Problem Set

1 Draw a plot of energy vs. interionic spacing for an ionic crystal showing the attractive and repulsive contributions, and the collective sum.
2 What is Madelung’s constant?
3 Why do ionic materials typically adopt packing structures?
4 How does cation/anion radius ratio influence crystal structure?
5 Sketch schematically a s and p bond between two p orbitals.
6 What are the orbital hybridizations for carbon in the diamond and graphitic phases?
7 Why are covalent bonds directional?
8 How is electrical conductivity in metals related to metallic bonding?
9 Draw clinographic (3-D) projections of the four basic lattice types indicating lattice points and the number of lattice points per unit cell.
10 What are the relationships between a, b, and c and a ,b, and g for cubic, orthorhombic, and monoclinic crystal systems?
11 What are the characteristic symmetry elements for rhombohedral, cubic, and tetragonal crystals?
12 By inspection, demonstrate if a side-centered lattice with side centers on (010) faces is consistent with tetragonal symmetry.
13 What is the difference between a lattice point and the basis (or motif) of a structure?
14 Sketch the (222) plane in a cubic unit cell (note 2 means -2, or “two-bar”)
15 Sketch the (1210) plane in a hexagonal unit cell
16 What are the three common structures of metals? Give the metal coordination, the number of atoms per unit cell, the ideal space filling, and the miller indices of the close packed planes in each.
17 Draw a schematic showing two layers of close packed planes indicating an octahedral and a tetrahedral interstitial position. Why are these interstitials named in this fashion?
18 Draw the unit cell projection of diamond cubic indicating all atomic positions. What is the lattice type, and what is the basis.
19 Draw the unit cell projection of rocksalt along the [001] and [110] directions.
20 Draw a schematic of the fluorite structure in projection that illustrates corner sharing of CaF8 cubes.
21 Describe in words the structure of zincblende, using a packing perspective.
22 Graphite and boron nitride are hexagonal layered structures featuring CC3 and BN3 planar triangular coordinated molecular building blocks. How and why is the stacking of the hexagonal layers different between these otherwise similar solids. Furthermore, indicate how and why the electrical properties are different.
23 Draw a unit cell projection of wurtzite along the [110]. Using this projection, explain the origin of the permanent unit cell dipole.
24 How can cation/anion radius ratios be used to understand the structure of ionic crystals?
25 What is the Goldschmidt tolerance factor formula and what information does it convey?
26 Describe the structure of inverse and normal spinels in terms of interstitial filling. What is the occupancy factor for spinels?
27 What are the coordination values for the A-site and B-site cations in perovskite?

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