NAME: ___KEY____________
Part 2. Solve the following problems completely.
1. A face-centered tetragonal crystal is one in which atoms occupy each of the corners of
the tetragon, and the center of each face of the tetragon.
a. Sketch the unit cell for a face-centered tetragonal crystal with a = b , and c = 1.05a .
b. Derive the Atomic Packing Factor for the face-centered tetragonal crystal structure.
c. Compute the linear density for the [011] direction. (Define linear density as the fraction of
length of the line occupied by atoms.)
2. A certain metal is known to have a cubic unit cell with an edge length of 0.288 nm. If this
metal has a density of 7.20 g/cm3 and an atomic weight of 52.0 g/mol,
a) What is its coordination number? Why?
b) What is the atomic radius?
3. A substitutional solid solution contains 998 g copper, and 2 g nickel.
a) Find the composition in weight percent of each of the components.
b) How many atoms of nickel will be in a 100-g sample of the above alloy?
c) How many atoms of nickel will be in a 1 cm3 sample of the above alloy. (Hint: You may
assume constant volume for alloy as nickel is added to copper.)
The atomic weights are 63.55 g/mol for copper, and 58.69 g/mol for nickel.
4. The steady-state diffusion flux through a metal plate is 7.8 X 10-8 kg/m2-s at a temperature
of 1200°C (1473 K) and when the concentration gradient is –500 kg/m4. Calculate the
diffusion flux at 1000°C (1273 K) for the same gradient and assuming an activation energy
for diffusion of 145,000 J/mol.
5. a) Determine the Miller indices for the planes A and B shown in the following unit cell.
b) Determine the indices of vectors 1, 2, and 3 shown in the unit cell.
Planes A and B for Problem 6a.
Vectors 1, 2, and 3 for Problem 6b.