List of questions (50 points total)
Intro to Materials (10 pts)
1) Fill the four missing groups of materials in the given Ashby plot below (10 pts)
Ceramic
Metal
Polymer s
FOAMS
Crystalline solids (20pts)
2) Show that the atomic packing factor for BCC is 0.68 (3pts)
3) Zinc has an HCP crystal structure, a c/a ratio of 1.856, and a density of 7.13 g/cm3. Compute
the atomic radius for Zn. (4pts)
4) Determine the indices for the directions shown in the following cubic unit cell: (3pts)
5) Considering X-ray diffraction (XRD) investigation of Iron(α) with BCC crystal structure and
atomic radius of 1.24 angstrom using X-ray wavelength of 0.1542 nm,
a. What is the FIRST possible plane (h k l) that allows for X-ray diffraction? (5pts)
b. What is the corresponding diffraction angle from that plane? (5pts)
Imperfections in solids (10pts)
6) What are the causes of the imperfections (defects) in solids and how do they manifest
themselves in both atomic and macroscopic scales? Can you suggest a way to mitigate the
undesirable effects from these imperfections? (4pts)
7) Calculate the number of vacancies per cubic meter in iron at 850°C. The energy for vacancy
formation is 1.08 eV/atom. Furthermore, the density and atomic weight for Fe are 7.65 g/cm3
and 55.85 g/mol, respectively. (6pts)
Ceramics (10 pts)
8) Why does ceramics tend to be more brittle than metals? (Please explain the mechanism in
detail) (5pts)
9) Order the following semiconductors from most covalent to most ionic (2pts)
ZnS, GaP, CuCl
10) On the basis of ionic radii, what crystal structure would you predict for ZnO? (radii are 0.074
nm for Zn2+ and 0.140 nm for O2−) (3pts)
Useful info and formulas
Periodic table and electronegativities
Bragg conditions
Interplanar spacing (D-spacing) formula for different lattice planes (h k l) is given by
Point defect concentration