasting : Layered Manufacturing by Slurry Extrusion
Synthesis and Processing of Composites by Reactive Metal Penetration
10.3 Electrical conduction in ionic ceramics and in polymers:
This requires creation of electron [e'] and hole [h⋅] pairs in ionic solid according to the
symbolic chemical reaction, which describes creation of carriers due to thermal activation
(this process results in intrinsic conductivity):
nil ⇔ e' + h⋅
K = [e'] + [h⋅ ] = n . p = exp (- ∆G0
/RT) = exp (∆S0
/R) exp (-Eg /RT)
Accordingly, a supply of "band gap" energy Eg is necessary, hence the strong
dependence of conductivity on temperature. The equilibrium constant of the above
reaction can be approximately expressed as: n.p ≈ 1019exp(Eg/kT), or, the carrier
concentration (assuming the same concentration of holes p and electrons e), c ≈
109.5exp(Eg/2kT).

The magnitude of the band gap Eg determines ability of a material to conduct. For Eg > 6
eV, materials are considered as insulators . This wide energy gap is typical for the
ionic oxides of metals having a single stable oxidation state: groups IA, IIA, IIIA. The
electrical resistivity of most stable insulators correlates with the ionic character of their
bond: the larger difference of electronegativity, the larger % of ionic bond, and the larger
energy gap Eg.
The band gap magnitude correlates also with the ionic bond energy, i.e. the most stable
ionic ceramic are also the best insulators. For example, the bond energy of alumina is
~6eV/equivalent (1/3 Al2O3) and Eg = ~7eV; the bond energy of one equivalent of
cadmium oxide (CdO) is ~4 eV/equivalent and Eg = ~2eV.
The oxides of metals able to have multiple oxidation states (such as transition elements,
with partially filled "d" orbitals) have narrower band gaps of the order of 2-5eV, resulting
in intrinsic semiconducting properties. The presence of point defects in ionic solids
(such as solutes, vacancies, interstistials) can dramatically decrease the energy required
for the creation of electron/hole pairs.
This is because these defects are typically located “within” the energy gap, either close to
the valence band (acceptors) or conduction band (donors). An example is KCl
containing VK', VCl
•, CaK
• , or MgO containing VMg'', VO
•,VMg', VC
0, AlMg
•.
The point defects are the key feature of extrinsic semiconductors, the basic components
of modern electronics.
Mixed and Ionic Ceramic Conductors
The variety of point defects present in ceramics gives frequently a mixed ionic and
electronic type of electrical conduction. To some extent, every ionic crystal is a mixed
conductor, but the share of electronic conductivity, expressed through the charge
transference number for electrons, can be negligible. If Ohm’s law is expressed in
terms of current density J [A/m2
], material conductivity σ [A/Vm] and electric field Ee,
[V/m] following relationship results:
J = - σ.Ee

where, for mixed a conductor, σ = Σσi, the sum of conductvities due to the various
charge-carrying species, i.e. ions, holes and electrons. The transference number ti of a
given species is then defined as: tj = σj/Σσi
For ionic conductors, the aim is to maximize the charge transference due to the
movement of ions and minimize the transference due to electrons and holes movement.
That is, tion ≈ 1 , te,h ≈ 0 . This is principle behind the operation of solid
electrolytes. The sub-class of solid electrolytes useful for solid-state electrochemical
devices (batteries, sensors) can be defined as "fast ionic conductors" as long as:
1. The activation energy Ed for diffusion is LOW, less than ~0.1 eV/atom, or
2.5 kcal/mole, or 10 kJ/mole, or ~10% of the energy needed to form a point defect in a
close packed ionic solid.
2. The corresponding D0 value (diffusion coefficient D = D0exp[-Ed/kT], so
D = D0 at T = ∞) is HIGH (D0 >10-4 cm2/s) and therefore the corresponding σ0 value
(ionic conductivity σ=σ0exp[-E/kT]) is HIGH, σ0 > 0.1 1/Ω.cm.
If the above conditions are fulfilled, the diffusivity at room temperature will be D > 10-6
cm2/s, and room temperature ionic conductivity will be σ > 0.01 1/Ωcm, or resistivity ρ
= 100 Ωcm . This magnitude of conductivity allows the use of solid state ionic
conductors in devices like batteries, sensors and fuel cells.
The resistivity of ionic conductor is the primary factor that determines internal resistance
of the cell, and thus maximum current that can be drawn from the cell. As resistance R
= ρ L/A (L being electrolyte thickness, typically 0.1-1 cm, and A area, typically 10-1000
cm2
), then the internal resistance of such battery is typically 1 Ω .

Applications and Processing of Ceramics
Module-10

1. Types and applications of ceramics
2. Fabrication and processing of ceramics
Contents

Introduction – Ceramics
The word ‘ceramic’ is originated from greek word
keromikos, which means ‘burnt stuff’.
Ceramics are compounds of metallic and non-metallic
elements.
Characteristics of ceramics are:
- high temperature stability
- high hardness
- brittleness
- high mechanical strength
- low elongation under application of stress

Classification – Ceramics - 1
Ceramics are classified in many ways. It is due to
divergence in composition, properties and applications.
Based on their composition, ceramics are:
- Oxides
- Carbides
- Nitrides
- Sulfides
- Fluorides etc.

Based on their specific applications, ceramics are classified
as:
- Glasses
- Clay products
- Refractories
- Abrasives
- Cements
- Advanced ceramics for special applications

Based on their engineering applications, ceramics are
classified into two groups as: traditional and engineering
ceramics.
Traditional ceramics – most made-up of clay, silica and
feldspar.
Engineering ceramics – these consist of highly purified
aluminium oxide (Al2O3), silicon carbide (SiC) and silicon
nitiride (Si3N4)

Introduction – Processing Ceramics
The very specific character of ceramics – high temperature
stability – makes conventional fabrication routes unsuitable
for ceramic processing.
Inorganic glasses, though, make use of lower melting
temperatures. Most other ceramic products are
manufactured through powder processing.
Typical ceramic processing route: powder synthesis –
green component (casting, extrusion, compaction) –
sintering / firing.

Processing Ceramics – Glasses
Most of them are silica-soda-lime variety.
Raw materials are heated to an elevated temperature where
melting occurs.
Glass melt is processed by different route to form different
products:
Pressing – to form shapes like plates and dishes
Blowing – used to produce objects like jars, bottles, light
bulbs.
Drawing – to form lengthier objects like tubes, rods,
whiskers, etc.

Ceramic Powder Processing
Ceramic powder processing route: synthesis of powder,
followed by fabrication of green product which is then
consolidated to obtain the final product.
Synthesis of powder involves crushing, grinding,
separating impurities, blending different powders.
Green component can be manufactured in different ways:
tape casting, slip casting, extrusion, injection molding and
cold-/hot- compaction.
Green component is then fired/sintered to get final product.

Ceramic Powder Processing - Casting
Slurry of ceramic powder is processed via casting routes –
tape casting, and slip casting.
Tape casting – also known as doctor blade process – used
for making thin ceramic tapes. In this slurry of ceramic
powder + binders + plasticizers is spread over plastic
substrate. Tape is then dried using hot air. Later tape is
subjected to binder burnout and sintering.
Slip casting – here aqueous slurry of ceramic powder is
poured into plaster of Paris mold. As water begins to move
out due to capillary action, thick mass builds along mold
wall. It is possible to form solid piece by pouring more
slurry.

Ceramic Powder Processing –
Extrusion & Injection Molding
Extrusion – viscous mixture of ceramic particles, binder
and other additives is fed through an extruder where
continuous shape of green ceramic is produced. Then the
product is dried and sintered.
Injection molding – it is similar to the process used for
polymer processing. Mixture of ceramic powder,
plasticizer, thermoplastic polymer, and additives is injected
into die with use of a extruder. Then polymer is burnt off,
before sintering rest of the ceramic shape. It is suitable for
producing complex shapes.
Extrusion and Injection molding are used to make ceramic
tubes, bricks, and tiles.

Compaction
Ceramic powder is compacted to form green shapes of
sufficient strength to handle and to machine.
Basis for compaction – application of external pressure
from all directions.
In cold iso-static pressing (CIP), pressure is applied using
oil/fluid, then green product is subjected to sintering.
In hot iso-static pressing (HIP), pressure is applied at high
temperatures thus compaction and sintering occurs
simultaneously. Its is expensive, but have certain
advantages.

Compaction, HIP
HIP is used
- when during CIP not enough strength is gained
- almost nil porosity is the requirement
- for Refractories and covalently bonded ceramics.
Sintering – process of subjecting the green ceramic to
elevated temperatures with the purpose of gaining
mechanical integrity.
Driving force for sintering – reduction in total surface area
and thus energy.
Diffusion (atomic- and bluk-) is responsible for growth of
bonds at contact points of particles (necks). This lead to
coalescence of particles, and eventual mechanical integrity.

