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Phase transition of chemically doped uniaxial relaxor ferroelectric

We report a neutron scattering study of the ferroelectric phase transition in Sr$_{0.585}$Ce$_{0.025}$Ba$_{0.39}$Nb$_2$O$_6$ (SBN-61:Ce). We find no evidence for a soft transverse optic phonon. We do, however, observe anisotropic diffuse scattering. This scattering has inelastic and elastic contributions. In the paraelectric phase the susceptibility associated with the elastic diffuse scattering follows well the anomaly of the dielectric susceptibility of SBN-61:Ce. In the ferroelectric phase the lineshape of the elastic scattering is consistent with the form expected for the ferroelectric domain walls. In contrast to the macroscopic observations, the scattering properties of Ce-doped crystal do not exhibit important changes with respect to those of pure Sr$_{0.61}$Ba$_{0.39}$Nb$_2$O$_6$.