  We use neutron scattering to characterize the acoustic phonons in the relaxor
PMN and demonstrate the presence of an anisotropic damping mechanism directly
related to short-range, polar correlations. For a large range of temperatures
above Tc ~ 210, K, where dynamic polar correlations exist, acoustic phonons
propagating along [1\bar{1}0] and polarized along [110] (TA2 phonons) are
overdamped and softened across most of the Brillouin zone. By contrast,
acoustic phonons propagating along [100] and polarized along [001] (TA1
phonons) are overdamped and softened for only a limited range of wavevectors.
The anisotropy and temperature dependence of the acoustic phonon energy
linewidth are directly correlated with the elastic diffuse scattering,
indicating that polar nanoregions are the cause of the anomalous behavior. The
damping and softening vanish for q -> 0, i.e. for long-wavelength acoustic
phonons, which supports the notion that the anomalous damping is a result of
the coupling between the relaxational component of the diffuse scattering and
the harmonic TA phonons. Therefore, these effects are not due to large changes
in the elastic constants with temperature because the elastic constants
correspond to the long-wavelength limit. We compare the elastic constants we
measure to those from Brillouin scattering and to values reported for pure PT.
We show that while the values of C44 are quite similar, those for C11 and C12
are significantly less in PMN and result in a softening of (C11-C12) over PT.
There is also an increased elastic anisotropy (2C44/(C11-C12)) versus that in
PT. These results suggest an instability to TA2 acoustic fluctuations in
relaxors. We discuss our results in the context of the debate over the
"waterfall" effect and show that they are inconsistent with TA-TO phonon
coupling or other models that invoke the presence of a second optic mode.
