| In this thesis, we performed a detailed study of the thermal conductivity in a wide range of quasicrystals. Three systems were studied: AlPdMn, AlCuFe and AlPdRe, and the samples were in both single and polycrystalline form. A further variable was added by introducing a controlled level of defects.; At low temperatures (below 20K), the thermal conductivity is defect limited, being controlled by boundary scattering, two level systems, stacking faults and dislocations. At high temperatures (above 20K), we find the thermal conductivity is limited by intrinsic properties of the quasicrystalline structure and phonon-phonon scattering.; From fitting the thermal conductivity to a detailed model we are able to predict the maximum thermal conductivity of a perfect quasicrystal. |