Chemistry 754 Homework Set #5 Spring 2000 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 DE (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.

  1. 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)  SrRuO3 (Perovskite)

(b)  ReO3 (ReO3)

(c)  Ti2O3 (Corundum)

(d)  Fe2O3 (Corundum)

(e)  ZrN (Rock salt)

(f)  b-MnO2 (Rutile)

  1. 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.

  1. 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 c = 5.567 Å b = 107.838°

Z = 4

Atom / Site / x / y / z
Bi(1) / 4c / ¼ / ¼ / 0
Bi(2) / 4e / 0 / 0.268 / ¼
O(1) / 8f / 0.179 / 0.063 / 0.652
O(2) / 8f / 0.093 / 0.416 / 0.973

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):

(a)  Describe the coordination environment of Bi(1) and Bi(2) in the VSEPR sense (tetrahedral, T-shaped, bent, trigonal pyramidal, etc.)

(b)  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).