CMPE 103 Electronic Materials
Assignment 1 Solution
1.5
Find the maximum fractions of the unit cell volume that can be filled by hard
spheres in the sc, bcc and diamond lattice.
Simple Cube [2 marks]
No. of atoms in 1unit cell = (1/8 x 8) = 1 atom
Radius of each atom = a / 2 where a is the lattice constant
Volume of 1 atom (sphere) = 4/3
π
r
3
= 4/3 x
π
x (a / 2)
3
=
π
/6 x a
3
Total volume taken up by atoms in 1 unit cell = No. of atoms in 1 unit cell x Volume of 1 atom
= 1 x
π
/6 x a
3
Volume of unit cell = a
3
Fraction of unit cell filled = Total volume taken up by atoms in 1 unit cell / Volume of unit cell
= (1 x
π
/6 x a
3
) / a
3
=
π
/6 = 0.52
Body Centered Cube [2 marks]
No. of atoms in 1unit cell = (1/8 x 8) + 1 = 2 atoms
Radius of each atom =
3
a/4 where a is the lattice constant
Volume of 1 atom (sphere) = 4/3
π
r
3
= 4/3 x
π
x (
3
a/4)
3
=
3
π
a
3
/ 16
Total volume taken up by atoms in 1 unit cell = No. of atoms in 1 unit cell x Volume of 1 atom
= 2 x
3
π
a
3
/ 16
Volume of unit cell = a
3
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 Spring '11
 PeterPan
 Gallium arsenide, Aluminium arsenide, Indium arsenide, Indium gallium phosphide

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