3-D mapping of diffuse scattering in PZN-xPT

High energy (67 keV) x-ray diffuse scattering measurements were performed on single crystals of Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-$x$PbTiO$_3$ (PZN-$x$PT). A novel technique was developed to map out the diffuse scattering distribution in all three dimensions around a large number of Bragg peaks simultaneously, taking advantage of the almost flat Ewald sphere of the high energy x-ray beam. For $x=0, 4.5%$, and 8%, the results are very similar, indicating same type of correlations of polarizations in these compounds. Our results show that the diffuse scattering intensity consists of six $<110>$ rod-type intensities around reciprocal lattice points. These rod-type intensities are very likely due to condensations of soft optic phonon modes, polarized in the perpendicular $<1\bar{1}0>$ directions. A simple model is suggested where these soft phonon modes condense into static \{110\} type planar or ``pancake'' shaped correlations of the in-plane $<1\bar{1}0>$ polarizations.