Anharmonic dynamics of defect pairs in soft-mode systems

Molecular-dynamics calculations have been performed for two-dimensional soft-mode systems with defects. An isolated defect, which is softer than the host crystal, produces a localized vibration below the phonon band whose frequency decreases with decreasing temperature T>$T_c$; finally, in the vicinity of $T_c$, there is a change from oscillator to relaxator behavior connected with the appearance of a central peak, whose height increases rapidly upon approaching $T_c$. For low defect concentrations c this effect leads to a linear c dependence of the central peak in the dynamical structure factor $S_{\mathrm{q}=0\mathrm{}}$(ω). In the case of defect pairs, the dynamical structure factors of the localized modes show a strong dependence on the defect distance. For finite defect concentrations this gives rise to a $c^2$ contribution to the central peak in $S_{\mathrm{q}=0\mathrm{}}$(ω) and a temperature-dependent distribution of relaxation times, which governs the central-peak shape. The connection to light scattering and dielectric measurements in systems with low defect concentrations is discussed.