Material Science/Applications and Processing of Polymers Lecture Notes
Chapter 11. Applications and Processing of Polymers
11.1 Mechanical behavior of polymers
The description of stress-strain behavior is similar to that of metals, but a very important
consideration for polymers is that the mechanical properties depend on the strain rate,
temperature, and environmental conditions.
The stress-strain behavior can be brittle, plastic and highly elastic (elastomeric or rubber-
like). Tensile modulus (modulus) and tensile strengths are orders of magnitude smaller
than those of metals, but elongation can be up to 1000 % in some cases. The tensile
strength is defined at the fracture point and can be lower than the yield strength.
Mechanical properties change dramatically with temperature, going from glass-like brittle
behavior at low temperatures (like in the liquid-nitrogen demonstration) to a rubber-like
behavior at high temperatures .
In general, decreasing the strain rate has the same influence on the strain-strength
characteristics as increasing the temperature: the material becomes softer and more
ductile.
11.2 Deformation of Polymers
Many semicrystalline polymers have the spherulitic structure and deform in the following
steps :
• elongation of amorphous tie chains
• tilting of lamellar chain folds towards the tensile direction
• separation of crystalline block segments
• orientation of segments and tie chains in the tensile direction
The macroscopic deformation involves an upper and lower yield point and necking.
Unlike the case of metals, the neck gets stronger since the deformation aligns the chains
so increasing the tensile stress leads to the growth of the neck. (Fig. 16.5).
Factors that Influence the Mechanical Properties of Polymers
The tensile modulus decreases with increasing temperature or diminishing strain rate.
Obstacles to the steps mentioned in strengthen the polymer. Examples are cross-linking
(aligned chains have more van der Waals inter-chain bonds) and a large mass (longer
molecules have more inter-chain bonds). Crystallinity increases strength as the secondary
bonding is enhanced when the molecular chains are closely packed and parallel. Pre-
deformation by drawing, analogous to strain hardening in metals, increases strength by
orienting the molecular chains. For undrawn polymers, heating increases the tensile

modulus and yield strength, and reduces the ductility - opposite of what happens in
metals.
.

11.3 Crystallization, Melting, and Glass Transition Phenomena
Crystallization rates are governed by the same type of S-curves we saw in the case of
metals (Fig. 16.7). Nucleation becomes slower at higher temperatures.
The melting behavior of semicrystalline polymers is intermediate between that of
crystalline materials (sharp density change at a melting temperature) and that of a pure
amorphous material (slight change in slope of density at the glass-transition temperature).
The glass transition temperature is between 0.5 and 0.8 of the melting temperature.
The melting temperature increases with the rate of heating, thickness of the lamellae, and
depends on the temperature at which the polymer was crystallized.
Melting involves breaking of the inter-chain bonds, so the glass and melting temperatures
depend on:
• chain stiffness (e.g., single vs. double bonds)
• size, shape of side groups
• size of molecule
• side branches, defects
• cross-linking
Rigid chains have higher melting temperatures.
11.4 Types of Polymers:
Thermoplastic and Thermosetting Polymers
Thermoplastic polymers (thermoplasts) soften reversibly when heated (harden when
cooled back)
Thermosetting polymers (thermosets) harden permanently when heated, as cross-linking
hinder bending and rotations. Thermosets are harder, more dimensionally stable, and
more brittle than thermoplasts.
11.5 Polymer synthesis and processing:
The large macromolecules of the commercially useful polymers must be synthesized
from substances having smaller molecules in a process termed polymerization.
Furthermore, the properties of a polymer may be modified and enhanced by the inclusion
of additive materials.
Polymerization

The synthesis of the large molecular weight polymers is termed polymerization; it is
simply the process by which monomer units are joined over, to generate each of the
constituent giant molecules. The reactions by which polymerization occurs are grouped
into two general classification- addition and condensation, according to the reaction
mechanisms.
Addition polymerization is a process by which bifuncational monomer units are attached
one at a time in chainlike fashion to form a linear macromolecules; the composition of
the resultant products molecule is an exact multiple for that of the original reactant
monomer. Three distinct stages- initiation, propagation and termination are involved in
addition polymerization.
Condensation polymerization is the formation of polymers by stepwise intermolecular
chemical reactions that normally involve more than one monomer species; there is
usually a small molecular weight by producer such as water, which is eliminated. No
reactant species has the chemical formula of the mer repeat unit, and the intermolecular
reaction occurs every time a mer repeat unit is formed

Applications and Processing of Polymers
Module-11

1. Polymer types and polymer synthesis and processing
2. Crystallization, melting and glass transition
3. Mechanical behavior of polymers
4. Mechanisms of deformation and strengthening of
polymers
Contents

Introduction – Polymers
The word ‘polymer’ is originated from Greek word meros,
which means ‘a part’.
Polymers are primarily organic compounds, however few
polymers are made of inorganic compounds.
Characteristics of ceramics are:
- low temperature stability
- low hardness
- low mechanical strength
- high elongation under application of stress
- high sensitivity of properties to their morphology

Classification – Polymers
Ceramics are classified in many ways. The prime
classification based on their industrial usage is: plastics and
elastomers.
Plastic polymers are again classified based on their
temperature dependence of their structure as follows:
- thermoplasts and
- thermosets

Thermoplasts
Plastics which softens up on heating and hardens up on
cooling where the softening and hardening are totally
reversible processes. Hence thermoplasts can be recycled.
They consist of linear molecular chains bonded together by
weak secondary bonds or by inter-winding.
Cross-linking between molecular chains is absent in
theromplasts.
E.g.: Acrylics, PVC, Nylons, Perspex glass, etc.

Thermosets
Plastics which are ‘set’ under the application of heat and/or
pressure. This process is not reversible, hence thermosets
can not be recycled.
They consist of 3-D network structures based on strong
covalent bonds to form rigid solids. linear molecular chains
bonded together by weak secondary bonds or by inter-
winding.
Characterized by high modulus / rigidity / dimensional
stability when compared with thermoplasts.
E.g.: Epoxies, Amino resins, some polyester resins, etc.

Elastomers
These polymers are known for their high elongations,
which are reversible upon release of applied loads.
They consist of coil-like molecular chains, which
straightens up on application of load.
Characterized by low modulus / rigidity / strength, but high
toughness.
E.g.: natural and synthetic rubber.

Polymer Synthesis - 1
Processing of polymers primarily limits to synthesis
followed by forming.
Polymers are synthesized by process known as
polymerization.
Polymerization is process in which multi-functional
monomers are attached to form linear/3-D macro molecular
chains.
When polymerization process involves single kind of
monomers i.e. in Additional polymerization, resultant
macro-molecule’s composition is an exact multiplication of
composition of individual monomer.

Additional polymerization process involves three stages
namely initiation, propagation and termination.
Initiation process will be started by an initiator (e.g.
benzoyl peroxide) which forms an reactive site where
carbon atom of another monomer is attracted, upon which
reaction site transfers to different place leading to
molecular chain growth.
As molecular chain grows longer, reaction rate decreases.
However the growth process is terminated either by the
combination or disproportionation process.

Condensation polymerization process involves more then
one monomer species. This process is also known as step
growth polymerization.
In condensation polymerization, smaller macro-molecule
by-product such as water is eliminated.
No resultant product has the chemical formula of mere one
monomer.
Repeat unit in condensation process itself is product of
polymerization involving basic constituents.
Reaction times for condensation polymerization is usually
longer than those for additional polymerization.

Degree Of Polymerization
Extant of polymerization is characterized in terms of
‘degree of polymerization’.
It si defined as number of mer units in molecular chain or
ration of average molecular weight of polymer to
molecular weight of repeat unit.
Average molecular weight is defined in two ways: Weight
average molecular weight (based on weight fraction) and
Number average molecular weight (based on the number
fraction).
Number average molecular weight is is always smaller than
the weight average molecular weight.

Polymer Forming
Thermoplasts usually formed above their glass transition
temperatures under application of pressure which ensures
detailed product shape.
Thermosets are formed in two stages – making liquid
polymer and then molding it.
Different molding techniques are employed to mold
polymers –
compression molding
transfer molding
injection molding
blow molding
extrusion

Polymer Forming Mechanics - 1
Polymer forming involves melting, cooling upon which
crystallization takes place. In addition, glass transition
occurs in polymers.
Crystallization rate depends on temperature and molecular
weight. It decrease with increase in molecular weight.
Polymer melting is different from that of metals as it takes
place over a temperature range.
Glass transition occurs in amorphous and semi-crystalline
polymers. Upon cooling, this transformation corresponds to
gradual change of liquid to rubbery material, and then rigid
solid.

