CE 241 MATERIALS

SCIENCE
Dr. Nihat ATMACA June 2021
Introduction to Materials
Science

2
 MATERIALS SCIENCE AND
ENGINEERING

 Materials Science: involves investigating the

relationships that exist between the structures and
properties of materials.

 Materials Engineering: is on the basis of these

structure–property correlations, designing or
engineering the structure of a material to produce a
predetermined set of properties.

3
Why do we study materials?

 Because, many scientists or engineers, whether

mechanical, civil, chemical, or electrical, will at one
time or another be exposed to a design problem
involving materials.

 Examples might include a transmission gear, the

superstructure for a building, an oil refinery
component, or an integrated circuit chip. Of course,
material scientists and engineers are specialists who
are totally involved in the investigation and design of
materials.

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 CLASSIFICATION OF
MATERIALS
 Solid materials have been conveniently grouped into three basic
classifications:

 Metals,
 Ceramics, and
 Polymers.

 In addition, there are other groups of important engineering

materials:

 Composites,
 Semiconductors, and
 Bio-materials.
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METALS:

Metallic materials are normally combinations of metallic

elements. They have large numbers of nonlocalized
electrons; that is, these electrons are not bound to particular
atoms. Many properties of metals are directly attributable
to these electrons.

Metals are extremely good conductors of electricity and

heat and are not transparent to visible light; a polished
metal surface has a lustrous appearance.

Furthermore, metals are quite strong, yet deformable,

which accounts for their extensive use in structural
applications. 6
METALS:

Atoms are located in regularly defined, repeating

positions - a crystal

Structure has ―free electrons‖ making metals good

electrical conductors

Strong but very dense

Moderate temperature resistance

Metals resist brittle fracture by bending - ductile

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METALS:

• Magnesium
• Aluminum
• Titanium • Aluminum alloys
• Iron – Copper
– Magnesium
• Nickel
– Zinc
• Iron alloys (steels)
– Carbon
– Chromium
– Nickel
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METALS:

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CERAMICS:

Ceramics are compounds between metallic and nonmetallic elements;

they are most frequently oxides, nitrides, and carbides. The wide range
of materials that falls within this classification includes ceramics that are
composed of clay minerals, cement, and glass.

These materials are typically insulative to the passage of electricity and

heat, and are more resistant to high temperatures and harsh
environments than metals and polymers.

With regard to mechanical behavior, ceramics are hard but very brittle.
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 CERAMICS:

 Combination of metallic and non-metallic atoms

 Many but not all ceramics are crystalline
 Bonding does not permit ―free electrons‖
 Very strong, moderate density
 High temperature stability, chemically resistant
 Ceramics bend little before they break - brittle
• Sand
• Window glass
• Clay
• Dinnerware
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CERAMICS:

CERAMIC MATERIALS

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CERAMICS:

CERAMIC MATERIALS

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POLYMERS:

Polymers include the familiar plastic and rubber

materials.

Many of them are organic compounds that are

chemically based on carbon, hydrogen, and other
nonmetallic elements; furthermore, they have very
large molecular structures. These materials typically
have low densities and may be extremely flexible.

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POLYMERS:

 Long chain molecules with repeating groups

 Relatively low strength, temperature sensitive
 Easy to form into complex shapes
 Low density, can be ductile or brittle
 Inexpensive

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 POLYMERS:

Cellulose (wood fiber)

Kevlar

Nylon

Polystyrene

Teflon
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SEMICONDUCTORS:

 Semiconductors have electrical properties that are

intermediate between the electrical conductors and
insulators.
 Furthermore, the electrical characteristics of these
materials are extremely sensitive to the presence of minute
concentrations of impurity atoms, which concentrations may
be controlled over very small spatial regions.
 The semiconductors have made possible the advent of
integrated circuitry that has totally revolutionized the
electronics and computer industries over a long time.

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SEMICONDUCTORS:

 Bonding similar to ceramics

 Mechanical properties similar to ceramics
 Used in electronic and optical devices

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COMPOSITES:

A number of composite materials have been engineered

that consist of more than one material type. Fiberglass is a
familiar example, in which glass fibers are embedded
within a polymeric material.

A composite is designed to display a combination of the

best characteristics of each of the component materials.

For instance, fiberglass acquires strength from the glass and

flexibility from the polymer. Many of the recent material
developments have involved composite materials.

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COMPOSITES:

 Two or more materials are combined

 Structural applications where rigidity, strength, and
low density are critical.

• Aluminum/silicon carbide
• Carbon/carbon
• Carbon/Epoxy
• Plywood
• Steel belted tires
• Reinforced concrete

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BIOMATERIALS:

 Biomaterials are employed in components implanted

into the human body for replacement of diseased or
damaged body parts.

 These materials must not produce toxic substances and

must be compatible with body tissues (i.e., must not cause
adverse biological reactions).

 All of the mentioned materials such as metals,

ceramics, polymers, composites, and semiconductors may
be considered as biomaterials.

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BIOMATERIALS:

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CORRELATED PROPERTIES OF MATERIALS

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 MATERIALS DESIGN PARADIGM

 Structure
Sub-Atomic / Atomic / Nano / Micro / Macro
 Property
Mechanical
Physical (electrical, magnetic, optical, thermal,
elastic, chemical)
Chemical
 Process
Material history
 Performance

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MATERIALS DESIGN PARADIGM

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REPRESENTATIVE EXAMPLES, APPLICATIONS AND
PROPERTIES OF MATERIALS

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REPRESENTATIVE EXAMPLES, APPLICATIONS AND
PROPERTIES OF MATERIALS

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PROPERTIES OF MATERIALS

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PROPERTIES OF MATERIALS

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PROPERTIES OF MATERIALS

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 SUMMARY

 Materials science and engineering (MSE) is an interdisciplinary field concerned with

inventing new materials and devices and improving previously known materials by
developing a deeper understanding of the microstructure-composition-synthesis processing
relationships.

 Engineered materials are materials designed and fabricated considering MSE principles.

 The properties of engineered materials depend upon their composition, structure, synthesis,
and processing. An important performance index for materials or devices is their
performance-to-cost ratio.

 The structure of a material refers to the arrangement of atoms or ions in the material.

 The structure at a microscopic level is known as the microstructure.

 Many properties of materials depend strongly on the structure, even if the composition of
the material remains the same. This is why the structure-property or microstructure property
relationships in materials are extremely important.
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 SUMMARY

 Materials are classified as metals and alloys, ceramics, glasses and glass-ceramics, composites,
polymers, and semiconductors.

