Department of

Materials I Energy

Lecturer: Van Tang NGUYEN

Email: nguyen-van.tang@usth.edu.vn
 Materials I
Module description:
 Being able to:

 Describe the basic chemical bonds, crystal structures and their relationship with
the properties. Analyze the microstructure of metallic materials

 Understand the mechanical properties of materials, read simple phase diagrams

of solids and alloys

 Describe the causes of corrosion and apply some protection against corrosion
methods.

 Describe heat treatment of steels methods and be able to apply them

Reference textbooks

[1] W.D. Callister , Materials Science and Engineering; John Wiley & Sons, 2014.
[2] W.F. Smith, Principles of Materials Science and Engineering: An Introduction; Tata Mc-
Graw Hill, 2008.
 Mechanics I

33 theoretical hours (3 ECTS)

9 theoretical classes
11 classes
2 exercise classes
 Mechanics I

3 practical hours
 Mechanics I
3 practical hours

 Tensile tests (3 hrs)

Why do we study materials?
 materials science and materials engineering

 involves investigating the  on the basis of these structure–property

relationships that exist correlations, designing or engineering the
between the structures and structure of a material to produce a
properties of materials predetermined set of properties.

 role of a materials scientist is  materials engineer is called upon to create

to develop or synthesize new newproducts or systems using existing
materials materials, and/or to develop techniques for
processing materials
 Chapter 1: Structure of solids

Classification of engineering materials

1. Metals

2. Ceramics

3. Polymers

4. Composites - Semiconductors

- Biomaterials
5. Advanced
- Smart materials

- Nanoengineered materials
 Metals

• is a material that, when freshly prepared, polished, or fractured, shows a

lustrous appearance, and conducts electricity and heat relatively well

• Atoms in metals and their alloys are arranged in a very orderly manner

• Metallic materials 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

 Ceramics
• Ceramics are compounds between metallic and nonmetallic elements;
they are most frequently oxides, nitrides, and carbides

• aluminum oxide (or alumina,Al2O3 ),silicon dioxide (or silica, SiO2),

silicon carbide (SiC), silicon nitride (Si3N4)

• typically very hard. but extremely brittle (lack ductility), and are highly
susceptible to fracture

• typically insulative to the passage of heat and electricity

 Polymers
• Polymers include the familiar plastic and rubber materials

• Mostly organic compounds that are chemically based on carbon, hydrogen,

and other nonmetallic elements (viz. O, N, and Si)

• Having large molecular structures, often chain-like in nature that have a

backbone of carbon atoms

• Polyethylene (PE), nylon, poly(vinyl chloride) (PVC), polycarbonate (PC),

polystyrene (PS), and silicone rubber
 Composites

• A composite is composed of two (or more) individual materials, which come

from the categories discussed above—viz., metals, ceramics, and polymers

 to achieve a combination of properties that is not displayed by any single

material, and also to incorporate the best characteristics of each of the
component materials

• glass fibers are embedded within

polymeric material (normally an epoxy or
polyester)

• glass fibers are relatively strong and stiff

(but also brittle), whereas the polymer is
ductile (but also weak and flexible)

• the resulting fiberglass is relatively stiff,

strong, flexible, and ductile Fiber glass
 Advanced materials

 Semiconductor

Semiconductors have electrical properties that are intermediate between the

electrical conductors and insulators

the electrical characteristics of these materials are extremely sensitive to

the presence of minute concentrations of impurity atoms

 Widely applied in electronic devices

 Biomaterials

Biomaterials are employed in components implanted into the human

body for replacement of diseased or damaged body parts

Examples: contact lenses, pacemakers, heart valves, orthopedic devices, and

much more.
 Advanced materials

 Smart materials

• a group of new and state-of-the-art materials

• these materials are able to sense changes in their environments

 Nanoengineered Materials

• Nanoengineering is a branch of engineering that deals with all aspects of

the design, building, and use of engines, machines, and structures on the
nanoscale

• Materials at nanoscale can show a totally different properties compared

to bulk materials at larger scale.
 General comparison in properties of materials

Bar-chart of room temperature Electrical conductivity ranges for metals,

ceramics, polymers, and semiconducting materials.
 General comparison in properties of materials

Resistance to Fracture (Fracture Toughness in units of MPa)

General comparison in properties of materials

Density (g/cm3 )
 Structure-property relationship in engineering materials

How component of materials is arranged in spaced and bonded together has a

strong influence on its properties

Examples

Allotrope of carbon : Diamond, graphite and fullerenes

They are all made from carbon atoms

 Structure-property relationship in engineering materials

Diamond

 colourless and transparent

 extremely hard and has a high melting point

 insoluble in water, and not conduct electricity.

