MSE 605, Crystallography & Crystal Chemistry
Name: _______________________________
Homework 8
Due 8 December 2015
The numbers following each question give the approximate percentage of marks allocated to that question.
1. Calculate the structure factor F for the following reflections of an ideal cubic perovskite (ABO
3
) in terms of f
A
, f
B
, f
O
. Your answers should have no imaginary parts. a) b) c) d)
Which is likely to be the weakest of the four?
The atomic positions are:
A
B
O
100
110
111
200
0 0 0
½ ½ ½
½ ½ 0
½ 0 ½
0 ½ ½
F
( hkl )
= n
1 f n e
2 π i ( hu n
+ kv n
+ lw n
)
5
5
5
5
3
Autumn 2015

MSE 605, Crystallography & Crystal Chemistry
2. For the electron diffraction pattern shown below: a. What are the indices of the reflection marked hkl ? b. What is the zone axis? c. What can you conclude about the structure based on the systematic absences and the different spot intensities ?
331
4
4
10
000 hkl 420
Autumn 2015

MSE 605, Crystallography & Crystal Chemistry
3. Explain the Curie Principle.
4. An object with point symmetry m 3 m (O h
) distorts under uniaxial stress along [001].
What is the point group of the distorted object? What is it when the stress is along
[111]?
5. Many space group notations are dependent upon the orientation of the axes which one chooses to describe a structure. In such cases there is a “standard” setting, but potentially many other “non-standard” ones as well. In the example of Pnma , if the axes were re-oriented such that abc cab , use what you know about symmetry operations and space-group notation to determine what the new notation would be, and explain your answer.
5
10
15
Autumn 2015

MSE 605, Crystallography & Crystal Chemistry
6. Carbon atoms in graphite are bonded within (001) via strong triangular (120°) sp 2 hybrid σ bonding. The remaining unbonded 2p electrons form delocalized π bonds, and the adjacent sheets are held together by weak Van der Waals forces. For this reason, both the electrical and thermal conductivities of graphite are higher in the
(001) than normal to it.
The thermal conductivity k ij
is a tensor that relates the heat flux h to the temperature gradient dT / dx according to: dT h i
= k ij dx j
The thermal conductivity tensor of graphite is:
355 0 0 k ij
= 0 355 0 Wm -1 K -1
0 0 89 a. If a gradient of 100 K/m is applied along the y direction, what is the resulting heat flow? b. If a gradient of 100 K/m is applied along the z direction, what is the resulting heat flow?
10
10
Autumn 2015

MSE 605, Crystallography & Crystal Chemistry
7. Compare and contrast the three space groups P3 (No. 143), R3 (no. 146), and P6
(no. 168) in terms of their lattices and crystal systems . For each of the three cases, determine the number of equivalent general positions ( x,y,z ) (equal to the order of the group multiplied by the appropriate factor for centring) and specify the axis system used. 9
Autumn 2015