PZT (PbZrxTi1-xO3) is a crystalline ceramic material which has attractive piezoelectric properties and is used to make microactuators. It can be made by reacting lead oxide (PbO), zirconia (ZrO2), and titania (TiO2) in the proper ratios. Its unit cell can be represented with a lead ion in the cube center, titanium or zirconium ions at the cube corners, and oxygen ions centered on the cube edges.
(A) Use the Miller index notation to describe the positions of each of these ions in the unit cell.
(B) Confirm that the unit cell contains 1 Pb ion, a total of 1 Ti or Zr ions, and 3 O ions.
(C) Confirm that the unit cell has a net neutral charge.
(D) Would the introduction of Zr into PbTiO3 be considered a substititional addition or an interstitial addition? Briefly justify.