EMSE 201 – Introduction to Materials Science & Engineering
Fall 2010
Case Western Reserve University
1 of 5
Case School of Engineering
Solution to Homework #1
Explain how answers were obtained. Give appropriate units for all numerical answers.
1)
(6 points)
C&R Problem 3.3; but instead of computing the density of molybdenum from the atomic radius,
compute the atomic radius of Mo from its density
. Then do the same for
a facecentered cubic metal
of your
choice, and for
one of the diamond cubic elements
(carbon diamond, silicon, or germanium).
Solution
Given information about a material’s composition and crystal structure, its density equals
the mass of atoms per unit cell divided by the volume of the unit cell (C&R eq. 3.5).
Given that molybdenum has the bodycentered cubic structure (so the number of atoms
per unit cell
N
C
= 2
, and the cell volume
V
C
=
a
3
where
a
is the lattice parameter), atomic mass
A
of 95.94 g mol
–1
, and a density of 10.22 g cm
–3
(from the inside front cover of C&R), eq. 3.5
becomes
(eq. 3.5)
The only unknown in this equation is the lattice parameter
a
. But the question asks for the
atomic radius of molybdenum, not the lattice parameter, so use the relationship between these
two parameters that applies for the bodycentered cubic structure:
(1 pt)
Substituting this into eq. 3.5 and solving for
r
gives
(1 pt)
in agreement with the value given in the problem.
To carry out this computation for a facecentered cubic metal, e.g. copper,
N
C
= 4 and
(1 pt)
Substituting this into eq. 3.5, using values for the density and atomic mass of copper from
the inside front cover of C&R, and solving for
r
gives
(1 pt)
in agreement with the value given in front inside cover of C&R.
Lastly, for an element like silicon with the diamond cubic structure,
N
C
= 8 and
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EMSE 201 – Introduction to Materials Science & Engineering
Fall 2010
Case Western Reserve University
2 of 5
Case School of Engineering
(1 pt)
Substituting this into eq. 3.5, using values for the density and atomic mass of silicon from
the inside front cover of C&R, and solving for
r
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 Spring '09
 Crystallography, Cubic crystal system, Crystal system, Atomic packing factor

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