Prerequisites: Basics of Physics & Chemistry Course

Description: This course will enable students to

I. Know about the basics of kinetics, chemical bonding and structure of materials.
II. Analyze the facts of conductors, resistors and dielectric materials.
III. Study different types and properties of semiconductors.
IV. Know about the concept of magnetic materials and their properties.
V. Measure different electrical and magnetic properties of materials.
Human Civilization Through materials
 Stone age
 Bronze age
 Iron age
 Glass age
 Steel age
 Aluminum age
 Plastic age
 Silicon age
 Designed/ Architectured materials age

 All technological advancements rely on availability of right material(s)

Material Science : Deals with structure –property correlations

Materials engineering: Design the structure of a material for

specific application (depends on structure –property correlations)

Structure: Arrangement of internal components. Structure is

scale dependent-subatomic, atomic, microscopic, macroscopic

Property: Characteristic response under the action of external

stimulus; Six categories: Mechanical, electrical, thermal,
magnetic, optical and deteriorative
According to nature
(i) Metals and alloys

 Capable of changing their shape permanently

 Good thermal and electrical conductivity

(ii) Ceramics and glasses

 Nonmetallic inorganic substances

 Brittle and have good thermal and electrical
insulating properties

(iii) Organic polymers

 Relatively inert, light

 Generally have a high degree of plasticity
According to 3 major applications
(i) Structures
(ii) Machines
(iii) Devices

 Relationship between material groups and categories of applications

Levels of structure
 The internal structure of a material

 magnification and resolution - measure of the level of observation

I. Macrostructure

II. Microstructure

III. Substructure

IV. Crystal structure

V. Electronic structure

VI. Nuclear structure

 Microstructure
Macrostructure
Al-pure and aluminum alloys

Crystal boundaries in nickel ferrite, Fe2NiO4, magnified 900 times

 Human eye resolution-0.1 mm

 Microscope-0.1um
 Substructure
Structure obtained by using a microscope with a much higher magnification and resolution

Substructure of a Ni–Fe–Cr alloy showing curved Field–ion micrograph of a hemispherical tip of platinum
dislocation lines, magnified 30 000 times in an electron The white dots arranged in circles are images of individual
microscope atoms
Crystal structure

 Atomic arrangement within a crystal

 Unit cell-Describe the arrangement of a few atoms within
 X-ray diffraction

Electronic structure

 The electrons in the outermost orbitals of individual atoms that constitute the solid
 Spectroscopic technique

Nuclear structure

Nuclear magnetic resonance (NMR) and Mossbauer studies

Structure–Property Relationships in Materials

 Microstructure, the substructure and the crystal structure- greatest interest in materials science and engineering

 Chemical, mechanical, electrical and magnetic properties-most important engineering properties

 Basic concepts pertaining to the levels of structure- concepts in equilibrium and kinetics, the geometry of crystals, the
arrangement of atoms in the unit cell of crystalline materials, the substructural imperfections in crystals, and the
microstructure of single phase and multi-phase materials

 Solid state diffusion and control of phase transformations by heat treatment

 The gross composition of a material is important in determining its Structure

 Fundamental changes in the structure and properties can be brought -subtle changes in the concentration and distribution of minute
quantities of impurities

 The same may also be possible by a thermal or a mechanical treatment that involves no change in the overall
composition of the material

 Materials Science and Engineering deals more with this kind of changes rather than with the effect of gross composition on the
properties
Stability and Meta stability

 Material with least potential energy (PE) is more stable

 The height of center of mass from base is the measure of its PE
 PE=mgH
 Equilibrium Unstable

Metastable Stable
Crystal Geometry
Crystal: A three dimensional periodic arrangement of atoms in a space

Unit cell:
Crystal: A three dimensional periodic Lattice: A three dimensional periodic
arrangement of atoms in a space arrangement of points in a space
 Weight, density, electrical  Geometrical property
conductivity

Crystal= Lattice+ Motif (Basis)

Motif or basis: An atom or a group of atoms associated with each lattice point
is called motif or basis
Lattice translation: Any vector from one lattice point to another lattice point
Unit Cell: a region of space which can generate the entire lattice (or crystal) by
repetition through lattice translations
 A lattice can have many (infinitely many) unit cells