 Metals and alloys have good strength, good ductility, and good formability. Metals have good
electrical and thermal conductivity. Metals and alloys play an indispensable role in many
applications such as automotives, buildings, bridges, aerospace, and the like.

 Ceramics are inorganic crystalline materials. They are strong, serve as good electrical and thermal
insulators, are often resistant to damage by high temperatures and corrosive environments, but are
mechanically brittle. Modern ceramics form the underpinnings of many microelectronic and
photonic technologies.

 Glasses are amorphous, inorganic solids that are typically derived from a molten liquid. Glasses
can be tempered to increase strength. Glass-ceramics are formed by annealing glasses to nucleate
small crystals that improve resistance to fracture and thermal shock.

 Polymers have relatively low strength; however, the strength-to-weight ratio is very favorable.
Polymers are not suitable for use at high temperatures. They have very good corrosion resistance,
and—like ceramics—provide good electrical and thermal insulation. Polymers may be either
ductile or brittle, depending on structure, temperature, and strain rate. 32
 SUMMARY

 Semiconductors possess unique electrical and optical properties that make them essential for
manufacturing components in electronic and communication devices.

 Composites are made from different types of materials. They provide unique combinations
of mechanical and physical properties that cannot be found in any single material.

 Functional classification of materials includes aerospace, biomedical, electronic, energy and

environmental, magnetic, optical (photonic), and structural materials.

 Materials can also be classified as crystalline or amorphous. Crystalline materials may be

single crystal or polycrystalline.

 Properties of materials can depend upon the temperature, level and type of stress applied,
strain rate, oxidation and corrosion, and other environmental factors.

 Selection of a material having the needed properties and the potential to be manufactured
economically and safely into a useful product is a complicated process requiring the
knowledge of the structure-property-processing-composition relationships.
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END OF CHAPTER 1
Atomic Structure

35
 Structure of Matter
 Empedocles (492 b.c. and 432 b.c.): All matter is composed
of four main elements

 Democritus (460 b.c. to 370 b.c.) : Infinitesimally small pieces

of matter called atomos, meaning "indivisible."

 Aristotle and Plato rejected Democritus and supported

Empedocles
 Dalton first proposed part of his atomic theory in 1803
36
 Atomic Structure
Atoms are the smallest structural units of all solids,
liquids & gases.

Atom: The smallest unit of an

element that retains the chemical
properties of the element. Atoms
can exist alone or in combinations with other atoms
forming molecules.

Element: One of less than 118 pure chemical

substances. An element is a substance composed
of atoms with identical atomic number. 37
 Atomic Structure

 Molecule: A particle formed by the chemical bonding of

two or more atoms. The molecule is the smallest particle of
a chemical compound that retains the chemical properties
of the compound.

 Compound: A material formed by the chemical

combination of elements in defined proportions.
Compounds can be chemically decomposed into simpler
substances.

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 Atomic Structure

Atom = nucleus (protons+neutrons) + electrons

 Proton: A sub-atomic particle with a positive charge of

1.60x10-19 coulombs and a mass of 1.672x10-27 kg. Protons
are found in the nucleus of atoms.
 Neutron: A sub-atomic particle with no charge and a mass
of 1.675x10-27 kg. Neutrons are found in the nucleus of
atoms.
 Electron: A sub-atomic particle with a negative charge
of 1.60 × 10-19 coulombs and a mass of 9.11 × 10-31 kg.
Electrons are generally found in orbit around the nucleus
of an atom, but may be gained or lost during ion
formation. 39
 Atomic Structure

The atomic mass (A) (mass number) of a specific atom may

be expressed as the sum of the masses of protons and
neutrons within the nucleus

The atomic mass (A)= mass of protons + mass of neutrons

Atomic number (Z): Each chemical element is

characterized by the number of protons in the nucleus, or
the atomic number (Z). For an electrically neutral or
complete atom, the atomic number also equals the number
of electrons.
Number of protons =atomic number (Z)
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 Atomic Structure

The atomic weight of an element corresponds

to the weighted average of the atomic masses of
the atom’s naturally occurring isotopes

Atomic weight of carbon is 12.011 amu. The

atomic weight is often specified in mass per mole.
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 Atomic Structure

The atomic mass unit (amu) is often used to express atomic

weight. 1 amu is defined as 1/12 of the atomic mass of the most
common isotope of carbon atom that has 6 protons (Z=6) and six
neutrons (N=6).
Mproton ≈ Mneutron = 1.66 x 10-24g = 1 amu.
The atomic mass of the 12C atom is 12 amu.
A mole is the amount of matter that has a mass in grams equal
to the atomic mass in amu of the atoms (A mole of carbon has a
mass of 12 grams).
In one mole of a substance there are 6.023 × 1023 atoms
(Avogadro’s number) or molecules. These two atomic weight
schemes are related through the following equation:
42
 Atomic Structure

Example:
Atomic weight of iron = 55.85 amu/atom = 55.85
g/mol
Some simple calculations:

The number of atoms per cm3, n, for material of

density d (g/cm3) and atomic mass M (g/mol):

Graphite (carbon): d = 2.3 g/cm3, M = 12 g/mol,

n = 6.023×1023 atoms/mol × 2.3 g/cm3 / 12 g/mol =

11.5 × 1022 atoms/cm3
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 Atomic Structure

Diamond (carbon): d = 3.5 g/cm3, M = 12 g/mol

n = 6×1023 atoms/mol × 3.5 g/cm3 / 12 g/mol

= 17.5 × 1022 atoms/cm3

Water (H2O): d = 1 g/cm3, M = 18 g/mol

n = 6×1023 molecules/mol × 1 g/cm3 / 18 g/mol
= 3.3 × 1022 molecules/cm3

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 Atomic Structure
Example: An intermetallic compound has the general chemical formula
Nix Aly , where x and y are simple integers, and consists of 42.04 wt%
nickel and 57.96 wt% aluminum. What is the simplest formula of this nickel
aluminide?

