Rutile is the name given to a crystal structure commonly adopted by compound s of the form AB2, where A rep resents a metal atom and B represents oxygen atoms. One form of r utile has atoms of element A at the unit cell coordinates (0, 0, 0) and (1/2, 1/2, 1/2) and atoms of element B at (1/4, 1/4, 0), (3/4, 3/4, 0), (3/ 4, 1/4, 1/2), and (1/4, 3/4, 1/2). The unit cell parameters are a = b ≠ c an d α = β = γ = 90˚. Note that the lattice parameter c is typically smaller than the lattice parameters a and b for the rutile structure.
(a) How many atoms of element A are there per unit cell?
(b) How many atoms of element B are there per unit cell?
(c) Is your answer to part (b) consistent with the stoichiometry of an AB 2 compound? Explain.
(d) Draw the unit cell for rutile. Use a different symbol for each type of atom. Provide a legend indicating w hich symbol represents which type of atom.
(e) For the simple tetragonal lattice, and a = b ≠ c and α = β = γ = 90 ˚. There is one lattice point per unit cell located at the corners of the simple tetragon al lattice. Describe the rutile structure as a simple tetragonal lattice and a basis.