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MT-201B MATERIALS SCIENCE

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Why Study Materials Science?

1. Application oriented Properties

2. Cost consideration

3. Processing route

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Classification of Materials

1. Metals

2. Ceramics

3. Polymers

4. Composites

5. Semiconductors6. Biomaterials

7. Nanomaterials

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1. Introduction to Crystallography

2. Principle of Alloy Formation

3. Binary Equilibria

4. Mechanical Properties

5. Heat Treatments

6. Engineering Materials

7. Advanced Materials

Syllabus

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Recommended Books

1. Callister W.D., Materials Science andEngineering an Introduction

2. Askeland D.R., The Science andEngineering of Materials

3. Raghavan V.,Materials Science and

Engineering- A first Course,4. Avener S.H, Introduction to Physical

Metallurgy,

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The Structure of Crystalline Solids

CRYSTALLINE STATE Most solids are crystalline with their atoms arranged in a

regular manner.

Long-range order: the regularity can extend throughout the

crystal. Short-range order: the regularity does not persist over

appreciable distances. Ex. amorphous materials such as glass

and wax.

Liquids have short-range order, but lack long-range order. Gases lack both long-range and short-range order.

Some of the properties of crystalline solids depend on the

crystal structure of the material, the manner in which atoms,

ions, or molecules are arranged.

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Sometimes the term lattice is used in the context of crystalstructures; in this sense lattice means a three-

dimensional array of points coinciding with atom positions

(or sphere centers).

A point lattice

Lattice

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Unit Cells

The unit cell is the basic structural unit or building block of the crystalstructure and defines the crystal structure by virtue of its geometry andthe atom positions within.

A point lattice A unit cell

This size and shape of the unit cell can be described in terms of theirlengths (a,b,c) and the angles between then (,,). These lengths and

angles are the lattice constants or lattice parameters of the unit cell.

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Table 1: Crystal systems and Bravais Lattices

Crystal systems and Bravais Lattice

Bravais Lattice

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Types of crystals

Three relatively simple crystal structures are found for mostof the common metals; body-centered cubic, face-centeredcubic, and hexagonal close-packed.

1. Body Centered Cubic Structure (BCC)

2. Face Centered Cubic Structure (FCC)

3. Hexagonal Close Packed (HCP)

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1. Body Centered Cubic Structure (BCC)

In these structures, there are 8 atoms at the 8 corners andone atom in the interior, i.e. in the centre of the unit cell withno atoms on the faces.

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2. Face Centered Cubic Structure (FCC)

In these structures, there are 8 atoms at the 8 corners,6 atoms at the centers of 6 faces and no interior atom.

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3. Hexagonal Close Packed (HCP)

In these structures, there are 12 corner atoms (6 at the bottomface and 6 at the top face), 2 atoms at the centers of theabove two faces and 3 atoms in the interior of the unit cell.

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Average Number of Atoms per Unit CellSince the atoms in a unit cell are shared by the neighboring

cells it is important to know the average number of atoms perunit cell. In cubic structures, the corner atoms are shared by 8cells (4 from below and 4 from above), face atoms are sharedby adjacent two cells and atoms in the interior are shared by

only that one cell. Therefore, general we can write:

Nav = Nc / 8 + Nf / 2 + Ni / 1

Where,

Nav = average number of atoms per unit cell.Nc = Total number of corner atoms in an unit cell.Nf = Total number of face atoms in an unit cell.Ni = Centre or interior atoms.

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Simple cubic (SC) structures: In these structures there are8 atoms corresponding to 8 corners and there are no atomson the faces or in the interior of the unit cell. Therefore,Nc = 8, Nf = 0 and Ni = 0Using above eqn. we get, Nav = 8/8 + 0/2 + 0/1 = 1

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2. Body centered cubic (BCC) structures: In thesestructures, there are 8 atoms at the 8 corners and one

atom in the interior, i.e. in the centre of the unit cell withno atoms on the faces. Therefore Nc = 8, Nf = 0 and Ni = 1Using above eqn. we get, Nav = 8/8 + 0/2 + 1/1 = 2

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3. Face Centered Cubic Structure (FCC): In these structures,there are 8 atoms at the 8 corners, 6 atoms at the centers

of 6 faces and no interior atomTherefore Nc = 8, Nf = 6 and Ni = 0Using above eqn. we get, Nav = 8/8 + 6/2 + 0/1 = 4

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4. Hexagonal Close Packed (HCP) Structures:In these structures, there are 12 corner atoms (6 at the bottom face and 6 atthe top face), 2 atoms at the centers of the above two faces and 3 atoms in

the interior of the unit cell.For hexagonal structures, the corner atoms are shared by 6 cells (3 frombelow and 3 from above), face atoms are shared by adjacent 2 cells andatoms in the interior are shared by only one cell. Therefore, in general thenumber of atoms per unit cell will be as: Nav = Nc / 6 + Nf / 2 + Ni / 1

Here Nc = 12, Nf = 2 and Ni = 3Hence, Nav = 12 / 6 + 2 / 2 + 3 / 1 = 6

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Co-ordination Number

Co-ordination number is the number of nearest equidistant

neighboring atoms surrounding an atom under consideration

1. Simple Cubic Structure:

Simple cubic structure has a coordination number of6

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2. Body Centered Cubic Structure:

Body centered cubic structure

has a coordination number of8

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3. Face Centered Cubic Structure:

Face centered cubic structure has a coordination number of12

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4. Hexagonal Close Packed Structure:

Hexagonal close packed structure has a coordination number of12

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Stacking Sequence for SC, BCC, FCC and HCP

Lattice structures are described by stacking of identical planes

of atoms one over the other in a definite manner

Different crystal structures exhibit different stacking sequences

1. Stacking Sequence of Simple Cubic Structure:

Stacking sequence of simple cubic structure is AAAAA..since the

second as well as the other planes are stacked in a similar manneras the first i.e. all planes are stacked in the same manner.

A

A

A

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2. Stacking Sequence of Body Centered Cubic Structure:

Stacking sequence of body centered cubic structure is ABABAB.

The stacking sequence ABABAB indicates that the second plane

is stacked in a different manner to the first.

Any one atom from the second plane occupies any one interstitial

site of the first atom. Third plane is stacked in a manner identical to the first and fourth

plane is stacked in an identical

manner to the second and so on.

This results in a bcc structure.

A

B

A

B

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3. Stacking Sequence of Face Centered Cubic Structure:

Stacking sequence of face centered cubic structure is ABCABC.

The close packed planes are inclined at an angle to the cube facesand are known as octahedral planes

The stacking sequence ABCABC indicates that the second plane

is stacked in a different manner to the first and so is the third from

the second and the first. The fourth plane is stacked in a similarfashion to the first

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4. Stacking Sequence of Hexagonal Close Packed Structure:

Stacking sequence of HCP structure is ABABAB..

HCP structure is produced by stacking sequence of the

type ABABAB..in which any one atom from the second

plane occupies any one interstitial site of the first plane.

Third plane is stacked similar to first and fourth similar to

second and so on.

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Atomic packing factor is the fraction of volume orspace occupied by atoms in an unit cell. Therefore,

APF = Volume of atoms in unit cellVolume of the unit cell

Atomic Packing Factor (APF)

APF = Average number of atoms/cell x Volume of an atomVolume of the unit cell

Since vol