Materials Science and Engineering

1. Dr. Jayanta Kr. Mahato
Associate Professor
Mechanical Engineering Dept.
Shobhit Deemed to-be University

2. Outline of the Lecture
• Lattice
• Basis
• Crystal Structure
– Poly Crystal
– Single Crystal
• Unit Cell
• Cubic Crystal System
– Simple Cubic(SC) ,
– Face Centered Cubic (FCC) ,
– Body Centered Cubic (BCC)
- The seven crystal system
- Hexagonal close pack unit cell (HCP)
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

3. Crystal structure = Lattice + Basis
Lattice:-
"An infinite periodic array of points in a space"
 The arrangement of points defines the lattice symmetry
 A lattice may be one, two or three dimensional (3D)
Basis (Motif):-
A group of one or more atoms, located in a particular way
with respect to each other and associated with each point,
is known as the Motif or Basis.
Lattice Basis (Motif)

4. Crystal structure = Lattice + Basis
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

5. Crystal structure = Lattice + Basis
When an atom or identical group of
atoms is attached to every lattice
point, we obtain a crystal structure.
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

6. Crystals: Classification
Crystals
Single Crystal Poly Crystal
• Single crystal: In this
type of crystal periodicity is
maintained throughout the
body.
• Poly crystal: In this type
of crystal periodicity is not
maintained throughout the
body.
Poly Crystal
Single Crystal

7. Lattice Point
Unit Cell
Unit Cell: Atoms or group of atoms forming a
building block of the smallest acceptable size of the
whole volume of a crystal is defined as a unit cell.
Atom
Point to be remember: Lattice points are located at
the corner of the unit cell and in some cases, at
either faces or the centre of the unit cell.

8. Types of Cubic Cells
Types of Cubic Cells
Simple Cubic Body Centered Cubic Face Centered Cubic
Simple Cubic Body Centered Cubic Face Centered Cubic
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

9. Body Centered Cubic (BCC) Crystal Structure
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

10. Face Centered Cubic (FCC) Crystal Structure
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

11. Hexagonal Close-Packed (HCP) Crystal Structure
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

12. Total Atomic Numbers per Simple Cubic Unit Cell
Total number of
atoms per Simple
Cubic unit cell is
8*(1/8) = 1 atom
Each corner atom
shared by 8 unit cells

13. Total Atomic Numbers per BCC Unit Cell
Total number of
atoms per BCC unit
cell is
8*(1/8) + 1 = 2 atom
Each corner atom
shared by 8 unit cells
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

14. Total Atomic Numbers per FCC Unit Cell
Total number of atoms per FCC unit cell is
8*(1/8) + 6*(1/2) = 4 atoms
Each corner atom
shared by 8 unit cells
Each face atom
shared by 2 unit cells
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

15. Total Atomic Numbers per HCP Unit Cell
Total number of atoms per HCP unit cell is
6*(1/6)*2 + 2*(1/2) + 3 = 6 atoms
Each corner atom
shared by three
primitive unit cells
3 inter
whole
atom
Each face atom
shared by 2 unit cells
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

16. 7 Unique Arrangements of Unit Cell
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

17. Properties of Unit Cell: Properties of Materials
1. No of Atoms Per Unit Cell
2. Coordination Number
3. Lattice Constant
4. Atomic Radius
5. Atomic Packing Fraction (APF)
 No of Atoms Per Unit Cell
Effective no of atoms per unit cell
Factors Responsible for Properties of Unit Cell:
Properties of Materials
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

18. Mechanical Properties of Materials: In General
Increasing Strength
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

19. Coordination Number
Coordination number (N): The highest number of nearest
neighbor atoms or ions surrounding an atom or ion.
Simple Cubic
N = 6
BCC
N = 8
FCC
N = 12
HCP
N = 12
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

20. Atomic packing factor (APF)
Atomic packing factor (APF): 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
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

21. Atomic Packing Factor for FCC
Dr. Jayanta Kr. Mahato, Asst. Prof., Mechanical Engineering

22. Home Work
Calculate the Atomic Packing
Factor (APF) for Simple Cubic
and BCC Structure.
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering

23.  About the crystal structure.
 Types of Crystal Structure
 About the Unit Cell.
 Cubic Crystal System
– Simple Cubic(SC) ,
– Body Centered Cubic (BCC)
– Face Centered Cubic (FCC)
- Hexagonal close pack unit cell (HCP)
 Coordination Number
 Atomic Paking Factor (APF)
 The seven crystal system
Summary
 From this lecture we have learned about:
Dr. Jayanta Kr. Mahato, Assoc. Prof., Mechanical Engineering