ME311
MATERIALS ENGINEERING
SPRING 2012
HOMEWORK #7
DUE DATE: April 5, before class
PROBLEM 1:
Estimate the number of spherical clusters in 1mm
3
of copper at its melting point that
contain a) 10 atoms and b) 60 atoms. The atomic volume of liquid copper is 1.6x10
29
m
3
,
γ
SL
is 0.177 J/m
2
, k =1.38x10
–23
J/K and T
m
is 1356 K.
Hint: Consider that at the melting temperature, the free energies per unit volume of the
liquid and the solid are the same.
PROBLEM 2:
Copper (FCC crystal structure) is normally alloyed with additional elements in order to
increase its strength. For an alloy with a composition of Cu (75 wt%) and Ag (25 wt%)
(check the CuAg phase diagram), when the first solid nucleates from the liquid,
spherical clusters of radius
r
form with interfaces having an interfacial energy of 250
mJ/m
2
. Assuming that the latent heat of melting, L
T
is 4.8x10
8
J/m
3
, determine the critical
radius for nucleation if the sample is cooled from the singlephase liquid region to a
temperature of 900 C.
PROBLEM 3:
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 Spring '08
 MEYERS
 Deformation, homogeneous nucleation rate, spherical clusters

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