Polymer Forming Mechanics - 2
Polymer melting and glass transition is heavily dependent
on polymer morphology.
Following factors has marked effect on these:
chain stiffness (e.g., single vs. double bonds)
size, shape of side groups
size of molecule
side branches, defects
cross-linking

Mechanical Behavior Of Polymers - 1
To an large extant, mechanical behavior of polymers is
similar to metals and ceramics.
However, polymers are distinct in the sense that parameters
namely temperature, strain rate, and morphology of
polymers has strong influence on mechanical behavior of
polymers.
Mechanical properties of polymers change dramatically
with temperature, going from glass-like brittle behavior at
low temperatures to a rubber-like behavior at high
temperatures.

Highly crystalline polymers behave in a brittle manner,
whereas amorphous polymers can exhibit plastic
deformation.
Due to unique structures of cross-linked polymers,
recoverable deformations up to very high strains / point of
rupture are also observed with polymers (elastomers).
Tensile modulus (modulus) and tensile strengths are orders
of magnitude smaller than those of metals, but elongation
can be up to 1000 % in some cases.

Typical stress-strain diagram for polymers:

Mechanisms Of Deformation In
Polymers
Elastic deformation – bending and stretching of covalent
bonds and slight adjustments of secondary vander Waals
forces.
Plastic deformation – NOT by dislocation movement, but
either rotation, stretching, sliding or disentanglement of
molecular chains, which may occurs in several stages.
Elastomers – simple uncoiling, and straightening of
molecular chains that are highly twisted, kinked, and coiled
in unstressed state. When an elastomer is stretched, causing
decrease in entropy, in-turn causes the modulus of elasticity
to increase with increasing temperature, which is opposite to
the behavior of other materials.

Strengthening Polymers
Polymers’ resistance to deformation – strength – is
influenced by many parameters.
For thermoplasts: average molecular mass, degree of
crystallization, presence of side groups, presence of polar
and other specific atoms, presence of phenyl rings in main
chains and addition of reinforcements.
For thermosets, its reinforcement methods.
Every parameter that influence the strength can be used as
means of strengthening the polymers.

Reinforcements For Polymers
Reinforcement strengthening in polymers is an important
mechanisms, applicable to both thermoplasts and
thermosets.
Fibers used as reinforcements are made of either glass,
carbon or aramid.
Glass fibers are two verities – E-glass and S-glass. The later
variety is costlier but offers more strength than former.
Aramid (aromatic polyamide) fibers – also known as Kevlar
– are commercially highly successful fibers. They are used
with plastics in many application including protection from
ballasts, ropes, aerospace, marine, and many other industrial
applications.

Material Science/Composites Lecture Notes
Chapter 12. COMPOSITES
12.1 Particle-reinforced composites
These are the cheapest and most widely used. They fall in two categories depending on
the size of the particles:
• large-particle composites, which act by restraining the movement of the matrix, if
well bonded.
• dispersion-strengthened composites, containing 10-100 nm particles, similar to
what was discussed under precipitation hardening. The matrix bears the major
portion of the applied load and the small particles hinder dislocation motion,
limiting plastic deformation.
12.2 Large-Particle Composites
Properties are a combination of those of the components. The rule of mixtures predicts
that an upper limit of the elastic modulus of the composite is given in terms of the elastic
moduli of the matrix (Em) and the particulate (Ep) phases by:
Ec = EmVm + EpVp
where Vm and Vp are the volume fraction of the two phases. A lower bound is given by:
Ec = EmEp / (EpVm + EmVp)
Concrete
The most common large-particle composite is concrete, made of a cement matrix that
bonds particles of different size (gravel and sand.) Cement was already known to the
Egyptians and the Greek. Romans made cement by mixing lime (CaO) with volcanic ice.
In its general from, cement is a fine mixture of lime, alumina, silica, and water. Portland
cement is a fine powder of chalk, clay and lime-bearing minerals fired to 1500o
C
(calcinated). It forms a paste when dissolved in water. It sets into a solid in minutes and
hardens slowly (takes 4 months for full strength). Properties depend on how well it is
mixed, and the amount of water: too little - incomplete bonding, too much - excessive
porosity.
The advantage of cement is that it can be poured in place, it hardens at room temperature
and even under water, and it is very cheap. The disadvantages are that it is weak and
brittle, and that water in the pores can produce crack when it freezes in cold weather.
Concrete is cement strengthened by adding particulates. The use of different size (stone
and sand) allows better packing factor than when using particles of similar size.

Concrete is improved by making the pores smaller (using finer powder, adding polymeric
lubricants, and applying pressure during hardening.
Reinforced concrete is obtained by adding steel rods, wires, mesh. Steel has the
advantage of a similar thermal expansion coefficient, so there is reduced danger of
cracking due to thermal stresses. Pre-stressed concrete is obtained by applying tensile
stress to the steel rods while the cement is setting and hardening. When the tensile stress
is removed, the concrete is left under compressive stress, enabling it to sustain tensile
loads without fracturing. Pre-stressed concrete shapes are usually prefabricated. A
common use is in railroad or highway bridges.
Cermets
are composites of ceramic particles (strong, brittle) in a metal matrix (soft, ductile) that
enhances toughness. For instance, tungsten carbide or titanium carbide ceramics in Co or
Ni. They are used for cutting tools for hardened steels.
Reinforced rubber
is obtained by strengthening with 20-50 nm carbon-black particles. Used in auto tires.
Dispersion-Strengthened Composites
Use of very hard, small particles to strengthen metals and metal alloys. The effect is like
precipitation hardening but not so strong. Particles like oxides do not react so the
strengthening action is retained at high temperatures.
12.3 Fiber-reinforced composites
In many applications, like in aircraft parts, there is a need for high strength per unit
weight (specific strength). This can be achieved by composites consisting of a low-
density (and soft) matrix reinforced with stiff fibers.
The strength depends on the fiber length and its orientation with respect to the stress
direction.
The efficiency of load transfer between matrix and fiber depends on the interfacial bond.
12.4 Structural Composites
Largest and most diverse use of composites due to ease of fabrication, low cost and good
properties.
Glass-fiber reinforced composites (GFRC) are strong, corrosion resistant and lightweight,
but not very stiff and cannot be used at high temperatures. Applications include auto and
boat bodies, aircraft components.

Carbon-fiber reinforced composites (CFRC) use carbon fibers, which have the highest
specific module (module divided by weight). CFRC are strong, inert, allow high
temperature use. Applications include fishing rods, golf clubs, aircraft components.
Kevlar, and aremid-fiber composite can be used as textile fibers. Applications include
bullet-proof vests, tires, brake and clutch linings.
Wood
This is one of the oldest and the most widely used structural material. It is a composite of
strong and flexible cellulose fibers (linear polymer) surrounded and held together by a
matrix of lignin and other polymers. The properties are anisotropic and vary widely
among types of wood. Wood is ten times stronger in the axial direction than in the radial
or tangential directions.

Material Science/Corrosion and Degradation of Materials Lecture Notes
Chapter 13. Corrosion and Degradation of Materials
13.1 Corrosion of Metals
The corrosion resistance of metals and alloys is a basic property related to the easiness
with which these materials react with a given environment. Corrosion is a natural
process that seeks to reduce the binding energy in metals. The end result of corrosion
involves a metal atom being oxidized, whereby it loses one or more electrons and leaves
the bulk metal. The lost electrons are conducted through the bulk metal to another site
where they are reduced. In corrosion parlance, the site where metal atoms lose electrons
is called the anode, and the site where electrons are transferred to the reducing species is
called the cathode.
The following links will lead to interesting information concerning specific metals and
indexes to relevant pages of the Corrosion Doctors site:
Aluminum
Cadmium
Chromium
Cobalt
Copper
Gold
Iron
Lead
Magnesium
Molybdenum
Nickel
Silver
Tin
Titanium
Zinc
Pure metals are used in many applications. Copper, for example, is used to make the wire
which goes inside electrical cables. Copper was chosen because it can be drawn into long
thin wires very easily (it is ductile) and because it is a good conductor of electricity. Pure
aluminum can also be used in wiring. It is also used as a cladding material for aluminum
alloy substrates.
Currently there are 86 known metals. Before the 19th century only 24 of these metals had
been discovered and, of these 24 metals, 12 were discovered in the 18th century.
Therefore, from the discovery of the first metals, gold and copper, until the end of the
17th century, some 7700 years, only 12 metals were known. Four of these metals,
arsenic, antimony , zinc and bismuth , were discovered in the thirteenth and fourteenth
centuries, while platinum was discovered in the 16th century. The other seven metals,
known as the Metals of Antiquity, were the metals upon which civilization was based.
These seven metals are Gold, Copper, Silver, Lead, Tin, Iron,Mercury.

