In order to test for the true intrinsic properties of icosahedral $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ quasicrystals, we performed investigations of magnetism, electrical resistivity, thermoelectric power, and thermal conductivity on a single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$ quasicrystal grown by the Czochralski technique. This sample shows superior quasicrystallinity, an almost phason-free structure, and excellent thermal stability. Magnetic measurements revealed that the sample is best classified as a weak paramagnet. Electrical resistivity exhibits a negative temperature coefficient with ${\rho }_{4\mathrm{K}}=3950\mu \Omega \mathrm{cm}$ and $R={\rho }_{4\mathrm{K}}∕{\rho }_{300\mathrm{K}}=1.8$, whereas the thermopower exhibits a sign reversal at $T=278\mathrm{K}$. Simultaneous analysis of the resistivity and thermopower using spectral-conductivity model showed that the Fermi energy is located at the minimum of the pseudogap in the spectral conductivity $\sigma \left(\epsilon \right)$. Thermal conductivity is anomalously low for an alloy of metallic elements. Comparing the physical properties of the investigated single-crystalline ${\mathrm{Al}}_{64}{\mathrm{Cu}}_{23}{\mathrm{Fe}}_{13}$ quasicrystal to literature reports on polycrystalline $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ material, we conclude that there are no systematic differences between the high-quality single-crystalline and polycrystalline $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ quasicrystals, except for the hindering of long-range transport by grain boundaries in the polycrystalline material. The so far reported physical properties of $i\text{−}\mathrm{Al}\text{−}\mathrm{Cu}\text{−}\mathrm{Fe}$ appear to be intrinsic to this family of icosahedral quasicrystals, regardless of the form of the material.

The Al-Pd-Mn system of intermetallics contains complex metallic alloy (CMA) phases, whose crystal structures are based on giant unit cells comprising up to more than a thousand atoms per cell. We performed investigation of the magnetic, electrical, and thermal transport and thermoelectric properties of the ${\xi }^{\prime }$ phase and the related $\Psi$ phase on single-crystalline samples grown by the Bridgman technique. The samples are diamagnets with a tiny paramagnetic Curie-like magnetization and an estimated fraction of magnetic Mn atoms about 100 ppm. The electrical resistivity between 300 and 4 K exhibits a temperature variation of less than 2%. The origin of this temperature-compensated resistivity is analyzed in terms of the spectral conductivity model. The thermal conductivity of the samples is small and can be described by the sum of the electronic and lattice contributions, which are of comparable size at room temperature. The lattice contribution can be reproduced by the sum of the Debye term (long-wavelength phonons) and the term due to hopping of localized vibrations. The thermoelectric power is small and negative, compatible with a low concentration of electrons as the majority charge carriers. The studied physical properties of the giant-unit-cell CMA phases in the Al-Pd-Mn system are in many respects intermediate between those of metals or simple intermetallics and quasicrystals, suggesting that both the polytetrahedral local atomic order and the large-scale periodicity influence the physical properties of the material.