Show that the radius of the largest sphere that can be placed in a tetrahedral interstitial site in an fcc lattice is 0.225r1, where r1 is the radius of the atoms making up the lattice. (Hint: Consider a cube with the centers of fourspheres placed at alternate corners, and visualize the tetrahedral site at the center of the cube. What is the relationship between r1 and the length of a diagonal of a face? The length of a body diagonal?)

3.8 An alloy of copper and gold has the structure shown in Fig. 3.75. Calculate the composition of this unit cell. What is the lattice type this structure? Given that 24 carat gold is pure gold, what carat gold does this alloy represent? of Au Cu Fig 3.75 The structure of Cu,Au.

On the basis of these models, explain why diamond is a very hard substance and graphite (e.g. pencil ‘lead’) is very soft.

GaAs is a compound semiconductor commonly used for LEDs. Talk about the chemical bonds and crystal structures of GaAs crystals and explain why they become semiconductors, not metal alloys (consider the electronic structure of each atom and sp3 hybrid orbit).