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We report a neutron scattering study of a ferroelectric phase transition inSr$_{0.61}$Ba$_{0.39}$Nb$_2$O$_6$ (SBN-61). The ferroelectric polarization isalong the crystallographic $c$-axis but the transverse acoustic branchpropagating along the $<$1, 1, 0$>$ direction does not show any anomalyassociated with the this transition. We find no evidence for a soft transverseoptic phonon. We do, however, observe elastic diffuse scattering. The intensityof this scattering increases as the sample is cooled from a temperature wellabove the phase transition. The susceptibility associated with this diffusescattering follows well the anomaly of the dielectric permittivity of SBN-61.Below T$_\mathrm{c}$ the shape of this scattering is consistent with thescattering expected from ferroelectric domain walls. Our results suggest thatdespite apparent chemical disorder SBN-61 behaves as a classic order-disorderuniaxial ferroelectric with critical fluctuations in the range $<10^{-11}$ s.

Phase Transition of the Uniaxial Disordered Ferroelectric Sr$_{0.61}$Ba$_{0.39}$Nb$_2$O$_6$