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ENG2000 Test on Atoms and Crystals
30 September 2003
a. What characteristics define a crystal and why are crystals useful in
engineering applications? 
b. Define the atomic packing factor (APF). Calculate the APF for the face-
centred cubic and the body-centred cubic crystal structures. 
c. For a cubic system, write down the indices of the individual members of
the <100> family of lattice directions and sketch them. 
d. For a cubic crystal structure, sketch the (1 1 1), (2 3 4) and (3 2 1) planes.
e. Determine which planes of the face-centred cubic structure have the
highest density of atoms and calculate this value for copper (aCu =
0.361nm). Hint, the answer is in units of atoms/nm2. 
a. Draw labelled diagrams to illustrate the four basic types of point defects in
a crystal. 
b. Draw labelled diagrams to illustrate edge and screw dislocations in a
c. Define the Burgers vector and show them for the situations in (a) and (b)
above (you can indicate them on the diagrams you drew above). 
d. The energy to form a vacancy (Qv) in aluminium and silicon is 0.75eV and
3.6eV, respectively. Calculate the fractional concentration of vacancies
(i.e. ratio of vacancies to atoms) at 660°C for Al and Si. 
e. Why do you think that the energies in part (d) are so different for the two
f. Speculate as to the importance of the Qv value for Si to chip manufacture.
1 eV = 1.6 x 10-19 J
k = 1.38 x 10-23 J/K = 8.62 x 10-5 eV/K
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