A two dimensional toy model is developed to study thermal transport in cage like structures such a skutterudites and clathrates. The model consists of host atoms on a rectangular lattice with fillers in the center of each rectangle. The thermal conductivity is calculated by using Green-Kubo equilibrium molecular dynamics simulations. It is generally believed that the smaller and the heavier the filler, the lower is the thermal conductivity. We show that the thermal conductivity decreases with atomic displacement parameter while it has local minima versus filler mass. Our study shows that it is very important to include the correct band dispersion to get the right features of the thermal conductivity. We show that by having a double well potential one can further reduce the thermal conductivity.

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