Download Chemistry 754 Homework Set #5 Spring 2000 Due – Wednesday

Chemistry 754
Spring 2000
Homework Set #5
Due – Wednesday, May 17
1. Using Sanderson’s methods, estimate the partial ionic character of NaF,
NaCl, NaBr and NaI. From these values calculate the radii of the atoms
involved and the unit cell parameters (all adopt the rock salt structure).
Compare your answers with the observed lattice constants of these
compounds.
2. Use the ideas of Phillips and van Vechten to arrange the following
semiconductors in order of increasing E (the energy separation between
the center of the valence band and the center of the conduction band)
GaAs, InSb, MgS, AlP and NaCl. Of these compounds two adopt the rock
salt structure and three the sphalerite structure, which compounds
crystallize with the rock salt structure?
3. MoO2 crystallizes in a distorted form of the rutile structure. Analysis of
the crystal structure and transport properties reveals the presence of
both localized Mo-Mo bonding and metallic conductivity. Sketch the
energy levels of the d-orbitals and indicate the filling of these orbitals,
then use this orbital energy diagram to provide an explanation for this
curious behavior. (Hint: Consider the orbital overlap not only between
neighboring octahedra along the edge sharing chains, but also between
octahedra in neighboring chains.)
4. Consider the following compounds which adopt the perovskite structure,
BaZrO3, KNbO3, BaMoO3 and PbZrO3. Of these four compounds two
exhibit ferroelectric/antiferroelectric properties, characterized by
cation shifts out of the center of their coordination polyhedra. Identify
these two compounds and indicate which cation drives the distortion in
each case.
5. For each of the following compounds indicate whether you would expect
to see (1) localized metal-metal bonding, (2) metallic conductivity, (3)
semiconducting/insulating behavior or a combination of these behaviors.
Provide a brief justification of your choices. The structure type is given
in parentheses
(a)
(b)
(c)
(d)
(e)
(f)
SrRuO3 (Perovskite)
ReO3 (ReO3)
Ti2O3 (Corundum)
Fe2O3 (Corundum)
ZrN (Rock salt)
-MnO2 (Rutile)
6. MoS2 adopts a structure type closely related CdI2 except that the Mo
ions are in trigonal prismatic coordination, rather than octahedral
coordination. However, both structures contain sheets of edge sharing
polyhedra (octahedrons or trigonal prisms) held together by van der
Waals interactions between sulfur atoms. Electrical resistivity
measurements show that MoS2 is a semiconductor.
(a)
Based on ionic arguments do you expect octahedral or trigonal
prismatic coordination to be more stable? Why?
(b)
Draw an energy level diagram for the d-orbitals of a transition
metal ion in trigonal prismatic coordination (showing the splitting
of these orbitals in this coordination environment). Indicate the
filling of these orbitals in MoS2.
(c)
When Li is intercalated between the sulfide layers the compound
becomes metallic and transforms to the CdI2 structure. How do
you account for this behavior?
(d)
TaS2 adopts the MoS2 structure, but is metallic. Offer an
explanation for this behavior.
7. The following data describe the crystal structure and relevant bond
distances in the compound Bi2O4:
Space Group = C2/c
a = 12.367 Å
b = 5.118 Å
Z=4
c = 5.567 Å
Atom
Site
x
y
z
Bi(1)
Bi(2)
O(1)
O(2)
4c
4e
8f
8f
¼
0
0.179
0.093
¼
0.268
0.063
0.416
0
¼
0.652
0.973
 = 107.838
Bond distances
Bi(1)-O(1)  2  2.080(5), 2  2.100(6)
Bi(1)-O(2)  2  2.123(5)
Bi(2)-O(1)  2  2.823(6), 2  2.965(7)
Bi(2)-O(2)  2  2.145(7), 2  2.316(5)
The coordination environment about each bismuth site is shown below (the
black bonds represent Bi-O contacts shorter than 2.4 Å, while the white
bonds represent Bi-O interactions between 2.4 and 3.0 Å):
Bi(2)
(a)
(b)
Bi(1)
Describe the coordination environment of Bi(1) and Bi(2) in the
VSEPR sense (tetrahedral, T-shaped, bent, trigonal pyramidal, etc.)
This structure clearly violates Pauling’s fifth rule which states
that all atoms of the same type would prefer to have coordination
environments as similar as possible. Suggest a reason for this
contradiction to Pauling’s rules (Hint : Calculate the valence of each
bismuth site).