A nonlinear lattice dynamical theory is proposed to explain the mode softening in intermediate valence compound Sm_0.75 Y_0.25 S. In this theory we consider the breathing motion of the electron shells of Sm-ion to be nonlinear, and depend on temperature, resulting in strong electron-ion coupling. We calculate the salient features of the nonlinear breathing potential, which resembles theφ⁴ potential for second order ferro-electric transitions. We also calculate the temperature dependence of LO(L) frequency for this compound, showing that at transition temperature (about 200 K) this mode freezes.

The softening of the IR active 300 cm⁻¹ phonon mode in Tl-2223 superconductor, aroundT_c has been explained by considering a sixth order polarization potential at the off-center oxygen ion site in the Tl-O plane, and by using a nonlinear lattice dynamical theory. The present theory explains, more or less satisfactorily, the unusual temperature dependence of oxygen ion vibration and frequency shifts at higher temperature. The existence of strong nonlinear electron-phonon interaction atT_c has been emphasized.