We report measurements of the specific heat $C_p\mathrm{}\left(T\right)\mathrm{}$ and of the thermal conductivities ${\lambda }^p\mathrm{}\left(T\right)\mathrm{}$ along the periodic direction and ${\lambda }^q\mathrm{}\left(T\right)\mathrm{}$ along a direction in the quasiperiodic plane for decagonal Al-Ni-Co at low temperatures. The coefficient $\gamma =0.63\mathrm{}$ mJ ${\mathrm{mol}}^{\mathrm{-}1}$ ${\mathrm{K}}^{\mathrm{-}2}$ of the linear term to $C_p\mathrm{}\left(T\right)\mathrm{}$ indicates a low density of electronic states at $E_F.$ The magnitude of the cubic-in-$T$ term to the low-temperature specific heat is in fair agreement with the acoustic contribution to $C_p\mathrm{}\left(T\right)\mathrm{}$ calculated from the results of low-temperature measurements of the elastic stiffness constants $c_{\mathrm{ij}}.$ The phonon contribution to ${\lambda }^p\mathrm{}\left(T\right)\mathrm{}$ shows a distinct maximum at 25 K, typical for periodic crystals. The dominant feature in the phonon contribution to ${\lambda }^q\mathrm{}\left(T\right)\mathrm{}$ is an extended plateau between 30 and 70 K, in agreement with the concept of generalized Umklapp processes in quasicrystals. This distinct difference between the phonon contributions to ${\lambda }^p\mathrm{}\left(T\right)\mathrm{}$ and ${\lambda }^q\mathrm{}\left(T\right)\mathrm{}$ is similar to that previously observed for ${\mathrm{Al}}_{65}{\mathrm{Cu}}_{20}{\mathrm{Co}}_{15}.$ The optical conductivity ${\sigma }_1\left(\omega \right)$ is obtained from reflectivity data in the frequency range between 1 meV and 12 eV. At low frequencies the optical conductivity ${\sigma }_1\left(\omega \right)$ is characterized by an anisotropic Drude contribution. At high frequencies an additional absorption for the periodic and the quasiperiodic direction is observed centered at approximately 1 and 2 eV, respectively, which can be associated with electronic excitations across a pseudogap.

• Received 25 November 1997

DOI:https://doi.org/10.1103/PhysRevB.58.3046