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 crystalstructure projected down [001]

The F atoms have how many Ca nearestneighbors (i.e., how many Ca atomstouch each F atom)? 4

Since a = 5.462 Å, what is the Ca-Fbond distance? (A simple geometrycalculation.) 1/4 x 1.732 x 5.462

= 2.365 Å

(9 mins)

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 crystalstructure projected down [001]

The F atoms have how many Ca nearestneighbors (i.e., how many Ca atomstouch each F atom)? 4

Since a = 5.462 Å, what is the Ca-Fbond distance? (A simple geometrycalculation.) 1/4 x 1.732 x 5.462

= 2.365 Å

(9 mins)

0.25,0.750.25,0.75

0.25,0.75 0.25,0.75

0.5

0.5

0.5

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)

4. For characteristic x-radiation, why is K > K? (1 min)

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)

4. For characteristic x-radiation, why is K > K? (1 min)

AB

C

AB

ccp - ABCABC hcp - ABAB

layer sequence is different

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 crystalstructure 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

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 crystalstructure 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

• 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.

a

c

a*

c*

*