  We performed x-ray diffraction studies on a series of
(1-$x$)Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-$x$PbTiO$_3$ (PZN-$x$PT) single crystals
with different incident photon energies, and therefore different penetration
depths. Our results show that outer-layers of $\sim 10$ to 50 $\mu$m thick are
present in all samples. The structure of those outer-layers is different from
that of the inside of the crystals, by having much greater (rhombohedral)
distortions. With increasing $x$, rhombohedral-type lattice distortions
develop, both in the outer-layer and the inside.
