Chapter 12, Problem 118IAE

In some barbecue grills the electric lighter consists of a small hammer-like device striking a small crystal, which generates voltage and causes a spark between wires that are attached to opposite surfaces of the crystal. The phenomenon of causing an electric potential through
mechanical stress is known as the piezoelectric effect. One type of crystal that exhibits the piezoelectric effect is lead zirconate titanate. In this perovskite crystal structure, a titanium(IV) ion sits in the middle of a tetragonal unit cell with dimensions of $\text{0}\text{.403 nm × 0}\text{.398 nm × 0}\text{.398 nm}$ . At each corner is a lead(II) ion, and at the center of each face is an oxygen anion. Some of the Ti(IV) are replaced by Zr(IV). This substitution, along with Pb(ll), results in the piezoelectic behavior .

1. How many oxygen ions are in the unit cell?

How many lead(II) ions are in the unit cell?

How many titanium(IV) ions are in the unit cell?

What is the density of the unit cell?