Soft modes and thermal transport in guest-host crystalline structures

Abstract

We propose a simple phenomenological model describing vibrational dynamics in a class of materials (like clathrates), which are crystalline compounds with closed cavities in their structures. In the spirit of a minimalist approach, our model includes only the minimum of ingredients necessary to capture the generic features of this class of compounds as brought to light by experiments. We consider only two kinds of particles: strongly coupled host atoms, which form the structural cavities, and guest atoms confined in the cavities. In spite of the confinement, for relatively small amplitude vibrations of the guest atoms, their interaction with the host particles is assumed to be weaker than between the host atoms. We calculate self-consistently the vibrational mode (phonon) line broadenings for the empty and filled (by the guest atoms) cavities. We show that the soft phonon dispersion sheet, which appears for weakly bonded guest atoms, yields to large mode broadening via three waves anharmonic mode coupling. In turn the Umklapp part of this broadening reduces drastically the phonon thermoconductivity coefficient. We conclude that for a system with a soft mode component in the vibrational spectrum phonon broadening is always larger and thermal conductivity is always appreciably smaller than for a system without this soft mode (provided all other characteristics are the same). Although our model is minimal, in the sense of ignoring the complexity of actual guest-host structures, when properly interpreted, it can yield quite reasonable values for a variety of measurable quantities.