13.2 Corrosion of Ceramics:
It is often said that one of the biggest advantages which ceramics have over other
materials is their corrosion resistance, that is, their chemical inertness in corrosive
environments. Is this always true?
Corrosion is generally understood as property degradation due to environmental attack.
As it will be shown in this section, there are a number of environments in which ceramics
can degrade at a rapid rate. There exists a tremendous need for reliable and corrosion
resistant structural ceramic or partly ceramic materials which can be used in aggressive
environments such as:
- high energy battery systems (such as sodium-sulphur): beta-alumina is being
investigated
- gas turbines: silicon nitride and/or carbide are being investigated
- heat exchangers: SiC, composites are being investigated
Ceramics are indeed much more environmentally stable, as compared to any other group
of engineering materials, e.g. metals or plastics. Still, the potential for ceramics as
corrosion resistant engineering structural materials are far from being fully realized,
because of:
• mechanical nonreliability of structural ceramic components
• difficult design with brittle materials
• a shortage of information and standardization of ceramics
• human reluctance to use non-ductile materials
Issues of particular importance when considering corrosion of ceramics:
• The resistance of many ceramics to wetting by a corrosive liquid is a valuable
property. Little corrosion is expected if a liquid does not wet a ceramic. This is why, for
example, born nitride (BN) and graphite are useful in handling melts and including the
extremely corrosive melts of silicate glasses. BN and graphite are not wetted by these
liquids.

• The solubility of the reaction product in the corrosive environment (liquid) is
critical to the extent of corrosion. Reaction barriers can form and prevent corrosion.
Some examples are silica on silicon carbide or nitride, and alumina on Al. On the other
hand, continuous dissolution of the reaction product can occur and sustain corrosion even
for small chemical driving force, for instance Al2O3 in molten KOH.
• Even if a major component of the ceramic is resistant to a given corrosive
environment, a minor phase (especially a grain boundary phase, in particular under stress)
could be corroded (leached), leading to the general failure of the component. Some
examples include:
- Alumina in water, where preferential attack of the grain boundary glassy (silicate)
phases occurs.
- The preferential attack of free Si in reaction bonded SiC, by alkalis or molten metals.
- The oxide grain boundary phases in nonoxides (B2O3 in BN, silicates in Si3N4 and
SiC) are sensitive to water.
Severe corrosion takes place if the ceramic is in contact with a substance which can
combine with it and form low-melting liquids (i.e. with eutectic point below ambient
temperature).
The example of above situation is the system composed of metallurgical slag in contact
with refractories. If the reaction is thermodynamically possible, the corrosion will
proceed at a dramatic rate if the refractory is wetted by the slag.
Degradation of polymers:
While the plastics industry searches for solutions to the problem of plastics waste, there
is, surprisingly, a growing band of people trying to save plastics.Although the
manufacturers of early ‘plastics’ such as horn buttons, Bois Durci paperweights or
celluloid collars would be astonished to see how well many of their goods have survived,
many other plastics have begun to show disturbing signs of instability. Every collection
of plastics worldwide, from the Science Museum and Tate Gallery to the Comb &
Plastics Museum in Oyonnax, has already lost or is losing unique and beautiful pieces
through degradation.
Plastics, Not as Long-Lasting as Once Thought

The crucial fact is that plastics are organic and have been described as a time bomb
ticking away since cellulose nitrate based plastics were invented around 130 years ago. It
can of course be argued that manufacturers’ foremost intentions have never been to make
beautiful objects for museums. However, museums have a duty to preserve their
acquisitions.
Recognition of Polymer Degradation
It was not until the late 1980s that attention was paid to the fact that plastics artefacts had
been physically changing, showing signs of acid vapour, tackiness, warping,
embrittlement and crazing. Cellulose nitrate and cellulose acetate were particularly
affected. By 1991 John Morgan of the Plastics Historical Society had collected enough
data to write Conservation of Plastics -An Introduction, a joint PHS /Conservation Unit
publication, and the Conservation Unit launched a survey to identify objects at risk with
the aim of setting up a research programme. The survey included everything from radios
and cables to textiles and sculptures.
Deterioration of Acrylic Paintings and Pieces of Art
By 1992 acrylic based paintings worth millions of pounds by leading artists of the 1960s
including David Hockney and Jackson Pollock had begun to suffer discolouration,
cracking and greyness due to the absorption of dust and atmospheric pollutants. These
paints seemed particularly vulnerable. At room temperature they are relatively soft and
attract dirt which becomes embedded. However, to date no method has been found of
cleaning them.
Impact on the Photographic Film Industry
The photographic film industry was also badly hit when irreplaceable archive nitrate
stock started to decompose. Today, the National Film Archive transfers cellulose nitrate
and cellulose triacetate onto more stable polyester at the rate of a million metres a year.
Preserving Plastics Pieces in Museums
The PHS/CU survey unearthed some interesting facts. For example, 40% of museums
surveyed contain plastics objects manufactured and collected since 1980, and modem
plastics are also showing symptoms of decay. Polyurethane foam appears to be one of the
worst victims, and many early video and audio tapes on magnetic media are already
unplayable. The curator who has to supervise a collection of high-tech, mixed material
products such as space suits is confronted with a conservation dilemma: which material
deserves priority treatment when each separate plastic has different requirements?
Factors Affecting Polymer Degradation
The degradation of plastics can be said to begin as soon as the polymer is synthesised,
and is increased by residual stresses left by moulding processes. This can be followed by

exposure to light (especially UV), humidity, oxygen, heat, bacteria and stress. Plastics
can also be contaminated by other materials, including other plastics. A polystyrene
camera body, for example, can be attacked by plasticiser migrating from a PVC strap.
Ideally the conservator needs information about the history of an object before
prescribing treatment, but even before this, the plastics ‘doctor’ must jump another
hurdle. Specific conservation action cannot be taken until the polymer has been
identified, and this is a technical area full of pitfalls. A 1920s black brooch could be made
of at least six different plastics materials, or simply painted as was common practice in
the 19th century. Even a patent number, one of the few ‘hallmarks’ found on plastics and
an obvious aid to identification, may refer to a fixing mechanism and not to the
moulding.
Preserving Plastics
Derek Pullen, a conservator at the Tate Gallery, explains, ‘Plastics are giant molecules
held together by forces which can be broken by attacking energy forces such as light. All
the conservator can do is to keep mouldings in a very stable, low energy environment (the
burial chambers of the Pyramids were ideal)’.
Types of Polymer Degradation
There are two main types of plastics degradation being researched at present: physical
and chemical, and both are closely inter-connected. Physical degradation can involve
environmental stress cracking and plasticiser migration and loss. Chemical reactions
include oxidation and hydrolysis, and are a problem particularly affecting the cellulose
esters (cellulose nitrate and cellulose acetate), which emit acidic degradation products. If
not removed, these catalyse further reactions and eventually cause serious crazing and
total destruction of the object. If degrading cellulose esters are not isolated, the acidic
fumes will infect similar objects stored close by and initiate degradation there.
Solutions to Polymer Degradation
As the recognition of polymer degradation improves, conservation guidelines are
beginning to emerge. High-tech solutions which could help in theory are prohibitively
expensive, but tailor made scavengers such as activated charcoal or Ageless help to create
a low oxygen environment. Ageless is a reactive powdered iron and is normally used to
prolong the shelf-life of dry foods by absorbing oxygen. Epoxidised soyabean oil
(ESBO), has also been tested with encouraging results as an acid absorbing coating on
degrading cellulose nitrate.

Conclusion
Compared to traditional materials with long established technologies such as metals and
glass, the complex chemical nature of plastics is providing conservators with possibly
their most formidable challenge yet.