Every atom in a diamond is bonded to its neighbours by four strong covalent bonds,
leaving no free electrons and no ions

Graphite
 Graphite contains layers of carbon atoms.

 Graphite is black, shiny and opaque

 Graphite is insoluble in water. It has a high melting

point and is a good conductor of electricity,
 Structure-property relationship in engineering materials

the three specimens below are all made of aluminum oxide

 Important to understand structure of a material

 The Structure of Crystalline Solids

 A crystalline material is one in which the atoms are situated in a

repeating or periodic array over large atomic distances

 The atoms will position themselves in a repetitive three-dimensional

pattern, in which each atom is bonded to its nearest-neighbor atoms
 Crystal Structures

 Some of the properties of crystalline solids depend on the crystal

structure of the material, the manner in which atoms, ions, or
molecules are spatially arranged

 There is an extremely large number of different crystal structures all

having long-range atomic order, these vary from relatively simple
structures for metals to exceedingly complex ones
 UNIT CELLS

 The atomic order in crystalline solids indicates that small groups of atoms
form a repetitive pattern

 it is often convenient to sub-divide the structure into small repeat entities

called unit cells

 A unit cell is chosen to represent the symmetry of the crystal structure,

wherein all the atom positions in the crystal may be generated by
translations of the unit cell integral distances along each of its edges
 CRYSTAL SYSTEMS

 The unit cell geometry is completely defined in terms of six parameters:

the three edge lengths a, b, and c, and the three interaxial angles 𝛼, 𝛽, 𝛾

 termed the lattice parameters of a crystal structure

 CRYSTAL SYSTEMS

there are seven different possible combinations of a, b, and c and 𝛼, 𝛽, 𝛾

each of which represents a distinct crystal system.
CRYSTAL SYSTEMS
 Definitions

coordination number

In chemistry and crystallography, the coordination number describes the

number of neighbor atoms with respect to a central atom

Example: coordination number of faced center cubic is: 12

coordination number of body

center cubic is ?
 Definitions

atomic packing factor (APF)

The APF is the sum of the sphere volumes of all atoms within a unit cell
(assuming the atomic hard sphere model) divided by the unit cell volume

𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎𝑡𝑜𝑚𝑠 𝑖𝑛 𝑎 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙

𝐴𝑃𝐹 =
𝑡𝑜𝑡𝑎𝑙 𝑢𝑛𝑖𝑡 𝑐𝑒𝑙𝑙 𝑣𝑜𝑙𝑢𝑚𝑒

Calculate the APF of faced center cubic in terms of atomic radius

 Definitions

DENSITY COMPUTATIONS

Theoretical density of metallic solid can be calculated through the fomula:

𝑛𝐴
𝜌=
𝑉𝐶 𝑁𝐴

𝑛: number of atoms associated with each unit cell

A : atomic weight
VC: Volume of the unit cell
NA: Avogadro’s number (6.023 x 1023 atoms/mol)
 SINGLE CRYSTALS

 For a crystalline solid, when the periodic and repeated arrangement of atoms
is perfect or extends throughout the entirety of the specimen without
interruption, the result is a single crystal

 Single crystals exist in nature, but they may also be produced artificially

Photograph of a garnet single crystal

that was found in Tongbei, Fujian Province, China.
 POLYCRYSTALLINE MATERIALS

 Most crystalline solids are composed of a collection of many small

crystals or grains

such materials are termed polycrystalline

Schematic diagrams
of the various stages
in the solidification
of a polycrystalline
material
 Crystallographic Points, Directions, and Planes

 Point coordinates

The position of any point located within a unit cell may be specified in terms of its
coordinates as fractional multiples of the unit cell edge lengths

The position of P is designated as a

fractional length of a along the x axis, r is
some fractional length of b along the y axis,
and similarly for s
 Crystallographic Points, Directions, and Planes

 Point coordinates

Specify point coordinates for all atom positions for a BCC unit cell.
 Crystallographic Points, Directions, and Planes
Crystallographic direction
A crystallographic direction is defined as a line between two points, or a vector

The following steps are utilized in the determination of the three directional
indices:
1. A vector of convenient length is positioned such that it passes through the origin
of the coordinate system. Any vector may be translated throughout the crystal
lattice without alteration, if parallelism is maintained

2. The length of the vector projection on each of the three axes is determined;
these are measured 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, not separated by commas, are enclosed in square brackets,
thus: [uvw]. The u, v, and w integers correspond to the reduced projections
along the x, y, and z axes, respectively.
 Crystallographic Points, Directions, and Planes
Crystallographic direction

negative indices are also possible, which are

represented by a bar over the appropriate
index
 Crystallographic Points, Directions, and Planes
Crystallographic direction

