It's about crystal system. In which we know how to find packing factor of simple, body centered and face centered cubic structures.

1. By
Zumar Atta Ullah
B.Z.U. Multan, Pakistan

2. Crystal Systems
 Fourteen Bravais Lattices are grouped into seven
crystal systems.

3. Crystal Systems

4. What is Lattice
 A lattice is a collection of points, called lattice points, which
are arranged in a periodic pattern so that the surroundings of
each point in the lattice are identical.
 The collection of imaginary array of points in a periodic way.
 The unit cell is a subdivision of a lattice that still retains the
overall characteristics of the entire lattice.

5. Lattice Parameters
 There are three axis and three
angles in a crystal lattice. These
six components are known as
lattice parameters.
 They describe the size and shape
of the unit cell, include the
dimensions of the unit cell and the
angles between the sides.

6. Number of Atoms per Unit Cell
 In the simple cubic unit cell, number of atom per unit
cell is 1
(8 corners)(1/8)=1
 In the body-centered cubic unit cell, number of atoms
per unit cell is 2
(8 corners)(1/8)+(1 center)(1)=2
 In the face-centered cubic unit cell, number of atoms
per unit cell is 4
(8 corners)(1/8)+(6 faces)(1/2)=4

7. Coordination Number
 The coordination number is the number of atoms touching
a particular atom, or the number of nearest neighbors for
that particular atom.
 Each atom in the SC structure has a coordination number
of six.
 Each atom in the BCC structure has eight nearest
neighbors.
 Each atom in the FCC structure has a coordination number
of twelve, which is the maximum.

8. Packing Factor
 The packing factor is the fraction of space occupied by
the atoms, assuming that atoms are hard spheres sized so
that they touch their closest neighbor.
 The general expression for the packing factor is:
 The packing factor of S.C., F.C.C. and B.C.C. is
described in next slides:

9. Packing Factor of the Simple Cube
Calculation:
Packing Factor = 52%
Empty Spaces = 48%

10. Packing Factor of B.C.C.
Calculation:
Packing Factor = 68%
Empty Spaces = 32%

11. Packing Factor of F.C.C.
Calculation:
Packing Factor = 74%
Empty Spaces = 26%

12. For consult
Please contact
Email: Zumar.atta.ullah.18@gmail.com
or Zumar.attaullah@outlook.com