Material Science/Electrical Properties Lecture Notes
Chapter 14. Electrical Properties
14.1 Electrical Conduction
Ohm’s Law
When an electric potential V is applied across a material, a current of magnitude I flows.
In most metals, at low values of V, the current is proportional to V, according to Ohm's
law:
I = V/R
where R is the electrical resistance. R depends on the intrinsic resistivity ρ of the material
and on the geometry (length l and area A through which the current passes).
R = ρl/A
Electrical Conductivity
The electrical conductivity is the inverse of the resistivity: σ = 1/ρ.
The electric field in the material is E=V/l, Ohm's law can then be expressed in terms of
the current density j = I/A as:
j = σ E
The conductivity is one of the properties of materials that varies most widely, from 107
(Ω-m) typical of metals to 10-20
(Ω-m) for good electrical insulators. Semiconductors
have conductivities in the range 10-6
to 104
(Ω-m).
Electronic and Ionic Conduction
In metals, the current is carried by electrons, and hence the name electronic conduction.
In ionic crystals, the charge carriers are ions, thus the name ionic conduction.
Energy Band Structures in Solids
When atoms come together to form a solid, their valence electrons interact due to
Coulomb forces, and they also feel the electric field produced by their own nucleus and
that of the other atoms. In addition, two specific quantum mechanical effects happen.
First, by Heisenberg's uncertainty principle, constraining the electrons to a small volume
raises their energy, this is called promotion. The second effect, due to the Pauli exclusion
principle, limits the number of electrons that can have the same property (which include

the energy). As a result of all these effects, the valence electrons of atoms form wide
valence bands when they form a solid. The bands are separated by gaps, where electrons
cannot exist. The precise location of the bands and band gaps depends on the type of
atom (e.g., Si vs. Al), the distance between atoms in the solid, and the atomic
arrangement (e.g., carbon vs. diamond).
In semiconductors and insulators, the valence band is filled, and no more electrons can be
added, following Pauli's principle. Electrical conduction requires that electrons be able to
gain energy in an electric field; this is not possible in these materials because that would
imply that the electrons are promoted into the forbidden band gap.
In metals, the electrons occupy states up to the Fermi level. Conduction occurs by
promoting electrons into the conduction band, that starts at the Fermi level, separated by
the valence band by an infinitesimal amount.
Electrical Resistivity of Metals
The resistivity then depends on collisions. Quantum mechanics tells us that electrons
behave like waves. One of the effects of this is that electrons do not scatter from a perfect
lattice. They scatter by defects, which can be:
o atoms displaced by lattice vibrations
o vacancies and interstitials
o dislocations, grain boundaries
o impurities
One can express the total resistivity ρtot by the Matthiessen rule, as a sum of resistivities
due to thermal vibrations, impurities and dislocations. Fig. 19.8 illustrates how the
resistivity increases with temperature, with deformation, and with alloying..
14.2 Semiconductivity:
Intrinsic Semiconduction
Semiconductors can be intrinsic or extrinsic. Intrinsic means that electrical conductivity
does not depend on impurities, thus intrinsic means pure. In extrinsic semiconductors the
conductivity depends on the concentration of impurities.
Conduction is by electrons and holes. In an electric field, electrons and holes move in
opposite direction because they have opposite charges. The conductivity of an intrinsic
semiconductor is:
σ = n |e| µe + p |e| µh

where p is the hole concentration and µh the hole mobility. One finds that electrons move
much faster than holes:
µe > µh
In an intrinsic semiconductor, a hole is produced by the promotion of each electron to the
conduction band. Thus:
n = p
Thus, σ = 2 n |e| (µe + µh) (only for intrinsic semiconductors).
Extrinsic Semiconduction
Unlike intrinsic semiconductors, an extrinsic semiconductor may have different
concentrations of holes and electrons. It is called p-type if p>n and n-type if n>p. They
are made by doping, the addition of a very small concentration of impurity atoms. Two
common methods of doping are diffusion and ion implantation.
Excess electron carriers are produced by substitutional impurities that have more valence
electron per atom than the semiconductor matrix. For instance phosphorous, with 5
valence electrons, is an electron donor in Si since only 4 electrons are used to bond to the
Si lattice when it substitutes for a Si atom. Thus, elements in columns V and VI of the
periodic table are donors for semiconductors in the IV column, Si and Ge. The energy
level of the donor state is close to the conduction band, so that the electron is promoted
(ionized) easily at room temperature, leaving a hole (the ionized donor) behind. Since this
hole is unlike a hole in the matrix, it does not move easily by capturing electrons from
adjacent atoms. This means that the conduction occurs mainly by the donated electrons
(thus n-type).
Excess holes are produced by substitutional impurities that have fewer valence electrons
per atom than the matrix. This is the case of elements of group II and III in column IV
semiconductors, like B in Si. The bond with the neighbors is incomplete and so they can
capture or accept electrons from adjacent silicon atoms. They are called acceptors. The
energy level of the acceptor is close to the valence band, so that an electron may easily
hop from the valence band to complete the bond leaving a hole behind. This means that
conduction occurs mainly by the holes (thus p-type).
The Temperature Variation of Conductivity and Carrier Concentration
Temperature causes electrons to be promoted to the conduction band and from donor
levels, or holes to acceptor levels. The dependence of conductivity on temperature is like
other thermally activated processes:
σ = A exp(–Eg/2kT)

where A is a constant (the mobility varies much more slowly with temperature). Plotting
ln σ vs. 1/T produces a straight line of slope Eg/2k from which the band gap energy can
be determined. Extrinsic semiconductors have, in addition to this dependence, one due to
the thermal promotion of electrons from donor levels or holes from acceptor levels. The
dependence on temperature is also exponential but it eventually saturates at high
temperatures where all the donors are emptied or all the acceptors are filled.
This means that at low temperatures, extrinsic semiconductors have larger conductivity
than intrinsic semiconductors. At high temperatures, both the impurity levels and valence
electrons are ionized, but since the impurities are very low in number and they are
exhausted, eventually the behavior is dominated by the intrinsic type of conductivity.
Semiconductor Devices
A semiconductor diode is made by the intimate junction of a p-type and an n-type
semiconductor (an n-p junction). Unlike a metal, the intensity of the electrical current that
passes through the material depends on the polarity of the applied voltage. If the positive
side of a battery is connected to the p-side, a situation called forward bias, a large amount
of current can flow since holes and electrons are pushed into the junction region, where
they recombine (annihilate). If the polarity of the voltage is flipped, the diode operates
under reverse bias. Holes and electrons are removed from the region of the junction,
which therefore becomes depleted of carriers and behaves like an insulator. For this
reason, the current is very small under reverse bias. The asymmetric current-voltage
characteristics of diodes is used to convert alternating current into direct current. This is
called rectification.
A p-n-p junction transistor contains two diodes back-to-back. The central region is very
thin and is called the base. A small voltage applied to the base has a large effect on the
current passing through the transistor, and this can be used to amplify electrical signals
(Fig. 19.22). Another common device is the MOSFET transistor where a gate serves the
function of the base in a junction transistor. Control of the current through the transistor
is by means of the electric field induced by the gate, which is isolated electrically by an
oxide layer.
Conduction in Ionic Materials
In ionic materials, the band gap is too large for thermal electron promotion. Cation
vacancies allow ionic motion in the direction of an applied electric field, this is referred
to as ionic conduction. High temperatures produce more vacancies and higher ionic
conductivity.
At low temperatures, electrical conduction in insulators is usually along the surface, due
to the deposition of moisture that contains impurity ions.

14.3 Superconductivity:
Superconductivity is the ability of certain materials to conduct electrical current with no
resistance and extremely low losses. This ability to carry large amounts of current can be
applied to electric power devices such as motors and generators, and to electricity
transmission in power lines. For example, superconductors can carry as much as 100
times the amount of electricity of ordinary copper or aluminum wires of the same size.
Scientists had been intrigued with the concept of superconductivity since its discovery in
the early 1900s, but the extreme low temperatures the phenomenon required was a barrier
to practical and low-cost applications. This all changed in 1986, when a new class of
ceramic superconductors was discovered that "superconducted" at higher temperatures.
The science of high-temperature superconductivity (HTS) was born, and along with it
came the prospect for an elegant technology that promises to "supercharge" the way
energy is generated, delivered, and used.
14.5 Dielectric Behavior
A dielectric is an electrical insulator that can be made to exhibit an electric dipole
structure (displace the negative and positive charge so that their center of gravity is
different).
Capacitance
When two parallel plates of area A, separated by a small distance l, are charged by +Q, –
Q, an electric field develops between the plates
E = D/εε0
where D = Q/A. ε0 is called the vacuum permittivity and ε the relative permittivity, or
dielectric constant (ε = 1 for vacuum). In terms of the voltage between the plates, V = E
l,
V = Dl/εε0 = Q l/Aεε0 = Q / C
The constant C= Aεε0/l is called the capacitance of the plates.
Field Vectors and Polarization
The dipole moment of a pair of positive and negative charges (+q and –q) separated at a
distance d is p = qd. If an electric field is applied, the dipole tends to align so that the
positive charge points in the field direction. Dipoles between the plates of a capacitor will
produce an electric field that opposes the applied field. For a given applied voltage V,
there will be an increase in the charge in the plates by an amount Q' so that the total

charge becomes Q = Q' + Q0, where Q0 is the charge of a vacuum capacitor with the
same V. With Q' = PA, the charge density becomes D = D0 E + P, where the polarization
P = ε0 (ε–1) E .
Types of Polarization
Three types of polarization can be caused by an electric field:
• Electronic polarization: the electrons in atoms are displaced relative to the
nucleus.
• Ionic polarization: cations and anions in an ionic crystal are displaced with
respect to each other.
• Orientation polarization: permanent dipoles (like H2O) are aligned.
Frequency Dependence of the Dielectric Constant
Electrons have much smaller mass than ions, so they respond more rapidly to a changing
electric field. For electric field that oscillates at very high frequencies (such as light) only
electronic polarization can occur. At smaller frequencies, the relative displacement of
positive and negative ions can occur. Orientation of permanent dipoles, which require the
rotation of a molecule can occur only if the oscillation is relatively slow (MHz range or
slower). The time needed by the specific polarization to occur is called the relaxation
time.
Dielectric Strength
Very high electric fields (>108
V/m) can free electrons from atoms, and accelerate them
to such high energies that they can, in turn, free other electrons, in an avalanche process
(or electrical discharge). This is called dielectric breakdown, and the field necessary to
start the is called the dielectric strength or breakdown strength.
Dielectric Materials
Capacitors require dielectrics of high ε that can function at high frequencies (small
relaxation times). Many of the ceramics have these properties, like mica, glass, and
porcelain). Polymers usually have lower ε.
14.6 Ferroelectricity
Ferroelectric materials are ceramics that exhibit permanent polarization in the absence of
an electric field. This is due to the asymmetric location of positive and negative charges
within the unit cell. Two possible arrangements of this asymmetry results in two distinct
polarizations, which can be used to code "0" and "1" in ferroelectric memories. A typical
ferroelectric is barium titanate, BaTiO3, where the Ti4+
is in the center of the unit cell and
four O2-
in the central plane can be displaced to one side or the other of this central ion .