Solution: Determine the gram –mole fractions of Ni and Al. Using 100g
basis of the compound, we have 42.04g of Ni and 57.96g of Al
No. of gram-moles of Ni = (42.04g)/(58.71g/mol) = 0.7160 mol
No. of gram-moles of Al = (57.96g/(26.989g/mol) = 2.1483 mol
+ ---------------
2.8643 mol
Thus,
Gram-mole fraction of Ni = (0.7160mol/2.8643mol) = 0.25
Gram-mole fraction of Al = (2.1483mol/2.8643mol) = 0.75
So, Ni0.25Al0.75 is the simplest formula on a mole-fraction basis. The
simplest formula on an integral basis is obtained by multiplying both the
45
0.25 and 0.75 by 4 to give NiAl3. (nickelaluminide)
 All the elements have been
classified according to electron
configuration in
the periodic table

The elements are

situated, with Seven Group number indicates the
increasing atomic horizontal rows, number of electrons
46
number called periods available for bonding
Elements arrayed in a Group-0: Group-IA:
given column or group Inert gases (He, Ne, Alkali metals (Li, Na,
have similar valence Ar...) which have filled K…) have one electron in
electron structures, electron shells and outermost occupied s
as well as chemical and stable electron subshell -eager to give
physical properties configurations : chem. up electron – chem.
inactive active 47
 Groups IIIA,
Group-VIIA: The elements between IVA, and VA (B, Si, Ge,
Halogens (F, Br, Cl...) the Group IIA and IIIA As, etc.) are
missing one electron in are transition metals intermediate between
outermost occupied p the metals and
shell -want to gain nonmetals
electron -chem. active
48
 The electronegativity values for the elements
Electropositive elements: indicating that they are capable of giving up their
few valence electrons to become positively charged ions

Electronegative elements: readily accept electrons to form negatively

charged ions, or sometimes they share electrons with other atoms. the elements
situated on the right-hand side of the table. Electronegativity increases in
moving from left to right and from bottom to top
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Subshells with one electron - low electronegativity

Subshells with one missing electron -high electronegativity

Metals are electropositive –in nature and give up electrons in chemical
reactions to produce positive ions (cations).

The oxidation number is the number of electrons given up by an

electropositive element.
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Electronegative elements are non-metallic in nature and accept electrons in
chemical reactions to produce negative ions (anions). The most electronegative
elements are in groups 6A and 7A in the periodic table while the most
electropositives are in 1A and 2A.

Some elements in group 4A to 7A can behave in either an electronegative or

electropositive manner depending on the nature of the chemical reactions. Carbon,
silicon, germenium, arsenic, antimony and phosphorus show this dual behavior

Electronegativity helps in understanding the bonding behavior of the elements

51
and described as the degree to which an atom attracts electrons to itself
 Summary

Metals Non-metals
Have few electrons Have four or more
in outer shells usually electrons in outer
three or less shells
Form cations losing Form anions by
electrons gaining electrons
Have low Have high
electronegativites electronegativities

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 INTERATOMIC BONDING

 Atoms link to form materials. When this linkage is self-

sufficient, the resultant will be a gas, a liquid or a solid.

For example;
 Atoms bond to form long chains→Polymers
 Atoms bond in regular 3-D arrays→Metals

 The bonding b/w atoms is the result of the universal

tendency of all systems to take up their lowest energy
state. Atoms achieve their lowest energy level by the
possession of 8 electrons in their outer most shell (except
for the first shell which is stable only with 2e-)
53
 Considering the periodic table, the elements having 8e- in their outermost
shell are inert gases.
 They are chemically inactive.
8e-
H He

Li Be B C N O F Ne

Na Mg Al Si P S Cl Ar
K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
N
Rb Sr Y Zr Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
b
T
Cs Ba * Hf W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
a
H
Fr Ra ** Rf Sg Ns Hs Mt
a

Light Transient Metals Non Metals

Metals
Electropositivity increases Electronegativity increases

* La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
** Ac Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 54
 INTERATOMIC BONDING

 Atoms of the elements having 5, 6, 7 e- in their outermost

shell accept 3, 2, 1 electrons respectively.

 Those having 1, 2 or 3 e- give up their outermost shell

electrons to remain with 8 e- in their underlaying shell.

 Atoms having 4 valance electrons may behave in either

way.

 Valance electrons: The electrons at the outermost shell.

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 INTERATOMIC BONDING

Atomic
Bonding

Secondary
Primary Bonds
Bonds

van der
Ionic Covalent Metallic
Waals

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 IONIC BONDING

 11Na & 17Cl These two ions are attracted to eachother by the
electrostatic force developed b/w them and an ionic
compound (NaCl) forms.

 The ionic bonding b/w the two atoms results from the
transfer of an electron from an electropositive atom to an
electronegative one, so a strong electrostatic attraction is
set up b/w the ions.

57
 IONIC BONDING

Cation Anion
Coulombic
interaction

Ionic Bonds are nondirectional ! Note the relative sizes of ions

Na+ shrinks and Cl- expands

Cl- Na+ 58
 Properties of Ionic Bonding

 Force of attraction is electrostatic (coulombic)

 Bond is non-directional (each + ion is surrounded by as
many – ions as possible)
 Bond is strong, stable, brittle
 High melting point (as the # of e- involved in the bond
increases, melting point increases)
 Poor electrical conductivity
 Forms between atoms of different electronegativity values
(one high, one low).
 An obvious limitation is that it can form only b/w different
atoms.

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 COVALENT BONDING

 Covalent bond is the bond in which e- are shared b/w atoms.

 The elements showing covalent bond obey (8-N) rule.

 (8-N) rule: The number of the closest neighbors to each atom
is equal to (8-N)
N is the valance e-.
When N=7, such as Cl
8-7=1 → the atoms pair off as diatomic molecules.

Cl + Cl Cl Cl

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  When N=6 such as S

6
16S : 1s2 2s2 2p6 3s2 3p4
8-6=2

 each atom has two closest neighbors so they form long

chains.

O, Se, Te behave like S.

S S

S S

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When N=5, such as

33As : 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p3

8-5=3 → They require 3 closest neighbors so they form

sheets of atoms.

When N=4, such as 6C : 1s2 2s2 2p2

8-4=4 → They form 3-D structures.

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Ethylene
molecule

63
 Properties of Covalent Bonding

 It is based on electron sharing.

 Bond is directional (each atom is surrounded by a
definite amount of other atoms)
 Bond is hard and strong (slightly less than ionic)
 Very high melting point.
 Poor electrical conductivity.
 Forms b/w atoms with high electronegativity.
Covalent bonding is not limited to elements; many
compounds are covalent, like HCl, H2O.

64
 METALLIC BONDING

 Covalent bonding occurs in electronegative atoms

where they want to give away electrons.

 Metallic bond can be considered as a special type of

covalent bond in which instead of sharing particular
valance electrons, general sharing of valance e- is
responsible for the bond.

 Valance electrons are detached from atoms, and spread

in an ―electron cloud‖ that holds the ions together.
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 METALLIC BONDING

 The positive metal ions are arranged regularly in a

―crystal lattice‖ and a cloud of valance electrons
surround them.

