We present the results of inelastic x-ray scattering for magnetite and analyze the energies and spectral widths of the phonon modes with different symmetries in a broad range of temperature 125<T<293 K. The phonon modes with X_4 and Delta_5 symmetrie
s broaden in a nonlinear way with decreasing temperature when the Verwey transition is approached. It is found that the maxima of phonon widths occur away from high-symmetry points which indicates the incommensurate character of critical fluctuations. Strong phonon anharmonicity induced by electron-phonon coupling is discovered within ab initio calculations which take into account local Coulomb interactions at Fe ions. It (i) explains observed anomalous phonon broadening, and (ii) demonstrates that the Verwey transition is a cooperative phenomenon which involves a wide spectrum of phonons coupled to charge fluctuations condensing in the low-symmetry phase.
A strong Kohn anomaly in ZrTe_3 is identified in the mostly transverse acoustic phonon branch along the modulation vector q_P with polarization along the a* direction. This soft mode freezes to zero frequency at the transition temperature T_P and the
temperature dependence of the frequency is strongly affected by fluctuation effects. Diffuse x-ray scattering of the incommensurate superstructure shows a power law scaling of the intensity and the correlation length that is compatible with an order parameter of dimension n = 2.
