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Gulfam Hussain
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 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
 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.
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.
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
 Materials

having BCC structure are
harder and malleable.
 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%
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
 FCC

structure are usually soft and
ductile.
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




=0.74×100
=74%

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Packing factor

  • 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.
  • 5.
  • 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