Electron cloud

Metal ions

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 Properties of Metallic Bond

 It is based on electron sharing. Electrons are

shared among all atoms.
 Non directionality - desire for the largest number
of nearest neighbors.
 High thermal and electrical conductivity.
 Moderately lower melting point.
 Weakest primary bond.
 Forms between atoms with low electronegativity.

67
 High thermal and electrical conductivity ?

 Since the valance e- are not bound to any

particular atom, they can move through the lattice
under the application of an electric potential
causing a current flow.

 Also by a series of collisions with neighboring

electrons they transmit thermal energy rapidly
through the lattice.

68
 SECONDARY BONDS
(VAN DER WAALS BONDS)

Secondary bonds are universal to all atoms and

molecules, but as it is a very weak bond, it may be
neglected when primary bonds exist.

It can also be termed as a physical bond as

opposite to chemical bonding that involves e-
transfer.

Describes a dipolar attraction b/w neutral atoms.

69
 SECONDARY BONDS
(VAN DER WAALS BONDS)

 Since electrons move around nucleus (electronic charge

is in motion), it is possible for electrons to be located
unsymmetrically with respect to nucleus at a moment.
 In this way a dipole will be formed.
 Van der Waals bonding is a result of an attraction b/w
opposite poles of these dipoles.

 Dipole: Pair of equal and

opposite electric charges.

70
 HYDROGEN BOND

 As the valance electrons of water molecule spend more

of its time around Oxygen atom than the Hydrogen
atom, a dipole is formed.
The oxygen end of the molecule develops a partial
negative charge (because of the negative charge on
the electrons).
For the same reason, the hydrogen end of the
molecule develops a partial positive charge.

 Negative end of each water molecule is attracted by a

positive end of another water molecule.
 Ions are not formed; however, the molecule develops a
partial electrical charge across it called a dipole.

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72
73
Metals: Metallic bond
Ceramics: Ionic / Covalent bonds
Polymers: Covalent and Secondary bonds
Semiconductors: Covalent / Ionic bonds

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2nd & 3rd weeks (66 slides) 2017-
2018 75
Mixed Bondings:

76
 BONDING ENERGY, INTERATOMIC
SPACING

For two ions to come closer to each other, two types of

forces are in effect.
Attractive Forces (+) pull atoms together
Repulsive Forces (-) develop when atoms are brought into
close proximity (~nm). There is mutual electronic repulsion
between the two atoms because of the electrons around an
atoms.

77
 x0
Tensile (+)

Fa(x): Attractive force

Ft(x): Total force
Force

x, Interatomic Spacing
Compressive (-)

Fr(x): Repulsive force

78
 BONDING ENERGY, INTERATOMIC
SPACING

 When two atoms approach each other they exert forces on one
another.
 Forces of attraction (Fa)→Attractive forces b/w atoms
decrease with interatomic spacing, x.
(is inversely proportional with x)
 Forces of repulsion (Fr)→As atoms come closer, repulsive
forces dominate.
(is inversely proportional to a higher power of x than Fa)
 Total force ∑F = Fa+Fr
 When Fa=Fr → Equilibrium point → @ x=x0

 x0 is also known as equilibrium spacing and is a very specific

distance for a given pair of atoms or ions. A large amount of
force is needed to change (stretch or compress) that distance.
Therefore, generally atoms can be assumed as hard balls
when atomic arrangements are considered.
79
The strength of this attraction increases as the two atoms grow closer
together, because Coulomb’s Law tells us that the magnitude of the force
is inversely proportional to r2:

Fattractive= -kq1q2/r2 …

Where k=1/4πεo, q1=Z1e, q2=Z2e

The repulsive force is

Frepulsive =-nb/rn+1

n is a constant between 7 and 9, e.g. n=9 for NaCl, ―b‖ is

proportionality constant of repulsion

80
 Sometimes it is more convenient to work with the potential
energies between two atoms instead of forces.

where En, Ea, Er are the

net, attractive and
repulsive energies for two
isolated and adjacent
atoms.

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Eb is the bonding energy that
represents the energy required to
separate two atoms to an infinite
separation.
Eb
82
 BONDING ENERGY, INTERATOMIC
SPACING
 The magnitude of the bonding energy and the shape of E-
x curve vary from material to material and they both
depend on the atomic bonding.
 Furthermore a number of material properties depend on
atomic relationships (Eb, curve shape and bond type).
Melting point
Hardness
Modulus of Elasticity=dF/dx at x=x0
Thermal expansion
Conductivity of metals

83
84
 Factors Affecting the Atomic Radius

 Temperature: As T increases, x0 also increases.

 Ionic Value: An electropositive atom (Fe+2) has a smaller
radius than a neutral atom (Fe).

Similarly an
electronegativ
e atom (O-2)
has a higher
radius than a
neutral atom
(O).

85
 BONDING ENERGY, INTERATOMIC
SPACING

 Surrounding Atoms: As the number of

surrounding atoms around a bond increases,
the interatomic distance increases due to the
repulsive forces developed by electrons.

 Covalency: As the number of shared electrons

increases, atoms will attract each other more
and the radius decreases.

86
END OF WEEK 2
Structure of Materials

88
 Any material may be in either of the
following state.
• Gas state
• Liquid state
• Solid state
• The state of a material is governed by:
• Type of bond
• Energy of bond
• Stability of bond
• Sizes of atoms
• Temperature
• Pressure
89
 GAS STATE
Each individual molecule of a gas has an order.
However, the overall structure has no order.

Intermolecular bonding in gases is built by Van der

Waals bonding which is a weak bond.

Atoms are in continuous motion at high speeds

which prevents them of having a fixed shape.

The random movement of atoms will lead the gas to

fill any container into which it is introduced.
90
 LIQUID STATE
Liquids have more orderly structure than
gases. However, this order is short ranged.

The bond b/w particles is weak & limited. So,

liquids can take the shape of the container
easily.

The thermal expansion of liquids is less than

that of gases.
91
1. Liquids derived from Crystalline solids:
These consist of small group of atoms still
arranged in a crystalline structure. However,
bonds are not strong enough for them to form a
rigid mass.

2. Liquids derived from Amorphous solids:

These are composed of large molecules which
are flexible & mobile.
The major difference b/w two liquid types is their melting
point. First one has a definite melting point because all the
bonds in the crystalline structure have the same strength &
break down at the same temperature.

