Solid state physics (winter term 2016/2017)
Lecturer: Prof. Dr. Ullrich. Pietsch
Exercise tutor: Dr. Ali Abboud (ENC B-024)
Exercise sheet 2
1. Structure factor for fluorite
Calcium fluoride is an inorganic compound with the chemical formula CaF2
belonging to the space group Fm3m. Coordinate positions for fluorite atoms are
given below.
F
Ca
Ca
Ca
Ca
Ca
F
F
F
F
F
F
F
F
x
0
0.5
0.5
0
0.25
0.25
0.25
0.75
0.75
0.75
0.25
0.75
y
0
0.5
0
0.5
0.25
0.25
0.75
0.25
0.75
0.25
0.75
0.75
z
0
0
0.5
0.5
0.25
0.75
0.25
0.25
0.25
0.75
0.75
0.25
1- Determine the structure factor of fluorite.
2- Write a list of resulting structure factors for h, k and l ϵ {0, 1, 2} and discuss
the result in terms of allowed diffraction reflections, i.e. extinction rules.
2. Zincblende and Wurtzite structures
In the zincblende structure, a view along a [111] direction reveals that the atoms
of a given kind are stacked in the sequence …ABCABC…while maintaining
tetrahedral bonds with those of the other kind. The undelying Bravais lattice is
cubic. There is another arrangment that preserves the tetrahedral bond but stacks
the atoms of a given kind in the sequence …ABABAB… This is the wurtzite
structure, whose undelying Bravais lattice is hexagonal.
1- Give one example of each structure and plot it in 3D. Use different colors to
place different atoms on the lattice.
2- Cadmium Selenide can grow in a Zinc-blende (cubic) but also in a wurtzite
structure with 4 atoms in the unit cell placed at Cd: (0 0 0) (1/3 2/3 1/2)
and Se: (0 0 3/8) (1/3 2/3 7/8). Calculate the structure factor of both diatomic structures.
3. Ionic Crystals
CsCl consists of two simple cubic lattices of Cs and Cl ions displaced by (0.5 0.5
0.5).
Madelung constants can be derived by calculating a summation of coulombic
interactions, each term in the series indicates all the interactions for a specific ionion distance. Derive the first 10 terms (arising from the 10 shortest distances) for
determining the Madelung constant of CsCl.
4. Linear ionic crystal
Consider a long line of 2N ions of alternating charges ±q with a repulsive
potential energy 𝐶/𝑟 𝑛 acting only between nearest neighbors.
Calculate the equilibrium separation and the cohesive energy.
Please return on 07/11/2016