1. The following question makes use of www.nanohub.org. Using the crystal viewer tool available at

https://nanohub.org/resources/crystalviewer/about

(a) Make a silicon crystal lattice and highlight plane (100). Crystal viewer allows displayed crystals images to be saved as png files. (b) Make a silicon crystal lattice viewed along the [111] direction. A crystal plane is perpendicular to the direction with the same indices, e.g. the (100) plane is perpendicular to the [100] direction. (c) Make a silicon crystal lattice viewed along the [110] direction.

2. Density of Si and GaAs. (a) Calculate the volume density of atoms, namely the number of atoms/cm3) for Si and GaAs crystals, knowing the crystal structure for Si is diamond and for GaAs is zinc-blende, and that the lattice constant are 5.43 for Si and 5.66 for GaAs. Hint: calculate the number of atoms per unit cell and divide by the unit cell volume. (b) Knowing the atomic masses for Si (28), Ga(69.7) and As(74.9) calculate the density (g/cm3) for Si and GaAs. The atomic mass unit is 1.6610-27 Kg.

3. Lattice constant of InSb. The InSb crystal structure is zinc-blende. The atomic radii of In and Sb are 1.44 and 1.36 respectively. (a) Assuming that the atoms are hard spheres and they are closely packed in the InSb lattice, find the lattice constant of InSb. (b) Calculate the volumes of the unit and primitive cells.

4. Find the maximum fractions of the unit cell volumes that can be filled by hard spheres in the simple cubic, body centered cubic and diamond lattices.