Solid solutions of ${\mathrm{PbZr}}_{1-x}{\mathrm{Ti}}_x{\mathrm{O}}_3$ (PZT) with $x\le 0.06$ undergo a phase transition from the cubic paraelectric phase to a phase usually characterized as ferroelectric. In this case, a complex system of superstructure peaks appears in the vicinity of the positions $\vec{Q}=(h+\frac{1}{2}k+\frac{1}{2}l)$, indicating the formation of incommensurate modulation of the structure. The absence of extinctions indicates a connection between the superstructure and cation displacements. A clear understanding of the relevant critical dynamics is still absent. We analyze synchrotron radiation scattering data on a PZT2.4 single crystal, focusing on diffuse scattering around the $M$ point of the Brillouin zone. We describe the data using a model that explicitly accounts for the coupling between the transverse acoustic and antiferrodistortive (AFD) phonon branches, which become symmetry allowed along the $\mathrm{\Sigma }$ line. The inverse dynamical response is represented by a $2\times 2$ matrix, and the resulting hybridized modes are used to compute the energy-integrated diffuse intensity in the high-temperature limit. The temperature dependence is governed solely by the softening of the AFD mode, which follows a Curie-Weiss law. The model successfully reproduces the observed line shapes at several temperatures. The obtained dispersion curves reveal a mixed soft mode with a minimum at an incommensurate wave vector, whose position near the phase transition agrees qualitatively with the satellite peaks observed below $T_c$. The present analysis indicates that the satellites observed in the intermediate polar phase originate from an incommensurate phase transition, driven by a mixed soft mode. Based on the obtained results, we propose a description of the observed complete pattern of superstructure reflections as a result of a transition to an incommensurate phase characterized by a 24-ray star of the wave vector $\mathbf{q}=(1/2-\delta ,1/2-\delta ,\delta )$. In this case, the $M$-type reflections turn out to be second-order reflections. The proposed description resolves the contradictions between models that interpret the observed superstructure as arising from either oxygen octahedra rotations or antiparallel cation displacements. The proposed structure is in good agreement with selected area electron diffraction data.

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• Ferroelectric phase transition
• Structural phase transition
• Perovskites
• Single crystal materials
• X-ray diffuse scattering