Consider the CuAu crystal structure. It can be described as a simple cubic lattice with a basis of Cu (0, 0, 0), Cu (1 2, 1 2, 0), Au (1 2, 0, 1 2), and Au (0, 1 2, 1 2). (a) How many atoms of each type are there per unit cell? (b) Draw the unit cell for CuAu. Use a different symbol for each type of atom. Provide a legend indicating which symbol represents which type of atom. (c) Give an alternative lattice and basis representation for CuAu for which one atom of the basis is Au (0, 0, 0). (d) A related crystal structure is that of Cu3Au. This unit cell is similar to the face-centered cubic unit cell with Au at the corners of the unit cell and Cu at all of the face-centered positions. Describe this structure as a lattice and a basis. (e) The Cu3Au crystal structure is similar to the FCC crystal structure, but it does not have the face-centered cubic lattice. Explain briefly why this is the case.