1.  Consider a platinum crystal structure (FCC, R_Pt = .139 nm).

a.  Sketch the (100), (110), and (111) planes (including the atoms in the second layer if they can be observed below the first layer).

b.  What are the planar densities of these planes?

c.  What the directions with the highest linear densities within each plane?
 
2.  Consider platinum, tungsten (BCC, RW = 0.137 nm), and cobalt (HCP, RCo = 0.125 nm).  Calculate the (100) planar density for Pt and W and the (1000) planar density for Co.

3.  Consider platinum, silicon (diamond lattice with RSi = 0.118 nm), and gallium arsenide (zincblende lattice with ao = 0.5653 nm).

a.  Sketch the (100), (110) and (111) planes (including the atoms in the second layer if they can be observed below the first layer).

b.  What are the radii of the gallium and arsenic atoms/ions in this zincblende structure?

c.  What is the atomic packing factor of silicon and gallium arsenide?
 
1.  Calculate the percentage of atoms that would be surface atoms in a particle containing 125 atoms and 1000 atoms.  Assume simple cubic geometry.