14.7 Piezoelectricity
In a piezolectric material, like quartz, an applied mechanical stress causes electric
polarization by the relative displacement of anions and cations.

Material Science/Thermal Properties Lecture Notes
Chapter 15. Thermal Properties
15.1 Heat Capacity:
Heat Capacity is a property that is indicative of a materials ability to absorb heat from
external surroundings; it represnts tha amount of energy required to produce a unit
temperature rise.In mathematical terms, the heat capacity C is expressed as follows:
C=dQ/dT
Where dQ is the energy required to produce a dT temperature change. Unit of heat
capacity is J/kg-K.
15.2 Thermal expansion:
Most solid materials expand upon heating and contract when cooled. The change in
length with temperature for a solid material may be expressed as follows:
Over small temperature ranges, the linear nature of thermal expansion leads to expansion
relationships for length, area, and volume in terms of the linear expansion coefficient.
The coefficient of thermal expansion is generally defined as the fractional increase in
length per unit rise in temperature. The exact definition varies, depending on whether it is
specified at a precise temperature (true coefficient of thermal expansion) or over a
temperature range (mean coefficient of thermal expansion). The former is related to the
slope of the tangent to the length – temperature plot, while the latter is governed by the
slope of the chord between two points on this curve. Considerable variation in the value
of the CTE can occur according to the definition employed.
For metallic materials values in the range 10 x 10-6
to 30 x 10-6
K-1
are common, and the
thermal expansion of pure metals up to their melting points has been well characterised.
However data for engineering alloys at very high temperatures is often limited. This is
significant since there is generally a variation (usually an increase) in CTE with
temperature.
15.3 Thermal Conductivity:
The thermal conductivity of a material is equivalent to the quantity of heat that passes in
unit time through unit area of a plate, when its opposite faces are subject to unit
temperature gradient (e.g. one degree temperature difference across a thickness of one
unit).
Thermal conductivity = Heat flow rate ÷ (Area × Temperature gradient)
In the SI system of units, thermal conductivity is measured in watts per metre-kelvin,
(W·m-1
·K-1
) where a
• watt is the unit of power
• metre is the unit of distance

Material Science/Thermal Properties Lecture Notes
• kelvin is the unit of temperature
15.4 Thermal Stress
Thermal stresses are stresses induced in a body as a result of changes in temperature.
There are various types of thermal deformation.
Completely Constrained Thermal Deformation:
The thermal stress which develops if a structure or member is completely constrained
(not allowed to move at all) is the product of the coefficient of linear expansion and the
temperature change and Young's modulus for the material.
Partially Constrained Thermal Deformation:
A more normal situation in a structure, rather than completely constrained or completely
free thermal deformation, is a partially constrained thermal deformation. This means a
member may expand (or contract) but not as much as it would if unconstrained.
Stresses resulting from temperature gradients:
When a solid body is heated or cooled, the internal temperature distribution will depend
on its size and shape, the thermal conductivity pf the material and the rate of temperature
change. Thermal stresses may be established as a result of temperature gradients across a
body, which are frequently caused by rapid heating or cooling, in that the outside changes
temperature more rapidly than the interior.

Material Science/Magnetic Properties Lecture Notes
Chapter 16. Magnetic Properties
16.1 Diamagnetism and Para magnetism:
Diamagnetism is a very weak form of magnetism that is nonpermanent and persists only
while an external field is being applied. It is induced by a change in the orbital motion of
electrons due to an applied magnetic field. The magnitude of the induced magnetic
moment is extremely small and in a direction opposite to that of the applied field.
paramagnetic material is one whose atoms do have permanent dipole moments, but the
magic of ferromagnetism is not active. If a magnetic field is applied to such a material,
the dipole moments try to line up with the magnetic field, but are prevented from
becoming perfectly aligned by their random thermal motion. Because the dipoles try to
line up with the applied field, the susceptibilities of such materials are positive, but in the
absence of the strong ferromagnetic effect, the susceptibilities are rather small, say in the
range to . When a paramagnetic material is placed in a strong magnetic field, it
becomes a magnet, and as long as the strong magnetic field is present, it will attract and
repel other magnets in the usual way. But when the strong magnetic field is removed, the
net magnetic alignment is lost as the dipoles relax back to their normal random motion.
16.2 Ferromagnetism:
Certain metallic materials possess a permanent magnetic moment in the absence of an
external field, and manifest very large and permanent magnetizations. These are the
characteristics of ferromagnetism, and they are displayed by the transition metals iron,
cobalt, nickel, and some of the rare earth metals. Permanent magnetic moments in
ferromagnetic materials result from atomic magnetic moments due to electron spin-
uncancelled electron spins as a consequence of the electron structure. There is also an
orbital magnetic moments contribution that is small in comparison to the spin moment.
Furthermore, in a ferromagnetic material, coupling interactions cause net spin magnetic
moments of adjacent atoms to align with one another, even in the absence of an external
field. The maximum possible magnetization or saturation magnetization Ms of a
ferromagnetic material represents the magnetization that results when all the magnetic
diploes in a solid piece are mutually aligned with the external field; there is also a
corresponding saturation flux density Bs.
16.3 Antiferromagnetism:
This phenomenon of magnetic moment coupling between adjacent atoms or ions occurs
in materials other than those that are ferromagnetic. In one such group, this coupling
results in an antiparallel alignment; the alignment of the spin moments of neighbouring
atoms or ions in exactly opposite directions is termed antiferromagentism. Manganese
oxide(MnO) is one such material that displays this behavior. Manganese oxide is a
ceramic material that is ionic in character, having both Mn and O ions.No net magnetic
moment is associated with O ions, since there is a total cancellation of both spin and
orbital moments. However, the Mn ions possesses s nrt magnetic moment that is

Material Science/Magnetic Properties Lecture Notes
predominantly of spin origin.These Mn ions are arrayed in the crystal structure such that
the moments of adjacent ions are antiparallel. Obvioulsy, the opposing magnetic
moments cancel one another and as a consequence, the solid as a whole possesses no net
magnetic moment.
Ferrimagnetism
Some ceramics also exhibit a permanent magnetizations termed ferrimagentism. The
macroscopic magnetic characteristics of ferromagnets and ferrimagents are similar; the
distinction lies in the source of the net magnetic moments. The net ferrimagentic moment
arises from the incomplete cancellation of spin moments.
16.4 Influence of temperature on magnetic behavior:
Temperature can also influence the magnetic characteristics of materials. The atomic
magnetic moments are free to rotate, hence with rising temperature, the increased thermal
motion of the atoms tends to randomize the directions of any moments that may be
aligned.
For ferromagnetic, antiferromagentic and ferrimagentic materials, the atomic thermal
motions counteract the coupling forces between the adjacent atomic dipole moments,
causing some dipole misalignment, regardless of whether an external field is present. The
result is a decrease in the saturation magnetization for both ferro and ferrimagnets. The
saturation magnetization is a maximum at ) K, at which temperature the thermal
vibrations are a minimum. With increasing temperature, the saturation magnetization
diminishes gradually and then abruptly drops to zero at what is called the curie
temperature Tc. The magnitude of the curie temparature varies from material to material;
for example, for iron, cobalt, nickel., the respective values are 768,1120,335 and 585
degree Celsius. Antiferromagnetism is also affected by temperature; this behavior
vanishes at what is called the Neel temperature. At temperatures above this point,
antiferromagnteic materials also become paramagnetic.
16.5 Domains and Hysteresis:
Any ferromagnetic or ferromagnetic material that is at a temperature below Tc is
composed of small-volume regions in which there is a mutual alignment in the same
direction of all magnetic dipole moments. Such a region is called a domain, and each one
is magnetized to its saturation magnetization. Adjacent domains are separated by domain
boundaries or walls across which the direction of magnetization gradually changes.
Normally, domains are microscopic in size and for a polycrystalline specimen, each grain
may consist of a single domain. Thus, in a microscopic piece of material, there will be
large number of domains and all may have different magnetization orientations.

