(a) Draw the face-centered cubic structure. Find the positions of the atoms, and the positions of the octahedral and tetrahedral voids within the structure. How many lattice sites, octahedral and tetrahedral voids are contained in a cell?
(b) Let a material have the fcc structure, and consist of spherical atoms that just touch one another. What is the radius of the largest sphere that will fit inside an octahedral void without distorting the structure? What is the radius of the largest sphere that will fit in a tetrahedral void without distortion? [Hint: the geometry of the tetrahedral void is much easier to treat if you first show that the center of the void lies at the center of a cube that is 1/8 the size of the fcc unit cell.]