  Recent neutron scattering measurements performed on the relaxor ferroelectric
Pb[(Zn1/3Nb2/3)0.92Ti0.08]O3 (PZN-8%PT) in its cubic phase at 500 K, have
revealed an anomalous ridge of inelastic scattering centered ~0.2 A-1 from the
zone center (Gehring et al., Phys. Rev. Lett. 84, 5216 (2000)). This ridge of
scattering resembles a waterfall when plotted as a phonon dispersion diagram,
and extends vertically from the transverse acoustic (TA) branch near 4 meV to
the transverse optic (TO) branch near 9 meV. No zone center optic mode was
found. We report new results from an extensive neutron scattering study of pure
PZN that exhibits the same waterfall feature. We are able to model the dynamics
of the waterfall using a simple coupled-mode model that assumes a strongly
q-dependent optic mode linewidth Gamma1(q) that increases sharply near 0.2 A-1
as one approaches the zone center. This model was motivated by the results of
Burns and Dacol in 1983, who observed the formation of a randomly-oriented
local polarization in PZN at temperatures far above its ferroelectric phase
transition temperature. The dramatic increase in Gamma1 is believed to occur
when the wavelength of the optic mode becomes comparable to the size of the
small polarized micro-regions (PMR) associated with this randomly-oriented
local polarization, with the consequence that longer wavelength optic modes
cannot propagate and become overdamped. Below Tc=410 K, the intensity of the
waterfall diminishes. At lowest temperatures ~30 K the waterfall is absent, and
we observe the recovery of a zone center transverse optic mode near 10.5 meV.
