  High-pressure and variable temperature single crystal synchrotron X-ray
measurements combined with first-principles based molecular dynamics
simulations study diffuse scattering in the relaxor ferroelectric system PSN
(PbSc$_{1/2}$Nb$_{1/2}$O$_3$). Constant temperature experiments show pressure
induced transition to the relaxor phase at different temperatures characterized
by butterfly and rod shaped diffuse scattering around the $\{$h00$\}$ and
$\{$hh0$\}$ Bragg spots, respectively. The simulations reproduce the observed
diffuse scattering features as well as their pressure-temperature behavior, and
show that they arise from polarization correlations between chemically-ordered
regions, which in previous simulations were shown to behave as polar
nanoregions. Simulations also exhibit radial diffuse scattering (elongated
towards and away from {\bf Q}=(000)), that persists even in the paraelectric
phase, consistent with previous neutron experiments on
(PbMg$_{1/3}$Nb$_{2/3}$O$_3$) (PMN)