Material Science/Optical Properties Lecture Notes
Chapter 17. Optical Properties
17.1 Basic concepts:
Electromagnetic Radiation- In the classical sense, electromagnetic radiation is considered
to be wave-like, consisiting of electric and magnetic field components that are
perpendicular to each other and also to the direction of propagation. Light, heat, radio
waves, radar and x-rays are all forms of electromagnetic radiation. Each is characterized
primarily by a specific range of wavelengths, and also according to the technique by
which it is generated. The electromagnetic spectrum of radiation spans the wide range
from gamma rays having wavelengths on the order of 10-12
, through x-rays, ultraviolet,
visible, infrared and finally radio waves with wavelengths as long as 1015
All electromagnetic radiation traverses a vacuum at the same velocity, that of light.
This velocity,c, is related to the electric permittivity of a vacuum and the magnetic
permeability of a vacuum through . Thus there is an association between the
electromagnetic constant c and these electrical and magnetic constants. Furthermore, the
frequency ν and wavelength λ of the electromagnetic radiation are a function of velocity
according to:
C= ν/λ
Frequency is expressed in terms of hertz(Hz), and 1 Hz=1 cycle per second. Ranges of
frequency for the various forms of electromagnetic radiation are also included in the
spectrum.
The electromagnetic spectrum covers a wide range of wavelengths and photon energies.
Light used to "see" an object must have a wavelength about the same size as or smaller
than the object. The ALS generates light in the far ultraviolet and soft x-ray regions,
which span the wavelengths suited to studying molecules and atoms.
17.2 Optical properties of metals:
Consider the electron energy band schemes for metals; in both cases a high-energy band
is only partially filled with electrons. Metals are opaque because the incident radiation
having frequencies within the visible range excites electrons into unoccupied energy
states above the Fermi energy. All frequencies of visible light are absorbed by metals
because of the continuously available empty electron states, which permit electron
transitions. In fact, metals are opaque to all electromagnetic radiation on the low end of
the frequency spectrum, from radio waves, through infrared, the visible and into about the
middle of the ultraviolet radiation. Metals are transparent to high frequency radiation.
Most of the absorbed radiation is reemitted from the surface in the form of visible light of
the same wavelength, which appears as reflected light. Since metals are opaque and
highly reflective the perceived color is determined by the wavelength distribution of the
radiation that is reflected and not absorbed. A bright silvery appearance when exposed to
white light indicates that the metal is highly reflected beam; the composition of these
reemitted photons, in terms of frequency and number is approximately the same as for the
incident beam. Aluminum and silver are the two metals that exhibit this reflective
behavior. Copper and gold appear red orange and yellow, respectively, because some of

the energy associated with light photons having short wavelengths is not reemitted as
visible light.
17.3 Optical properties of non metals:
By virtue of their electron energy band structures, nonmetallic materials may be
transparent to visible light. Therefore, in addition to reflection and absorption, refraction
and transmission phenomena also need to be considered.
Refraction:
Light that is transmitted into the interior of transparent materials experiences decrease in
velocity and as result is bent at the interface; this phenomenon is termed refraction. The
index of refraction n of a material is defined as the ratio of the velocity in vacuum c to the
velocity in the medium ν , or
n=c/ν
The magnitude of n will depend on the wavelength of the light. This effect is graphically
demonstrated by the familiar dispersion or separation of a beam of white light into its
component colors by a class prism. Each color is deflected by a different amount as it
passes into and out of the glass, which results in the separation of colors. Not only does
the index of refraction affect the optical path of light, but also it influences the fraction of
incident light that is reflected at the surface. The phenomenon of refraction is related to
electronic polarization at the relatively high frequencies for visible light; thus the
electronic component of the dielectric constant may be determined from index of
refraction measurements.
Since the retardation of electromagnetic radiation in a medium results from electronic
polarization, the size of the constituent atoms or ions has a considerable influence on the
magnitude of this effect-generally, the larger an atom or ion, the greater will be the
electronic polarization, the slower the velocity and greater the index of refraction.
Reflection:
When light radiation passes from one medium into another having a different index of
refraction, some of the light is scattered at the interface between the two media even if
both are transparent. The reflectivity R represents the fraction of the incident light that is
reflected at the interface.
R=Ir/Io
Where Io and Ir are the intensities of the incident and reflected beams, respectively.Just
as the index of refraction of a solid depends on the wavelength of the incident light, so
does the reflectivity vary with wavelength.
Absorption:
Nonmetallic materials may be opaque or transparent to visible light; and, if transparent,
they often appear colored. In principle, light radiation is absorbed in this group of
materials by two basic mechanisms, which also influence the transmission characteristics
of these nonmetals. Absorption by electronic polarization is important only at light
frequencies in the vicinity of the relaxation frequency of the constituent atoms. The other
mechanism involves valence band-conduction band electron transitions, which depends
on the electron energy band structure of the material.

Transmission:
The phenomena of absorption, reflection and transmission may be applied to the passage
of light through a transparent solid. The fraction of incident light that is transmitted
through a transparent material depends on the losses that are incurred by absorption and
reflection. The sum of reflectivity R, absorptivity A and transmittivity T, is unity. Also,
each of of the variables R, A and T depends on light wavelength.
17.4 Applications of optical phenomena
Luminescence
Some materials are capable of absorbing energy and then reemitting visible light in a
phenomenon called luminescence. Photons of emitted light are generated from electron
transitions in the solid. Energy is absorbed when an electron is promoted to an excited
energy; visible light is emitted when it false back to a lower energy state. The absorbed
energy may be applied as higher energy electrons or by heat, mechanical or chemical
energy. Furthermore, luminescence is classified according to the magnitude of the delay
time between absorption and reemission events.
Luminescence is "cold light", light from other sources of energy, which can take place at
normal and lower temperatures. In luminescence, some energy source kicks an electron
of an atom out of its "ground" (lowest-energy) state into an "excited" (higher-energy)
state; then the electron gives back the energy in the form of light so it can fall back to its
"ground" state.
There are several varieties of luminescence, each named according to what the source of
energy is, or what the trigger for the luminescence is.
Fluorescence and Photoluminescence are luminescence where the energy is supplied by
electromagnetic radiation (rays such as light, which will be discussed later);
photoluminescence is generally taken to mean luminance from any electromagnetic
radiation, while fluorescence is often used only for luminescence caused by ultraviolet,
although it may be used for other photoluminescences also. Fluorescence is seen in
fluorescent lights, amusement park and movie special effects, the redness of rubies in
sunlight, "day-glo" or "neon" colors, and in emission nebulae seen with telescopes in the
night sky. Bleaches enhance their whitening power with a white fluorescent material.
Photoluminescence should not be confused with reflection, refraction, or scattering of
light, which cause most of the colors you see in daylight or bright artificial lighting.
Photoluminescence is distinguished in that the light is absorbed for a significant time, and
generally produces light of a frequency that is lower than, but otherwise independent of,
the frequency of the absorbed light.
Electroluminescence is luminescence caused by electric current. Cathodoluminescence is
electroluminescence caused by electron beams; this is how television pictures are formed.
Other examples of electroluminescence are neon lights, the auroras, and lightning
flashes. This should not be mistaken for what occurs with the ordinary incandescent

electric lights, in which the electricity is used to produce heat, and it is the heat that in
turn produces light.
Radioluminescence is luminescence caused by nuclear radiation. Older glow-in-the-dark
clock dials often used a paint with a radioactive material (typically a radium compound)
and a radioluminescent material. The term may be used to refer to luminescence caused
by X-rays, also called photoluminescence
Photoconductivity
Photoconductivity is an optical and electrical phenomenon in which a material becomes
more conductive when subjected to ultraviolet or gamma radiation. See photoconductor.
Photoconductivity is the tendency of a substance to conduct electricity to an extent that
depends on the intensity of light-radiant energy (usually infrared transmission or visible
light) striking the surface of a sample. Most semiconductor materials have this property.
When there is no illumination, a photoconductive sample has a conductance that
depends on its dimensions, on the specific material(s) from which it is made, and on the
temperature. In most cases, the greater the radiant energy of a specific wavelength that
strikes the surface, the higher the conductance of the sample becomes, up to a certain
maximum. When the maximum conductance is reached for a particular sample, further
increases in irradiation produce no change in the conductance. Photoconductive materials
are used in the manufacture of photoelectric devices. Typical photoconductive substances
consist of germanium, gallium, selenium, or silicon with impurities, also known as
dopants, added. Other common materials include metal oxides and sulfides.
Lasers
All the radioactive electron transitions are spontaneous; that is, an electron falls from a
high energy state to a lower one without any external provocation. These transition events
occur independently of one another and at random times, producing radiation that is
incoherent; that is, the light waves are out of phase with one another. With
lasers,however,coherent light is generated by electron transitions initiated by an external
stimulus;in fact,”laser” is just the acronym for light amplification by stimulated emission
of radiation.
Applications of Lasers
The light beam produced by most lasers is pencil-sized, and maintains its size and
direction over very large distances; this sharply focused beam of coherent light is
suitable for a wide variety of applications. Lasers have been used in industry for cutting
and boring metals and other materials, and for inspecting optical equipment. In medicine,
they have been used in surgical operations. Lasers have been used in several kinds of

