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Homework 3
1.
Ashby and Jones  I, Problem 6 (2nd edition)/Problem 4.1 (3rd edition)
2.
Ashby and Jones  I, Problem 7 (2nd edition)/Problem 4.2 (3rd edition)—followed by
the additional question: A material with this potential energy between atoms has a
simple cubic unit cell with atoms at each corner.
U(r
o
)
= 
kT
M
, where
r
o
is the
equilibrium separation of a pair of atoms,
k
is Boltzmann’s constant, and
T
M
is the
absolute melting temperature of the solid. Show that, when the material is stretched
parallel to one of the cube edges, Young’s modulus
E
is given by
Ω
=
m
mnkT
E
where
±
is the mean atomic volume.
3.
It is possible to measure the density of a material to a high degree of accuracy (4
significant figures). A sample of aluminum cooled rapidly from a temperature just
below the melting point has a density of 2.698 g/cm
3
. This is lower than the
theoretical density of Al, due to the presence of vacancies. Determine the fraction of
atomic sites occupied by vacancies if the lattice parameter of FCC aluminum is
0.4049 nm. The atomic weight of Al is 26.98 g/mol.
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 Spring '08
 Thouless

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