This document discusses atomic packing factors and unit cell structures for body centered cubic (BCC) and face centered cubic (FCC) crystal lattices. It provides the following key details: - The packing factor is the fraction of space occupied by atoms, assuming hard spheres, and is calculated as the number of atoms in the unit cell multiplied by the volume of each atom, divided by the volume of the unit cell. - A BCC unit cell has an atom at its center and eight atoms at the corners, for a total of two atoms. Its packing factor is 0.68 or 68%. - An FCC unit cell has an atom at the center of each face and eight corner atoms, for a

1. Gulfam Hussain
e_gulfam@yahoo.com
+923336275670

2.  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/cell)(volume of each atom)
volume of an atom

3.  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. 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.

6. 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.  Materials
having BCC structure are
harder and malleable.

8.  Packing
factor=
(No. of atoms/cell)(volume of each atom)
volume of an atom
 Packing
factor of BCC =0.68
 Packing Density=packing factor ×100
=0.68 ×100
=68%

9. A
FCC has a unit cell having an atom at
the center of each faces 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.  FCC
structure are usually soft and
ductile.

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

12. 

=0.74×100
=74%