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Department
Engineering
Course Code
ENG 2002
Professor
Xue Qing Xu

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ENG2000 Test on Atoms and Crystals
30 September 2003
1. [50]
a. What characteristics define a crystal and why are crystals useful in
engineering applications? [6]
b. Define the atomic packing factor (APF). Calculate the APF for the face-
centred cubic and the body-centred cubic crystal structures. [10]
c. For a cubic system, write down the indices of the individual members of
the <100> family of lattice directions and sketch them. [10]
d. For a cubic crystal structure, sketch the (1 1 1), (2 3 4) and (3 2 1) planes.
[12]
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. [12]
2. [50]
a. Draw labelled diagrams to illustrate the four basic types of point defects in
a crystal. [9]
b. Draw labelled diagrams to illustrate edge and screw dislocations in a
crystal. [9]
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). [12]
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. [10]
e. Why do you think that the energies in part (d) are so different for the two
materials? [5]
f. Speculate as to the importance of the Qv value for Si to chip manufacture.
[5]
Useful expressions:
1 eV = 1.6 x 10-19 J
k = 1.38 x 10-23 J/K = 8.62 x 10-5 eV/K
Nv=Ne
-QvkT
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Description
ENG2000 Test on Atoms and Crystals 30 September 2003 1. [50] a. What characteristics define a crystal and why are crystals useful in engineering applications? [6] b. Define the atomic packing factor (APF). Calculate the APF for the face- centred cubic and the body-centred cubic crystal structures. [10] c. For a cubic system, write down the indices of the individual members of the <100> family of lattice directions and sketch them. [10] d. For a cubic crystal structure, sketch the (1 1 1), (2 3 4) and (3 2 1) planes. [12] 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 atomsnm . [12] 2. [50] a. Draw labelled diagrams to illustrate
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