Low-Temperature Thermodynamic and Thermal-Transport Properties of Decagonal A${\mathrm{l}}_{65}$C${\mathrm{u}}_{20}$C${\mathrm{o}}_{15}$

We report measurements of the specific heat $C_p\left(T\right)$ and of the thermal conductivities ${\lambda }^p\left(T\right)$ along the periodic direction and ${\lambda }^q\left(T\right)$ along a direction in the quasiperiodic plane for decagonal ${\mathrm{Al}}_{65}{\mathrm{Cu}}_{20}{\mathrm{Co}}_{15}$ at low temperatures. The phonon contribution to ${\lambda }^p\left(T\right)$ shows a maximum at 25 K, typical for periodic crystals. The dominant feature in the phonon contribution to ${\lambda }^q\left(T\right)$ is an extended plateau between 30 and 70 K, in agreement with the concept of generalized umklapp processes in quasicrystals. The coefficient $\gamma =0.512\mathrm{}\mathrm{mJ}\mathrm{g}{\mathrm{atom}}^{-1\mathrm{}}{\mathrm{K}}^{-2\mathrm{}}$ of the linear term to $C_p\left(T\right)$ indicates a low density of electronic states at $E_F$.