CHEM 123: Practice Problems
page 1
of
30
B1.
Simple cubic packing.
The crystal lattic and unit cell for simple cubic packing are
shown below.
a)
# spheres
=
(
)
(
)
1
8
sphere/corner
8 corners
=
1 sphere
b) The coordination number of each sphere is 6. To see this, focus on an “interior” sphere
such as sphere “A” in the figure on the left. That sphere is in contact with 6 other spheres
– the one above it, the one below, the one in front, the one behind, the one to its left and
the one to its right.
c)
If the radius of each sphere is “
R
” then the edge length of the unit cell is
a
= 2
R
d) The volume of the unit cell is
V
cell
=
a
3
=
8
R
3
There is
one full sphere
contained within the unit cell so the volume of spheres
contained within the unit cell is
3
spheres
4
3
V
R
=
π
.
3
4
3
3
0.5236
6
8
spheres
cell
V
R
Packing
Efficiency
V
R
π
π
=
=
=
=
A

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