Origin of anisotropic nonmetallic transport in the Al80 Cr15 Fe5 decagonal approximant

We present a study of the anisotropic transport properties (electrical resistivity, thermoelectric power, Hall coefficient, and thermal conductivity) of a single-crystalline ${\mathrm{Al}}_{80}{\mathrm{Cr}}_{15}{\mathrm{Fe}}_{5}$ complex metallic alloy that is an excellent approximant to the decagonal quasicrystal with six atomic layers in one periodic unit. Temperature-dependent electrical resistivity along the $b$ and $c$ crystalline directions shows a nonmetallic behavior with a broad maximum, whereas it shows a metallic positive temperature coefficient along the $a$ direction perpendicular to the $(b,c)$ atomic planes. Ab initio calculations of the electronic density of states reveal that the nonmetallic transport occurs in the presence of a high density of charge carriers. The very different temperature-dependent electrical resistivities along the three crystalline directions can all be treated within the same physical model of slow charge carriers due to weak dispersion of the electronic bands, where the increased electron-phonon scattering upon raising the temperature induces transition from dominant Boltzmann (metallic) to dominant non-Boltzmann (insulatinglike) regime. The temperature dependence of the resistivity is governed predominantly by the temperature dependence of the electronic diffusion constant $D$ and the transition has no resemblance to the Anderson-type metal-to-insulator transition based on the gradual electron localization. Structural considerations of the ${\mathrm{Al}}_{80}{\mathrm{Cr}}_{15}{\mathrm{Fe}}_{5}$ phase show that the anisotropy of the transport properties is a consequence of anisotropic atomic order on the scale of nearest-neighbor atoms, suggesting that the role of quasiperiodicity in the anisotropic transport of decagonal quasicrystals is marginal. We also present a relaxed version of the ${\mathrm{Al}}_{4}(\mathrm{Cr},\mathrm{Fe})$ structural model by Deng et al. [J. Phys.: Condens. Matter 16, 2283 (2004)].