Identify some crystallographic directions in the picture below:

 Crystallographic Points, Directions, and Planes
Crystallographic direction

Within a cubic unit cell, sketch the following

directions:

(a) [101],
(b) [211 ],
(c) [102],
(d) [313 ],
(e) [111],
(f) [212 ],
(j) [312 ],
(h) [301].
 Crystallographic Points, Directions, and Planes
Crystallographic planes

The orientations of planes for a crystal structure are represented in a similar

manner

the unit cell is the basis, with the three-axis coordinate system

In all but the hexagonal crystal system,crystallographic planes are specified by

three Miller indices as (hkl)

Any two planes parallel to each other are equivalent and have identical indices.
 Crystallographic Points, Directions, and Planes
Crystallographic planes

The procedure employed in determination of the h, k, and l index numbers is

as follows:
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. A plane that parallels an axis may
be considered to have an infinite intercept, and, therefore, a zero index.

4. If necessary, these three numbers are changed to the set of smallest integers
by multiplication or division by a common factor

5. Finally, the integer indices, not separated by commas, are enclosed within
parentheses, thus: (hkl)
 Crystallographic Points, Directions, and Planes
Crystallographic planes

Since the plane passes through the selected origin O, a new origin must be
chosen at the corner of an adjacent unit cell O’

the plane is parallel to the x axis, and the intercept may be taken as ∞𝑎
The y and z axes intersections: -b and c/2, respectively.

These intersection is : ∞ , -1, 1/2, respectively.

 Crystallographic Points, Directions, and Planes
Crystallographic planes

The reciprocal of these intersection is 0. -1, and 2.

Planar (Miller) Indices: (0-12)

 Crystallographic Points, Directions, and Planes
Crystallographic planes

Identify Planar (Miller) Indices of the following plane

 Crystallographic Points, Directions, and Planes
Crystallographic planes

identify the intercepts on the x-, y- and z- axes.

Intercepts: a, ∞, ∞
 Crystallographic Points, Directions, and Planes
Crystallographic planes

identify the intercepts on the x-, y- and z- axes.

Intercepts: a, ∞, ∞

 Fractional Intercepts: a/a, ∞/𝑏, ∞/c

take the reciprocals of the fractional intercepts

 (100)
 Crystallographic Points, Directions, and Planes
Crystallographic planes

Identify Planar (Miller) Indices of the following plane

 Crystallographic Points, Directions, and Planes
Crystallographic planes

Identify Planar (Miller) Indices of the following plane

 Crystallographic Points, Directions, and Planes
Crystallographic planes

Identify Planar (Miller) Indices of the following plane

 X-RAY DIFFRACTION: DETERMINATION OF CRYSTAL STRUCTURES

The Diffraction Phenomenon

Diffraction occurs when a wave encounters a series of regularly spaced obstacles that
(1) are capable of scattering the wave,
(2) and have spacings that are comparable in magnitude to the wavelength

X-rays are a form of electromagnetic radiation that have high energies and short
wavelengths on the order of the atomic spacing for solids
When a beam of x-rays impinges on a solid material, a portion of this beam will be
scattered in all directions by the electrons associated with each atom or ion that
lies within the beam’s path
 Demonstration of a wave

• Fix time t, draw as a function of position x

 Interference of waves

Interference of two waves

Interference of 2 surface water waves

NGUYEN Van Tang_Vietnam French

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 Interference in two dimensions
Assume: S1 and S2 are identical

• At a: S1a = S2a
 S1 and S2 are in phase
 Amplitude is doubled
 Constructive interference

• At b: S2b = S1b + 2𝜆
 S1 and S2 are in phase
 Amplitude is doubled
 Constructive interference

• At c: S1c = S2c + 2.5𝜆

 S1 and S2 are out of phase
 Amplitude is zero
 Destructive interference

NGUYEN Van Tang_Vietnam French

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 Interference in two dimensions

 Source needed being coherent

• constant phase difference

• the same waveform.

NGUYEN Van Tang_Vietnam French

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 Interference in two dimensions

• Condition for constructive interference:

𝑟2 − 𝑟1 = 𝑛𝜆
P
(n = 0, ±1, ±2, ±3,…)

• Condition for destructive interference:

1
𝑟2 − 𝑟1 = 𝑛 + 𝜆
2

(n = 0, ±1, ±2, ±3,…)

NGUYEN Van Tang_Vietnam French

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 X-Ray Diffraction and Bragg’s Law

the path difference of the two diffracted beams is:

𝑑𝑠𝑖𝑛𝜃 + 𝑑𝑠𝑖𝑛𝜃 = 2𝑑𝑠𝑖𝑛𝜃

 constructive interference occurs when:

2𝑑𝑠𝑖𝑛𝜃 = 𝑛𝜆 (Bragg’s law)

 X-Ray Diffraction and Bragg’s Law

constructive interference occurs when?

