1
Assignment #3 Solutions
ME264 Materials Science for Mechanical Engineering
Spring 2009
Due Date: 4 March 2009
(5 pts)
1. (1pt)
(a)
Calculate the density of an f.c.c. packing of spheres of unit density.
(b)
If these same spheres are packed to form a
glassy
structure, the arrangement is
called “dense random packing” and has a density of 0.636. If crystalline f.c.c.
nickel has a density of 8.90 Mg m
3
, calculate the density of glassy nickel.
Solution:
(a)
Let the spheres have a diameter of 1. Then the unit cell has an edge length
2 ,
and a volume
2 2 . It contains 4 atoms, with a total volume
4
6
π
. Hence
density,
ρ
, is given by
( )
( )
4
0.740
6
2 2
ρ
=
=
(b)
Glassy nickel is less dense than crystalline nickel by the factor 0.636 / 0.740 .
The density is therefore
( )( )
3
8.90
0.636 / 0.740
7.65
Mg m

=
2. (2pts)
(a)
Sketch threedimensional view of the unit cell of b.c.c. crystal, showing a (100)
plane, a (110) plane, a (111) plane and a (210) plane.
(b)
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 Spring '09
 Asst.Prof.A.FethiOkyar
 Chemistry, Mechanical Engineering, Atom, 5 pts, Avogadro constant, 1pt

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