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ME311
MATERIALS ENGINEERING
SPRING 2012
HOMEWORK #4
PROBLEM 1:
The measured density of a sample of Iron is 7.87 g/cm
3
. If the lattice parameter of this
sample is 0.2866 nm, calculate the percentage of vacancies in this sample.
Hint:
In the absence of vacancies, bcc iron has 2 atoms/unit cell. Consider that the
density is mass/volume.
SOLUTION:
The density of Iron can be calculated by
In order for this expression to be correct, one should determine the number of atoms/unit
cell, which can be calculated from the equation above. This gives a value of 1.998
atoms/unit cell.
Because there should be 2 atoms/unit cell in a perfect BCC iron crystal, the difference
must be due to the presence of vacancies. Thus the percentage of vacancies is given by
%vacancies= (21.998)/2 *100 =0.1 %
PROBLEM 2:
You are an engineer working in a nuclear plant. In order to select the appropriate material
for the reactor you perform a series of experiments to determine the equilibrium mole
fraction of vacancies as a function of the working temperature. The results from your
experiments are shown in the table below. Based on the data you have generated,
determine a) the entropy/mole of vacancies, b) the enthalpy of vacancy formation /mole
of vacancies and c) the equilibrium mole fraction of vacancies at 400 C.
27 C
227 C
427 C
627 C
X
v
3.13E13
6.99E8
1.37E5
2.57E4
Work with the following units (Temperature in degrees Kelvin, Energy in Joules and the
molar gas constant R in Joules/mol.K).
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View Full DocumentHint:
Using the expression that relates the equilibrium mole fraction of vacancies with
temperature, first remove the exponential terms to obtain an equation of a straight line.
Subsequently, use a graphical form to answer the above questions.
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 Spring '08
 MEYERS

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