 Diffraction Techniques

powdered or polycrystalline specimen is exposed to monochromatic x-radiation

Schematic diagram of an x-ray diffractometer ; T = x-ray source,

S = specimen, C = detector, and O = the axis around which the specimen
and detector rotate.
 Diffraction Techniques

X ray diffraction pattern obtained after the measurement.

The result is then compared with an available library to match the correct structure
system.
 Diffraction Techniques

The magnitude of the distance between two adjacent and parallel planes
of atoms is a function of the Miller indices as well as the lattice parameter

for crystal structures that have cubic symmetry

𝑎
𝑑ℎ𝑘𝑙 =
ℎ2 + 𝑘 2 + 𝑙 2

a is the lattice parameter

 Diffraction Techniques

Application

For BCC iron, compute (a) the interplanar spacing, and (b) the diffraction angle for
the (220) set of planes. The lattice parameter for Fe is 0.2866 nm. Also, assume
that monochromatic radiation having a wavelength of 0.1790 nm is used, and
the order of reflection is 1.
 NONCRYSTALLINE SOLIDS

non-crystalline >< Crystalline

• has no systematic and regular • has systematic and regular

arrangement of atoms over arrangement of atoms over
relatively large atomic distances relatively large atomic distances
• also called amorphous

(SiO2) (SiO2)
 Imperfections in Solids

it has been assumed that perfect order exists throughout crystalline

materials on an atomic scale

However, such an idealized solid does not exist

exist “defects” or “imperfections”

Point Defects

Line Defects

Interfacial Defects

Bulk Defects
 Point Defects
VACANCIES AND SELF-INTERSTITIALS

The simplest of the point defects is a vacancy

A site normally occupied from which an atom is missing

A self-interstitial is an atom from the

crystal that is crowded into an
interstitial site, a small void space that
under ordinary circumstances is not
occupied
 Point Defects

The equilibrium number of vacancies Nv for

a given quantity of material depends on
and increases with temperature according to

𝑄𝑣
𝑁𝑣 = 𝑁𝑒𝑥𝑝 −
𝑘𝑇

N is the total number of atomic sites

𝑄𝑣 is the energy required for the formation of

a vacancy

T is the absolute temperature (K)

k: Boltzmann’s constant ( 1.38 x 10-23 J/atom-K)

 Point Defects
IMPURITIES IN SOLIDS

A pure metal consisting of only one type of atom just isn’t possible; impurity or
foreign atoms will always be present

Most familiar metals are not highly pure; rather, they are alloys, in which
impurity atoms have been added intentionally to impart specific characteristics
to the material

Solid solution: when impurity atom are well integrated

in the host crystal structure, or a new second phase,
it forms a solid solution

“Solvent” represents the element or compound that

is present in the greatest amount

“Solute” is used to denote an element or compound

present in a minor concentration
 Point Defects

IMPURITIES IN SOLIDS

There are two types of impurity defect in solid solution

1. substitutional solid solution

2. Interstitial solid solution

 SPECIFICATION OF COMPOSITION

It is often necessary to express the composition (or concentration) of an alloy in

terms of its constituent elements.

weight percent atom percent

is the weight of a particular element number of moles of an element in

relative to the total alloy weight relation to the total moles of the
elements in the alloy

𝑚1 𝑛 𝑚1
𝐶1 = × 100 𝐷1 = × 100
𝑚1 + 𝑚2 𝑛𝑚1 + 𝑛𝑚2

C1: weight concentration D1: atom percent

m1: weight of element 1 m1: moles of element 1
m2: weight of element 2 m2: moles of element 2
 DISLOCATIONS—LINE DEFECTS

A dislocation is a linear or one-dimensional defect around which some of the atoms

are misaligned

Edge dislocation

it is a linear defect that centers

around the line that is defined
along the end of the extra half-
plane of atoms

 dislocation line

Edge dislocation

an extra portion of a plane of

atoms, or half-plane, the edge of
which terminates within the crystal
 DISLOCATIONS—LINE DEFECTS

Screw dislocation

upper front region of the crystal is shifted one atomic distance to the right relative
to the bottom portion

formed by a shear stress that is applied to produce the distortion

 DISLOCATIONS—LINE DEFECTS

mixed dislocation