scientific research. The field of holography is based on the fact that actual wave-front
patterns, captured in a photographic image of an object illuminated with laser light, can
be reconstructed to produce a three-dimensional image of the object.
Lasers have opened a new field of scientific research, nonlinear optics, which is
concerned with the study of such phenomena as the frequency doubling of coherent light
by certain crystals. One important result of laser research is the development of lasers
that can be tuned to emit light over a range of frequencies, instead of producing light of
only a single frequency. Work is being done to develop lasers for communication; in a
manner similar to radio transmission, the transmitted light beam is modulated with a
signal and is received and demodulated some distance away. Lasers have also been used
in plasma physics and chemistry.
For years after its invention, the laser was spoken of as a solution without a problem.
That reputation soon disappeared as lasers found uses in a variety of industries. But now
several new lasers, particularly solid state instruments that operate at ultraviolet
wavelengths and those based on nonlinear materials, are finding uses in emerging areas.
Computing, telecommunications, and, in particular, medicine, stand to benefit from the
unique qualities of these new or improved systems.
Optical fibers in communications:
Our current "age of technology" is the result of many brilliant inventions and discoveries,
but it is our ability to transmit information, and the media we use to do it, that is perhaps
most responsible for its evolution . Progressing from the copper wire of a century ago to
today’s fiber optic cable, our increasing ability to transmit more information, more
quickly and over longer distances has expanded the boundaries of our technological
development in all areas. Today’s low-loss glass fiber optic cable offers almost unlimited
bandwidth and unique advantages over all previously developed transmission media. The
basic point-to-point fiber optic transmission system consists of three basic elements: the
optical transmitter, the fiber optic cable and the optical receiver.
The Optical Transmitter: The transmitter converts an electrical analog or digital signal
into a corresponding optical signal. The source of the optical signal can be either a light

emitting diode, or a solid state laser diode. The most popular wavelengths of operation
for optical transmitters are 850, 1300, or 1550 nanometers.
The Fiber Optic Cable: The cable consists of one or more glass fibers, which act as
waveguides for the optical signal. Fiber optic cable is similar to electrical cable in its
construction, but provides special protection for the optical fiber within. For systems
requiring transmission over distances of many kilometers, or where two or more fiber
optic cables must be joined together, an optical splice is commonly used.
The Optical Receiver: The receiver converts the optical signal back into a replica of the
original electrical signal. The detector of the optical signal is either a PIN-type
photodiode or avalanche-type photodiode.
Advantages of Fiber Optic Systems
Fiber optic transmission systems – a fiber optic transmitter and receiver, connected by
fiber optic cable – offer a wide range of benefits not offered by traditional copper wire or
coaxial cable. These include:
1. The ability to carry much more information and deliver it with greater fidelity than
either copper wire or coaxial cable.
2. Fiber optic cable can support much higher data rates, and at greater distances, than
coaxial cable, making it ideal for transmission of serial digital data.
3. The fiber is totally immune to virtually all kinds of interference, including lightning,
and will not conduct electricity. It can therefore come in direct contact with high voltage
electrical equipment and power lines. It will also not create ground loops of any kind.
4. As the basic fiber is made of glass, it will not corrode and is unaffected by most
chemicals. It can be buried directly in most kinds of soil or exposed to most corrosive
atmospheres in chemical plants without significant concern.
5. Since the only carrier in the fiber is light, there is no possibility of a spark from a
broken fiber. Even in the most explosive of atmospheres, there is no fire hazard, and no
danger of electrical shock to personnel repairing broken fibers.
6. Fiber optic cables are virtually unaffected by outdoor atmospheric conditions, allowing
them to be lashed directly to telephone poles or existing electrical cables without concern
for extraneous signal pickup.
7. A fiber optic cable, even one that contains many fibers, is usually much smaller and
lighter in weight than a wire or coaxial cable with similar information carrying capacity.
It is easier to handle and install, and uses less duct space. (It can frequently be installed
without ducts.)

8. Fiber optic cable is ideal for secure communications systems because it is very difficult
to tap but very easy to monitor. In addition, there is absolutely no electrical radiation
from a fiber.
How are fiber optic cables able to provide all of these advantages? This guide will
provide an overview of fiber optic technology – with sections devoted to each of the three
system components – transmitters, receivers, and the fiber cable itself. An appreciation of
the underlying technology will provide a useful framework for understanding the reasons
behind its many benefits.

Material Science/Economic, Environmental, and Social Issues of Material Usage Lecture Notes
Chapter 18. Economic, Environmental, and Social Issues of
Material Usage
18.1 Economic Considerations:
It is essential for the engineer to know about and understand economic issues simply
because the company/institution for which he or she works must realize a profit from the
products it manufactures. Materials engineering decisions have economic consequences
with regard to both material and production cost
18.2 Environmental and Social considerations:
Issues of environmental protection and sustainable development are gaining an increasing
importance in everyday life, and nowhere is this more so than in the field of Materials
Science and Engineering. Almost every aspect of materials usage, from extraction and
production, through product design and ultimately disposal issues, is now subject to
environmental considerations. Furthermore there are many cases where the developments
of novel ‘environmentally-friendly’ materials are providing new challenges for materials
scientists and engineers.
The growing awareness of environmental issues has increased the attention focused on
the materials industry. There is a danger that this could give a negative picture,
highlighting examples where materials production and use has led to environmental
problems. In many of these cases, materials, additives and production methods were used
for very good materials engineering reasons before environmental concerns were
established. The more positive image of materials engineering that can be portrayed is
one where the industry is at the forefront of technical advances - not only to 'deal with
past mistakes', but also to drive sustainable and safe use of materials for the future.
The topic of 'Environmental Materials' is broad and can touch on some relatively in-depth
aspects of materials structure, chemical and physical properties, processing and design as
well as more general areas such as legislative, economic and social aspects. Interesting
topics within this area can be presented at a range of levels: for instance the sustainable
use of materials in the IT sector can be discussed by 11 year olds with as much
enthusiasm as by post-graduate students - although the latter would be expected to grasp
the chemical details of identifying brominated flame-retardants, whereas the former
would consider much simpler aspects, that are nonetheless important.
18.3 Recycling issues:
It could easily be argued that steel is a very sustainable material; it is abundant, takes
relatively little energy to extract and is easy to recycle, however people living near a
steelworks would argue against this. It is probably sensible to define such materials as
those that have distinct differences that achieve environmental benefit compared to
conventional materials. With this definition, the list would include:

1. Materials of a significantly plant-based nature, including wood, natural fibre
composites, natural polymers.
2. Materials produced using a large proportion of waste material, including recycled
polymers, composites made from waste mineral powders, and arguably also much
steel and aluminum.
The most exciting developments in Materials Science are in the realm of functional
materials, and many of these serve an environmentally-beneficial purpose, particularly in
the production of green energy.
These include:
o Solar-cell materials
o Fuel-cell technology
o Catalytic pollution control
The figure below schematically shows how the disparate areas under the heading of
'environmental materials' can be linked via a life cycle analysis approach.

18.4 Life Cycle Analysis and its use in design:
Life Cycle Analysis is essentially a method of considering the entire environmental
impact, energy and resource usage of a material or product. It is often known as a 'cradle-
to-grave' analysis and can encompass the entire lifetime from extraction to end-of-life
disposal. Life cycle analysis can be an extremely effective way of linking many different
aspects of the environmental impacts of materials usage. The scope of a life cycle
analysis can be adjusted to suit a particular case. For instance it could cover the
environmental impact of the global aluminium industry or simply that of one single
plastic injection moulding machine. In order to gain most learning benefit from this area,
students would be expected to have a good grasp of the necessary underlying technical
areas, which could be quite complex and so this ideally suits more advanced degree level
students. The most conventional way of approaching a life cycle analysis is to follow a
particular material or product through its lifetime. Therefore the first consideration would
be the impact of materials extraction, and then production and manufacture, product use
and finally end-of-life considerations. This approach is followed below. Various aspects,
such as energy usage, economic and legislative issues occur throughout the cycle.

Material science notes

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