1.
Construct the two point group diagrams for point group 32. (45 secs)
symmetry elements
equivalent points
2. CaF2 is Fm3m, a = 5.462 Å, Ca in 4 a,
F in 8c. Make a drawing of the crystal
structure projected down [001]
The F atoms have how many Ca nearest
neighbors (i.e., how many Ca atoms
touch each F atom)? 4
Since a = 5.462 Å, what is the Ca-F
bond distance? (A simple geometry
calculation.) 1/4 x 1.732 x 5.462
= 2.365 Å
(9 mins)
0.5
0.25,0.75
0.25,0.75
0.5
0.5
0.25,0.75
0.25,0.75
0.5
3. Metals with the ccp and hcp structures are both close packed.
How are they different? Explain; you must use drawings in your
discussion. (2 mins)
layer sequence is different
ccp - ABCABC
hcp - ABAB
C
B
A
B
A
4. For characteristic x-radiation, why is K > K? (1 min)
4. For characteristic x-radiation, why is K > K? (1 min)
electron transition for  is greater in energy; thus,  is smaller
1.
Construct the two point group diagrams for point group 6mm. (45 secs)
symmetry elements
equivalent points
2. PtO2 is Pnnm, a = 4.533, b = 4.488, c = 3.138 Å, Pt in 2a,
O in 4g, x = 0.652, y = 0.281. Make a drawing of the crystal
structure projected down [001]. See list of equipoints on next slide.
What is the coordination number for the Pt atoms (i.e., how many O
atoms touch each Pt atom)?
6
What is the shape of the Pt coordination polyhedron.
octahedron
2.
3. a. Are rutile and anatase polytypes?__no__
b. Are rutile and anatase polymorphs?__yes__
c. Discuss how (in what way) the crystal structures of
rutile and anatase are different.
TiO6 octahedron in rutile
is regular; in anatase, TiO6 octahedron is distorted
4. A monoclinic crystal has a = 6, b = 4, c = 10 Å,  = 110°. Draw the
k = 0 level of the reciprocal lattice. You will have to estimate
(guess) what the distances and angles are on your drawing.
Show (mark) the reciprocal lattice vectors and angle for the
reciprocal lattice unit cell.
c
c*
*
a
a*