EMSE 201 — Introduction to Materials Science & Engineering
14 December 2010
Department of Materials Science and Engineering
1 of 10
Case Western Reserve University
Name:
S O L U T I O N
Final Exam — 180 minutes; 200 points; 8 questions; 10 pages; 20% of course grade
You may use a calculator, pencils or pens, eraser, and a straight edge. Handwritten notes on both sides of a
single 8.5
″×
11
″
sheet of paper are permitted.
Please turn in your note page with your test.
No other form of
stored information is permitted.
Write all answers on these pages; use the back if needed.
Partial credit
will be given for correct set-ups and reasoning. On numerical answers use the
correct number of significant
figures
and give appropriate
units.
Constants
:
Avogadro’s number,
N
A
= 6.023
×
10
23
mol
–1
Boltzmann’s constant,
k
B
= 1.381
×
10
–23
J K
–1
= 8.620
×
10
–5
eV K
-1
gas constant,
R
: 8.314 J mol
-1
K
–1
Charge on an electron, |
q
e
| = 1.602
×
10
-19
C
Faraday’s constant,
F
= 96,500 C mol
–1
1) The unit cell of a compound of molybdenum (Mo) and silicon (Si) has the following characteristics:
f201s04
Mo:
0, 0, 0
1
2
,
1
2
,
1
2
Si:
0, 0,
1
3
0, 0,
2
3
1
2
,
1
2
,
1
6
1
2
,
1
2
,
5
6
a
=
b
= 0.3202 nm
c
= 0.7851 nm
α
=
β
=
γ
= 90°
a)
(6 points)
In the space at right,
sketch
the
unit cell. Clearly
identify
the atoms.
b)
(4 points)
How many atoms
of each type
are in the unit cell?
(
2 pts
each)
Mo:
2
Si:
4
c)
(4 points)
What is the
Bravais lattice
of
this structure?
(
2 pts + 2 pts
)
body-centered tetragonal
d)
(2 points)
How many nearest-neighbor Si atoms
does each Mo atom have?
10
(Hint: the Si atoms at 0, 0,
1
3
and
1
2
,
1
2
,
1
6
are almost exactly equidistant from the Mo atom at
1
2
,
1
2
,
1
2
.)
e)
(2 points)
How many nearest-neighbor Mo atoms does each Si atom have?
5
Sketch
the arrangement of atoms on the specified planes in this structure.
Label
the atoms in your sketches.
f)
(5 points)
(100)
g)
(7 points)
(110)
continued on next page
Si
Mo
Si
Mo
Si
Mo