This document discusses packing factors for different crystal structures. It defines packing factor as the fraction of space occupied by atoms in a unit cell, assuming hard spheres. Simple cubic structure has a packing factor of 0.52 or 52%. Body centered cubic (BCC) has two atoms per unit cell, a packing factor of 0.68 or 68%. Face centered cubic (FCC) has four atoms per unit cell and the highest packing factor of 0.74 or 74%. Materials properties depend on their crystal structure and packing efficiency.

1. Presented By
Gulfam Hussain

2. Packing factor
The packing factor or atomic packing fraction is the
fraction of space occupied by atoms, assuming that the
atoms are hard spheres.
Expression to calculate packing factor is
=(No. of atoms/unit cell)(volume of each atom)
volume of a unit cell

3. Unit cell
The unit cell is subdivision of a lattice that still retain
the overall characteristics of the entire lattice.
A lattice is a collection of point called lattice point
which are arranged in a periodic pattern.

4. Number of atoms per unit cell
A specific number of lattice points define each of the
unit cell.
For example the corner of the cell are easily identified
as are the body centered and face centered position.

5. Packing factor of Simple cubic
Unit cell of Simple cubic structure has eight corner atoms which are
bonded to eight other atoms.
All sides of cube are equal in length a=b=c
Volume of a unit cell=a³=r³
Packing factor of simple cube=0.52
Packing density= 0.52× 100
= 52%

6. Body Centered cubic
Body centered cubic structure has a unit
cell having an atom at its center and eight
atoms at corners.
Each corner atom is bonded to 8 other
atoms and 1 atom is present in the center.
So no of atom in BCC unit cell=2
As (8×1/8)+1

7. Sodium an α-iron are example of BCC.
The BCC structure has a coordination number of eight.
Materials having BCC structure are soft and malleable.

8. General expression for packing factor is
Packing factor=
(No. of atoms/cell)(volume of each atom)
volume of a unit cell
Packing factor of BCC =0.68
Packing Density=packing factor ×100
=0.68 ×100
=68%

9. Face Centered Cubic
A FCC has a unit cell having an atom at the center of
each face of unit cell and 8 corner atoms.
Each of 8 corner atom contribute 1/8 and each face
atom contribute ½ in each unit cell.
No. of atoms in FCC unit cell=4
As (8 ×1/8)+(1/2 × 6)=4

10. Copper and aluminium has FCC structure.
The FCC structure has a coordination number of twelve.
FCC structure are usually harder.

11. Packing factor of FCC
As
packing factor = (No. of atoms/cell)(volume of each atom)
volume of a unit cell
 And volume of a unit cell= 4r ³
√2
Volume of an atom= 4πr³
3
So
The packing factor of FCC =0.74

12. packing density=packing factor×100
=0.74×100
=74%