This paper presents an inelastic neutron scattering study of the proper ferroelectric and elastic neutron scattering results on the satellite diffraction pattern which characterizes the modulated phase. The temperature dependences of the satellite intensities and modulation wavevector are in fair agreement with results from previous x-ray experiments. Close to the incommensurate-to-ferroelectric transition temperature , an unexpected intensity overshoot is observed, similar to that seen in birefringence and dilatation experiments. The relationship between the lattice dynamics and the observed phase transition sequence is examined. The dispersion of the ferroelectric soft optic phonon (-polarization) and of the acoustic phonons is followed along the and -directions. In the ferroelectric phase, the TO mode shows a considerable softening as the incommensurate phase is approached from below. In the paraelectric and incommensurate phases, the response from the TO (-polarization) and TA ( strain) branches has been investigated via a series of constant-q scans in the -direction (approximately the modulation wavevector direction). The combined inelastic line-shapes, as observed in a number of non-equivalent Brillouin zones, could all be analysed in terms of a coupled-mode damped harmonic oscillator model. In addition, a diverging, resolution-limited, central peak is observed close to . It is suggested that the TO-TA coupling lies at the origin of the incommensurate instability. A phenomenological free energy is developed, in the continuum approximation, in which the TO-TA interaction is included via a pseudo-Lifshitz term of the type .

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