92
 SOLID STATE
Solid materials are classified according to the
regularity with which atoms or ions are arranged
with respect to one another.
 Crystalline Solids
 Amorphous Solids

 In crystalline materials atoms are situated in a

repeating or periodic array over large atomic
distances. (long range order)
 In amorphous materials long range order do not
exist
93
Upon solidification of a liquid the atoms will
position themselves in a repetitive 3-D pattern
in which each atom is bonded to its nearest
atoms.
Therefore, speed of solidification has a great
effect on the type of solid.
• Solidification occurs gradually → Crystalline

• Solidification occurs suddenly → Amorphous

94
 The type of bond also affects the type of solid
• Ionic and Metallic Bonds → Crystalline
• Covalent Bonds → Amorphous

 While passing from liquid state to solid state there is

no definite dividing line. (Gels are in between)

 Gels are formed by very fine particles of solid

trapping liquid molecules within themselves.
According to the type, strength and number of bonds,
gels may be more liquid or more solid.
95
 CRYSTALLINE SOLIDS
 In a crystalline solid, particles which may be
(atoms, molecules or ions) are surrounded by
like neighbors according to a definite
geometrical repetitive pattern.

 When describing crystalline structures, atoms or

ions are thought of as being solid spheres having
well-defined diameters.

96
•Solids can be either crystalline or non-crystalline
(amorphous)

•Crystalline material (solid) is one in which the atoms are

situated in a repeating or periodic array over large atomic
distances

Example: All metals, many ceramic materials, and certain

polymers form crystalline structures under normal
solidification conditions
97
98
When describing crystalline structures, atoms (or ions)
are thought of as being solid spheres having well-defined
diameters. This is termed the atomic hard sphere model
in which spheres representing nearest-neighbor atoms
touch one another.

A hard
An aggregate of sphere unit cell
many atoms. representation, 99
An example of the hard sphere model is the
atomic arrangement of some common elemental
metals shown in the figure.

In this example:
• All atoms are identical.
• Sometimes the term
“lattice” is used in the
context of crystal
structures.
• Space-Lattice: 3-D
arrays of points in space
coinciding with atom
positions. 100
Unit cell: is the smallest unit of a space
lattice which repeats itself to form the
lattice.
In other words space-lattice is formed by
face to face packing of unit cells.

101
 Unit Cell Configurations
1. Simple Unit Cell: Lattice points are at every
corner of the cell.

2. Base Centered Unit Cell: Extra lattice points in

the center of two parallel faces.

3. Body Centered Unit Cell: An extra lattice points

in the interior.

4. Face Centered Unit Cell: Extra lattice points at the

center of each face.
102
 CRYSTAL
SYSTEMS
Based on unit cell
configurations
and atomic
arrangements

103
104
105
Simple Cubic (SC or PC) Structure
The unit cell has an atom at each corner and touch each
other along the lattice. The example for this structure is polonium.

A hard sphere unit cell

A reduced-sphere representation

unit cell
The coordination number (the number of nearest atoms
directly surrounding a given atom) is six for SC structure
Total number of atoms =
1/8x8=1 atom

106
 a

a
r r
a

a
2r a  r  r  2r  r 
2

107
Atomic Packing Factor

Atomic packing factor shows us how dense the unit cell is:

Volume of atoms in a unit cell

APF 
Total unit cell volume

APF = 1 ......... Unit cell is filled with atoms

APF = 0 ......... Unit cell is empty

108
•For SC

Atoms Per unit cell = 1

a
a  2r  r 
2

4 3 4 a 3 a 3
Vat  r   ( ) 
3 3 2 6

Vuc  a 3
a 3
Vat 6 
APF   3   0.52
Vuc a 6 2r

APF  52 %

109
Face Centered Cubic (FCC) Structure

Two representations of a unit cell

The coordination number for the FCC crystal structure is
12; that is, each corner atom has 12 touching nearest
neighboring atoms. 110
 Atomic Packing Factor of FCC
Remember!!! Atoms are hard spheres and they touch one
another along cube diagonal for an FCC structure.
H G
a 2  a 2  ( 4r ) 2
E F
r a  2r 2
2
rD Volume of unit cell, Vc
C
r
A
a B
a
Vc  a  (2r 2 )  16 r
3 3 3
2

Number of atoms per unit cell:

• Face atoms – 6 x 1/2 = 3
• Corner atoms – 8x1/8 = 1
Total number of atoms in the unit cell = 4 111
Atomic Packing Factor of FCC
H G
Volume of atoms in a unit cell
E F APF 
r Total unit cell volume
2
rD C (4) * (4 / 3 r 3 )
r a APF 
A
a B
16r 3 2

APF  0.74

112
113
Body Centered Cubic (BCC) Structure

How many atoms are there in BCC

H
G
r
E F structure?
a
2r
APF of BCC?
D
r a 2 C

A
What is the coordination number of
BCC?
B 114
 DENSITY COMPUTATION
Since the entire crystal can be generated by the
repetition of the unit cell, the density of a
crytalline material can be calculated based on the
density of the unit cell.
r : Density of the unit cell
nM
r n : Number of atoms in the unit cell

Vc M : Mass of an atom
Vc : Volume of the cell
Mass of an atom is given in the periodic table in atomic mass units
(amu) or gr/mol. To convert (amu) to (gr) use avagadro’s number.
115
DENSITY COMPUTATION
Avagadro’s number, NA= 6.023x1023
atoms/mol
Therefore, r : Density of the unit cell
n : Number of atoms in the unit cell
nA
r A : Atomic mass

Vc N A Vc : Volume of the cell

NA : Avagadro’s number

116
POLYCRYSTALLINE MATERIALS

z Most crystalline solids are composed of many small

crystals or grains termed as polycrystalline.
z During the solidification of a polycrystalline solids,
the crystallization may start at various nuclei with
random crystallographic orientations.
z Upon solidification, grains of irregular shapes may
form.
z The structure will have grain boundaries that could
be seen under a microscope.

117
Stage 1 Stage 2

118
Stage 3 Stage 4
POLYMORPHIC TRANSFORMATION

z Materials having the same chemical composition can

have more than one crystal structure. These are
called allotropic or polymorphic materials.
y Allotropy for pure elements.
y Polymorphism for compounds.
z These transformations result in changes in the
properties of materials and form the basis for the
heat treatment of steels and alloys.

119
 POLYMORPHISM
z Carbon may exist in two forms:

Graphite Diamond
( 2D layers) (3D structure) 120
 POLYMORPHISM
Iron (Fe) may also exist in several forms:
 BCC at room temperature → α iron
 FCC at 910°C → γ iron
 BCC at above 1400°C → β iron
 Above 1539°C → liquid

Upon heating an iron from room temperature to

above 910°C, its crystal structure changes from
BCC to FCC accompanied by a contraction
(reduction in volume).