Unit cell
Primitive and non primitive unit cells

Primitive : Lattice point only at the corners of the cell

Non-primitive : lattice points at its corners as well as at some other points
Crystal coordinate system

Lattice parameters: The lengths of the three edges of the unit cell (or of
three basis vectors) and the three interaxial angles between them are called
lattice parameters
 Crystal system Conventional unit cell Bravais Lattice

1. Cubic a=b=c; α=β=γ=900 P I F

Classification
2. Tetragonal of lattices
a=b≠c; α=β=γ=900 P I
7 crystal systems
3. Orthorhombic
14 bravais lattices a≠b≠c; α=β=γ=900 P I F c

4. Hexagonal a=b≠c; α=β=900; γ=1200 P

5. Trigonal or Rhombphedral a=b=c; α=β=γ≠900 P

6. Mono clinic a≠b≠c; α=γ=900; β=1200 P C

7. Triclinic a≠b≠c; α≠β≠γ P

P Primitive or simple Lattice points are only at the corners
I Body -centred Corners + Body centre
F Face-centred Corners+ All face centres
C End-centred or base-centred Corners+ One of parallel face centers
Three cubic Bravais lattices (P, I, F)

Cubic P Cubic I Face –centred Cubic (F)

Simple Cubic Body –centred Cubic
Primitive Cubic
Three Cubic Bravais Lattices (P, I, F)
Symmetry: An object is said to be symmetric with respect to a geometric operation if it can brought
into self-coincidence
by that operation

Translational Symmetry of a Lattice :

Miller indices of directions
 Miller index is a method to specify the various directions and planes in a crystal

1. Choose a point on the direction as the

origin
2. Choose a coordinate system with axes
parallel to the unit cell edges
3. Find the coordinates of another point on
the direction in terms of a, b and c (1,0,0)
4. Reduce the coordinates to smallest integers.
1,0,0
5. Put in square brackets [100]
[1 1 2]
Miller indices of a family of symmetry related directions

<UVW> = [UVW] and all other directions related to [UVW] by the symmetry of the crystal
Miller indices for planes

I. Select crystallographic coordinate system

with origin not on the plane
II. Find the intercepts along axes in terms of
respective lattice parameters 1 1 1
III. Take reciprocal 1 1 1
IV. Convert to smallest integers in the same
ratio 1 1 1
V. Enclose in parenthesis (1 1 1)
 Plane ABCD

Origin O

Intercepts 1∞ ∞

Reciprocals 10 0

X Small integers 100

Miller indices (1 0 0)
Zero represents that the plane is parallel to the corresponding axis
 Plane OCBE

Origin O*

Intercepts 1 -1 ∞

Reciprocals 1 -1 0

Small integers 100

Miller indices (1 1 0)
Bar represents negative intercepts
 Miller indices of a plane specifies only its orientation in
space not its position
 All parallel planes have the same miller indices
{100} Tetragonal= (100), (010), (001)
(100), (010) (001)
Importance of Miller Indices
• In Materials Science it is important to have a notation system
for atomic planes since these planes influence

• Optical properties

• Reactivity

• Surface tension

• Dislocations
Why are planes in a lattice important?
(A) Determining crystal structure

* Diffraction methods measure the distance between parallel lattice planes of atoms.
• This information is used to determine the lattice parameters in a crystal.
* Diffraction methods also measure the angles between lattice planes.
(B) Plastic deformation

* Plastic deformation in metals occurs by the slip of atoms past each other in the crystal.
* This slip tends to occur preferentially along specific crystal-dependent planes.
(C) Transport Properties

* In certain materials, atomic structure in some planes causes the transport of electrons
and/or heat to be particularly rapid in that plane, and relatively slow not in the plane.
• Example: Graphite: heat conduction is more in sp2-bonded plane.
• Example: YBa2Cu3O7 superconductors: Cu-O planes conduct pairs of electrons
(Cooper pairs) responsible for superconductivity, but perpendicular insulating.
+ Some lattice planes contain only Cu and O
First law of thermodynamics

 The amount of energy in the universe is finite

 Energy cannot be created or destroyed
 Energy can be expressed as heat or work
 Enthalpy: heat change associated with the chemical process

