  PbZr_{1-x}Ti_xO_3 (PZT) and Pb(Mg_{1/3}Nb_{2/3})_{1-x}Ti_xO_3 (PMN-$x$PT) are
complex lead-oxide perovskites that display exceptional piezoelectric
properties for pseudorhombohedral compositions near a tetragonal phase
boundary. In PZT these compositions are ferroelectrics, but in PMN-xPT they are
relaxors because the dielectric permittivity is frequency dependent and
exhibits non-Arrhenius behavior. We show that the nanoscale structure unique to
PMN-xPT and other lead-oxide perovskite relaxors is absent in PZT and
correlates with a greater than 100% enhancement of the longitudinal
piezoelectric coefficient in PMN-xPT relative to that in PZT. By comparing
dielectric, structural, lattice dynamical, and piezoelectric measurements on
PZT and PMN-xPT, two nearly identical compounds that represent weak and strong
random electric field limits, we show that quenched (static) random fields
establish the relaxor phase and identify the order parameter.