121
NONCRYSTALLINE SOLIDS

Amorphous
Structures

122
 AMORPHOUS SOLIDS
 Materials which don’t have the long range repetitive
pattern of crystals are called amorphous materials.
Amorphous means ―without form‖.
Ceramic Compound
SiO2

Crystalline Amorphous 123

AMORPHOUS SOLIDS

During the rapid cooling of a liquid, if atoms or

molecules do not find sufficient time to arrange
themselves in a long-range repetitive pattern
amorphous solids will form unlike crystalline solids
obtained by gradual cooling.
 Glasses
 Polymeric materials
 Some ceramics

124
 Summary

Single Polycrystalline Amorphous

crystalline Solid Solid Solid

125
 CRYSTALLOGRAPHIC POINTS,
DIRECTIONS, PLANES
&
THE MILLER SYSTEM OF INDICES

126
 When dealing with crsytalline materials, it is often
necessary to specify a particular point within a
unit cell, a particular direction or a particular
plane of atoms.
 Planes are important in crystals because if
bonding is weak between a set of parallel planes,
then brittle shear fracture may occur along these
planes.
 Therefore, it is necessary to be able to specify
individual crystal planes and in the case of shear
to specify directions within these planes.

Such identification is carried out by means of

Miller Indices. 127
 POINT COORDINATES

The position of any point

located within a unit cell
is specified in terms of its
coordinates as fractional
multiplies of the unit cell
edge lengths.
To determine the point
The “q” coordinate (which is a coordinates of point P, the
fraction) corresponds to the manner in which the q, r, s
distance “qa” along the x-axis coordinates of point P within
where “a” is the unit cell length the unit cell are determined.
128
along x-axis.
CRYSTALLOGRAPHIC DIRECTIONS
A crystallographic direction is defined as a line
between two points (a vector).
1. A vector of convenient length is positioned such that it
passes through the origin of the coordinate system.
(Any vector can be translated throughout the crystal
lattice, if parallelism is maintained).
2. The length of the vector projection on each of the three
axes is determined in terms of the unit cell dimensions a,
b, and c.
3. These three numbers are multiplied or divided by a
common factor to reduce them to the smallest integer
values.
4. The three indices are enclosed in brackets as [uvw].
The u, v, and w integers correspond to the reduced
projections along x, y, and z-axes respectively.
129
1. The vector as drawn passes
through the origin of the
coordinate system, and
therefore no translation is
necessary.
2. Projections of this vector
along x, y, and z axes are
a/2, b, and 0c. In terms of
unit cell dimensions ½, 1, 0.
3. Reduction of these numbers
to the lowest set of integers
could be done through
multipliying these numbers
by 2 to yield 1, 2, and 0
4. The crystallographic
direction is then [120]
130
 z

A
y
a
B
a

a
x

z Vector A → a, a, a 1/a, 1/a, 1/a [1 1 1]

z Vector B → [1 1 0]
z Vector C → [1 1 1] 131
z For some crystal structures, several nonparallel
directions with different indices are actually
equivalent. (The spacing of atoms along each
direction is the same)
z For example in cubic crystals, all the directions
represented by the following indices are
equivalent.
[100 ], [ 1 00 ], [010 ], [0 1 0], [001], [00 1 ]
 As a convenience, equivalent directions are
grouped into a “family” which are grouped in angle
brackets.
[100 ], [ 1 00 ], [010 ], [0 1 0], [001], [00 1 ]
  
10 0
132
 Sometimes the angle between two
directions may be necessary.
A [u1 v1 w1] and B [u2 v2 w2] → the angle
between them is a.

A . B=|A| |B| cos a

u1u2 + v1v2 + w1w2

cos a =
(u12+v12+w12) (u22+v22+w22)
133
 Draw the following direction vectors in cubic
unit cells

z
z

[112]
[110]
y
y
[000]
x
x

134
CRYSTALLOGRAPHIC PLANES
z The orientations of planes for a crystal
structure are represented in a similar
manner.
z In all except for the hexagonal crystal
system, crystallographic planes are
specified by three Miller Indices as (hkl).
z Any two equispaced parallel planes are
equivalent and have identical indices.
z The following procedure is employed in
determining the h, k, and l index numbers
of a plane: 135
1. If the plane passes through the selected origin,
either another parallel plane must be constructed
within the unit cell by an appropriate translation, or
a new origin must be established at the corner of
another unit cell.
2. At this point the crystallographic plane either
intersects or parallels each of the three axes; the
length of the planar intercept for each axis is
determined in terms of the lattice parameters a, b,
and c.
3. The reciprocals of these numbers are taken.
4. If necessary, these three numbers are changed to
the set of smallest integers by multiplication or
division by a common factor.
5. The integer indices are enclosed within parantheses
as (hkl). 136
1. The plane passes
through the
selected origin O.
Therefore, a new
origin must be
selected at the
corner of an
adjacent unit cell.

137
2. The plane is parallel
to the x’-axis and the
intercept can be
taken as ∞a. The y’
and z’ intersections
are –b and c/2.
Lattice parameters
are ∞, -1, and 1/2.
3. Reciprocals are 0, -1,
2.
4. All are integers no reduction is necessary.
5. The crystallographic plane is (012)

138
Any two equispaced parallel planes are equivalent and have identical
indices.

139
140
 Various non-parallel planes may have similarities
(crystallographically equivalent ). Such planes are
referred to as ―family of planes‖ and are
designated as {h k l}
Example: Faces of a cubic unit cell.

(100) (010) (001)

(100) (010) (001)

Ξ {100}
141
142
 The interplanar distance

Copper has an FCC crystal structure and a unit cell with

a lattice constant of 0.361 nm. What is its interplanar
spacing d220?

143
 PLANAR DENSITY
 When slip occurs under stress, it takes place
on the planes on which the atoms are most
densely packed.

# of atoms in a plane
δ(hkl) =
area
z
Example: FCC unit cell

4*1/4+1 2
δ(100)= = a2
a2
4 1 y
a= r δ(100)= (100)
2 4r2
x a2
144
 LINEAR DENSITY
 When planes slip over each other, slip
takes place in the direction of closest
packing of atoms on the planes.

 The linear density of a crystal direction [h k

l] is determined as:

# of atoms
δ[h k l] =
Length of
direction
145
  Example: [100] of cubic unit cell

δ[100] = 1/a

a
 Example: Calculate planar density of the face plane
(100) and linear density on the face diagonal [011]
of an FCC structure.