Second law of thermodynamics

 In any spontaneous process, entropy (disorder) of the universe increases
 Entropy (S) is the degree of disorder
 Matter changes from a more ordered state to less ordered state
 S solid < S liquid << Sgas

Gibbs free energy

 Predicts the direction for a chemical reaction

 Negative ΔG
 Spontaneous reaction
 Or the forward reaction is favored
 Positive ΔG
 Non-spontaneous reaction
 Or a spontaneous reverse reaction
 ΔG=0
 Equilibrium position has been attained
A spontaneous reaction is a reaction that favors the formation of products at the conditions
under which the reaction is occurring. A roaring bonfire is an example of a spontaneous reaction

Enthalpy and entropy can be combined to predict reaction spontaneity

ΔG= ΔH -TΔS

ΔH ΔS ΔG Comments on reaction
- + - Always spontaneous

+ - + Never spontaneous

+ + +/- Spontaneous at high

temperature
- - +/- Spontaneous at low
temperature
 The concepts of equilibrium and kinetics are intimately associated with the basic
thermodynamic parameters Pressure P and temperature T

 Internal energy E (also denoted by U) at temperature T

E0 is the internal energy of the material at 0 K

Cv is the specific heat at constant volume

 The enthalpy or the heat content of a material H is defined

H0 is the enthaply at 0 K
Cp is the specific heat at constant pressure

 E and H are related through P and V, where V is the volume of the material:
H = E + PV

 PV represents the external energy and is equal to the work done

 For liquid and the solid state, at atmospheric pressure, the PV term is negligible so that E ≈ H
H0 represents the energy released when the individual atoms of the material are brought together from the gaseous
state to form a solid at 0 K

 The gaseous state (where there is no interaction between the atoms) is taken as the reference
zero energy state

 As the temperature increases from 0 K, the material absorbs heat from the surroundings and H increases

 The solid melts on reaching the melting point and a further quantity of heat ΔH called the enthalpy of fusion is
added at the melting temperature

 When all the solid has melted, the temperature of the liquid may further increase with the absorption of more
energy

 All the energy that a system possesses is not available as work during a
chemical change

 That part of the energy which can become available as work is called the Gibbs free energy (or simply the Gibbs
energy)

 The part which cannot be released as work is called the bound energy
 Entropy defines the relationship between the total energy and the
Gibbs energy. At constant pressure, the entropy S of a system is given

 The entropy of a material is zero at 0 K, in contrast to the enthalpy

 The entropy increases with increasing temperature

 It is a measure of the thermal disorder introduced in the solid, as it is heated above 0 K

 In addition to thermal entropy, a system may also possess configurational entropy, which is dependent on the
configurations of the system

 Boltzmann’s definition, the configurational entropy can be written as

S = k ln w
k is Boltzmann’s constant
w is the number of different configurations of equal potential energy
 Gibbs Free Energy Equation
Gibbs free energy is equal to the enthalpy of the system minus the product of the
temperature and entropy

G = H – TS

G = Gibbs free energy

H = enthalpy
T = temperature
S = entropy

 Gibbs free energy, also known as the Gibbs function, Gibbs energy, or free enthalpy, is a quantity that is
used to measure the maximum amount of work done in a thermodynamic system when T and P constant
  The Gibbs energy is used as a criterion of stability. The most stable state of a material is
that which has the minimum Gibbs energy

 For a process to occur spontaneously, the Gibbs energy must decrease during the process
ΔG=Gfinal – G initial
 At a constant temperature and pressure, we can write this condition for a spontaneous change as

 In the example of the tilting block, where no entropy change occurs during the tilt, we were justified in defining
the stable state as a state of lowest potential energy (or enthalpy)
 In general, the entropy change may not be negligible, in such cases, TΔS > Δ H
The Kinetics of Thermally Activated Processes

 Arrhenius first measured the rate of a chemical reaction as a function of

temperature
 The rate is an exponential function of temperature

Q = activation energy
A= pre-exponential constant
V = vibrational frequency
N = total number of species
ΔH*=Height of the barrier
n= number of species with energy equal to or
greater than that of the activation barrier,