We have calculated the phonon and periodon dispersion relations in IV–VI semi-conducting bulk PbTe and SnTe and their superlattice structure. The model used here is a one-dimensional lattice which includes harmonic interactions up to second neighbours as well as on-site nonlinear electron-ion interactions at the anion site. We calculate the phonon and periodon dispersion relations in bulk and PbTe-SnTe superlattice for the transverse optic and acoustic modes using the transfer matrix method. Our analysis has predicted correct nature of the folding of acoustic and confinement of optical phonons at various frequency intervals corresponding to pass and stop bands of the superlattices.

The dynamics of the nonlinear excitations in a two-dimensional (2D) φ⁴-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT_s (>T_c), not at critical temperatureT_c. This occurs due to the anisotropy of such 2D systems.

We present a complete theoretical analysis of the periodic and non-periodic travelling waves in a diatomic chain model, in the continuum limit by incorporating nonlinear sixth order polarization potential (φ⁶) at the anion site. We have formulated a nonlinear lattice dynamical theory in which various energy curves are obtained for different types and magnitudes of the core-shell force constants. For periodic solutions, we have obtained two types of commensurate wave amplitudes which propagate in the opposite direction with respect to each other. For nonperiodic solutions, we have obtained various travelling excitations such as kink, antikink, excitons etc. for different values of the mass ratio and velocity parameter. The dipole moment per unit charge for SrTiO₃ has been calculated and it is found that the nonlinear excitations in this model carry large amount of energy as compared to those obtained from harmonic and anharmonic optical phonons in the φ⁴-polarizable model.