(100)
2
a0 [011]  [ 011] 
a0 2
a0 146
Example:

147
148
Example:

149
Example:

150
151
152
Example:

153
154
155
Example:

156
157
158
Example:

159
160
161
Example:

162
163
164
Example:

165
166
Example:

167
168
169
Example:

170
171
172
173
END OF WEEK 3
Imperfections

175
Solidification of metals or alloys is generally
divided into two steps:

 Formation of stable nuclei in the melt (

nucleation)

 The growth of nuclei into crystals and the

formation of a grain structure.
liquid grains





nuclei
crystals which will grain boundries
form grains

176
 Two main mechanisms by which
nucleation of solid particles in liquid metal
occurs (when it is cooled) are :

i) heterogeneous nucleation,
ii) homogeneous nucleation

177
 Heterogeneous Nucleation
Heterogeneous nucleation is a nucleation that occurs in a
liquid on the surfaces of its container or insoluble impurities
or other structural materials which lower the critical free
energy required to form a stable nucleus. Since large
amount of undercooling do not occur usually range between
0.1o and 10o, the nucleation is not homogeneous.
Homogeneous Nucleation
Homogenous nucleations occur when the metal itself
provides the atoms to form nuclei. In this nucleation the same
kind of atoms come close together and form the nucleus as a
result of sufficiently undercooling from the melting point of the
melt of the metal.

178
 Two types of energies are involved in the formation of a
nucleus:

•Volume free energy which is released during the formation of

nucleus when it changes the volume of liquid phase to the
volume of solid phase.

•Surface formation energy which is required when the solid

phase is formed.

 If Gv is the change in free energy between the liquid and

solid per unit volume of metal, the free energy change for a
spherical nucleus is:

∆GV=(4/3)πr3Gν

 If γ is the specific surface free energy (i.e. the energy per

unit surface) of the spherical particle, the retarding surface
free energy is:
∆GS=4r2γ
179
Total free energy for the formation of a spherical
solid nucleus is

∆Gtot= ∆GV +∆GS= (4/3)πr3Gν+4r2γ

∆GV changes
significantly with
temperature but ∆GS
does not. So the
critical nucleus size is
determined mainly by
∆GV rather than ∆GS.
180
  r*(or rc) is the critical radius below which the nucleus is not stable i.e. it is
formed and deformed during agitation of the molten metal, and above which
it is stable and nucleus continuous to grow with time. A cluster of atoms
bonded together which is less than the critical size is called an embryo and
one which is larger than the critical size is called nucleus.

Critical radius of nucleus: r*=2γTm/∆Hf∆T

r*:critical radius of nucleus, γ:surface free energy, ∆Hf : latent heat of fusion,
Tm: melting temperature and ∆T: amount of undercooling at which nucleus is
formed. 181
a) Calculate the critical radius (in cm) of a homogeneous nucleus that forms
when pure liquid copper solidifies, assume
∆T=0.2Tm, Tm=1083oC, γ=177x10-7J/cm2, ∆Hf=1826J/cm3,
b) Calculate the number of atoms in the critical sized nucleus at this
undercooling.
a) r*=2γTm/∆Hf∆T r*=9.7x10-8cm
b) Volume of critical sized nucleus = (4/3)πr*3=3.82x10-21cm3,
Volume of unit cell of Cu (a=0.361nm)=a3=4.7x10-23cm3

Since there are four atoms per FCC unit cell

Volume of FCC unit cell (Cu)/atom:

=4.7x10-23cm3/4atoms =1.175x10-23cm3/atom

The number of atoms per homogeneous critical nucleus :

= volume of nucleus/(volume of FCC unit cell/atom)
=3.82x10-21cm3/1.175-23cm3 =325 atoms
182
 Metallic Solid Solutions

A metallic alloy can be made of two or more element mixture. Alloys show
different properties from their constituent elements.

A solid solution is a solid which is consisted of two or more elements

dispersed atomically in a single phase structure.

Solid solutions are made of a host (the solvent or matrix) component

which dissolves the minor component (solute). The ability to dissolve is
called solubility.

In an alloy:
Solvent is the element or compound present in greater amount.
Solute is the element or compound present in less amount.

Solid Solution
- should be homogeneous,
-should maintain crystal structure,
-may contain randomly dispersed impurities (substitutional or interstitial)
183
Second Phase: as more solute atoms are added, new compounds /
structures are formed, or solute forms local precipitates.

 Whether the addition of impurities results in formation of solid

solution or second phase, depends the nature of the impurities, their
concentrations and temperature, pressure…

There are generally two types of solid solutions;

i) substitutional solid solution

ii) interstitial solid solution
Solventatoms

Some solute atoms substituted solvent

atoms in an FCC structure
Solute atoms

184
 iron


  carbon

In interstitial structure, the


crystal structure of solvent
element does not change but
there can be some distortions
voids
interstitial atoms
due to the atomic size of solute
atoms.

The conditions for elements to make solid solutions;

-The diameters of the atoms of the elements must not differ

by more than about 15%.
-The crystal structures of the two elements must be the
same.
-There should be no appreciable difference in the
electronegativities of the two elements so that compounds will
not form.
-The two elements should have the same valence
185
Calculate the radius of the largest interstitial void in the FCC γ-iron lattice.
The atomic radius of the iron atom is 0.129nm in the FCC lattice and the
largest interstitial voids occur at the (1/2,0,0), (0,1/2,0), (0,0,1/2) etc. type
positions.

z a=2R+2r
(100)
plane (2R)2=(a2/4)+(a2/4)=a2/2
y
a=22 R
x a

  2R+2r=22 R=a
2R
(½) a  a

(½) a
   r=(2-1)R
R 2r
(0,1/2,0)
=0.414R
186
 Composition in a solution can be expressed in as ;

- Weight percent, useful when making the

solution

-Atom percent, useful when trying to understand

the material at the atomic level

Weight percent (wt %): weight of a particular

element relative to the total alloy weight. For two-
component system, concentration of element 1 in wt.
% is ;

187
Atom percent (at %): the number of moles (atoms) of a
particular element relative to the total number of moles
(atoms) in alloy. For two-component system, concentration of
element 1 in at. % is;

where:
nm1 = m1/A1. (m1 is weight in grams of element
1, A1 is atomic weight of element 1)

188
189
190
Why Study Imperfections in
Solids?
 The properties of some materials are profoundly
influenced by the presence of imperfections.
Consequently, it is important to have a knowledge
about the types of imperfections that exist, and the
roles they play in affecting the behavior of materials.

 For example, the mechanical properties of pure metals

experience significant alterations when alloyed (i.e.,
when impurity atoms are added)—e.g., sterling silver
(92.5% silver-7.5% copper) is much harder and
stronger than pure silver.

191
 In reality, crystals are never perfect and contain various types of
imperfections (defects and impurities) which affect their
properties.

Impurities are atoms which are different from the host:

All real solids are impure. Very pure metals have
99.9999% purity, generally
-one impurity per 106 atoms

May be, intentional or unintentional impurities are

created. Examples: carbon added in small amounts to iron makes
steel, which is stronger than pure iron. Boron added to silicon
changes its electrical properties.

Alloys are deliberately impured structures, i.e.

deliberate mixtures of metals.

Defects in crystals may be classified into four categories depending on

their dimensions:

192
STRUCTURAL
IMPERFECTIONS
(DEFECTS)
IN CRYSTALLINE
SOLIDS

193
 Real Crystalline solids are almost never
perfect. These imperfections can be
classified according to their dimensionality:

1. Point defects (0-Dimension)

2. Line defects (1-D)
3. Interfacial defects (2-D)
4. Bulk defects (3-D)

194
 Relative Size Ranges of Defects

Interfacial defect
Electronic
point Atomic
defect point
defect

Line defect Bulk defect

10-12 10-8 10-6 10-4 10-2 100 101 102 cm

195
 1. POINT DEFECTS
 These are defects of atomic dimensions
that usually result from:
1. The presence of an impurity atom
 Substitutional →larger atoms
 Interstitial → smaller atoms
2. The absence of a matrix atom (vacancy)
3. The presence of a matrix atom in a wrong
place (self-interstitial)

196
Point Defects
• Vacancies:
-vacant atomic sites in a structure.

Vacancy
distortion
of planes

• Self-Interstitials:
-"extra" atoms positioned between atomic sites.

self-
interstitial
distortion
of planes

197
Presence of an impurity atom:
-"extra" atoms positioned between atomic sites.

Interstitial

Substitutional

198
199
 The point defects discussed so far occur in metallic
structures. Those in ionic structures differ because of the
charge neutrally requirement.

An anion
and a cation
is missing

An anion or a
cation is at an
insterstital site

200
The equilibrium number of vacancies NV for a given
quantity of material depends on and increases with
temperature according to

• N is the total number of atomic sites

•QV is the energy required

for the formation of a vacancy

• The number of vacancies increases

exponentially with temperature
201
Example: Calculate the equilibrium number of vacancies
per cubic meter for copper at 1000oC. The energy for vacancy
formation is 0.9 eV/atom (or 86731.2J/mol); the atomic
weight and density (at 1000oC) for copper are 63.5 g/mol and
8.4 g/cm3, respectively.
Hint: R=k NA where k=8.62x10-5eV/K and
NA= 6.023X1023atoms/mol.,
1eV=1.6x10-19J, therefore R =8.31J/(mol.K)
Solution:

202
2. Line Defects (Dislocations)
Dislocations:
• are line defects,
• slip between crystal planes result when dislocations move,
• produce permanent (plastic) deformation.

Schematic of Zinc (HCP):

• before deformation • after tensile elongation

slip steps

203
Linear Defects (Dislocations)
Are one-dimensional defects around which
atoms are misaligned
 Edge dislocation:
extra half-plane of atoms inserted in a
crystal structure
b  to dislocation line
 Screw dislocation:
spiral planar ramp resulting from shear
deformation
b  to dislocation line

Burger’s vector, b: measure of lattice distortion

204
 First a closed circuit is
drawn around the
dislocation by jumping
from one atom to another.
 The same number of jumps
will be made in a perfect
system.
 The vector needed to
complete the circuit is
called BURGER VECTOR.

205
Edge Dislocations

Burger’s vector is
perpendicular to
dislocation in edge
dislocations.

206
Motion of Edge Dislocation
• Dislocation motion requires the successive bumping
of a half plane of atoms (from left to right here).
• Bonds across the slipping planes are broken and
remade in succession.

Atomic view of edge

dislocation motion from
left to right as a crystal
is sheared.

207
Screw Dislocations

Burger’s vector is
parallel to dislocation in
screw dislocations.

208
209
210
 Dislocations are simply slide or slip of one portion of
crystal system over another as dislocations move one part
of the system relative to the other.

 When dislocations pass through the whole system, the

system permanently deforms.

 Dislocations are on boundary between the regions where

slip has occured and where it has not.

 On either side of the dislocation crystalline system is

essentially perfect. 211
3.INTERFACIAL DEFECTS
(BOUNDARIES)
 Boundaries could be summarized into three:

1. Free surfaces: Interfaces between liquids

and gases.
2. Grain boundaries: Interfaces between
crystal systems having different orientation.
In each crystal system the atoms are
arranged orderly. However, at the boundary
there is a transition zone which is not
alinged with either of the crystal systems.
212
213
3. Interphase boundaries: similar to grain
boundaries both in shape and behavior.
However, in these systems there are two or
more materials having different crystal
structures. Multiphase materials having a
change in physical and/or chemical
characteristics will also have interphase
boundaries. (Ex: ice-water)

214
Grain Boundaries

Tilt boundary: Result of a

set of edge dislocations.
215
Demonstration of how a tilt
boundary having an angle of
misorientation results from an
alignment of edge dislocations

216
 Grain Boundaries

Twist boundary: Result of a set of screw

dislocations 217
Schematic
diagram showing low and
high-angle grain
boundaries and
the adjacent atom
positions.

218
4. BULK DEFECTS

 They are either introduced during the

production of the material or during its
fabrication.

 For example → inclusions (cracks,

notches, air bubbles & etc.) added during
production.

219
High-purity polycrystalline
lead ingot in which the
individual grains may be
discerned. 0.7X. (Reproduced
with permission from Metals
Handbook, Vol. 9, 9th edition,
Metallography and
Microstructures, American
Society for Metals, Metals
Park, OH, 1985.)

220
IMPORTANCE OF IMPERFECTIONS
Most of the properties of materials are affected by
imperfections:
 Small amount of impurity atoms may increase the
electrical conductivity of semi-conductors.
 Dislocations are responsible for ductility. Strength of
materials can be increased to a large extent by the
mechanism ―strain-hardening‖ which produces line
defects that act as a barrier to control the growth of
other imperfections.
 Presence of bulk defects such as cracks, notches,
holes causes brittle materials, which break at very
low stresses without showing large deformations.
221
 Grain size is measured by the ASTM (American
Society for Testing and Materials) method.
The grain size number n is defined by

N=2n-1
N is the number of grains per square inch on a
polished and etched material surface at a
magnification of 100x and n is the ASTM grain size
number and it is an integer.

Example: What is the ASTM grain size number n of

the metal if there are 64 grains per square inch
observed in a metal photograph magnified at 100x

Solution: N=2n-1 64(grain/inch2)= 2n-1n=7

222
END OF WEEK 4