Abstract
We have investigated the anisotropy of physical properties (the magnetic susceptibility, the electrical resistivity, the thermoelectric power, the Hall coefficient, and the thermal conductivity) of single-grain icosahedral $i$-Ag${}_{42}$In${}_{42}$Yb${}_{16}$ quasicrystal along the two-, three-, and fivefold symmetry directions of the crystallographic structure. The specific heat, being a scalar quantity, was determined as well. The symmetry analysis predicts that the tensorial physical properties reduce to scalars for the ideal icosahedral symmetry. The experiments have shown that the anisotropy of the electronic transport coefficients of $i$-Ag${}_{42}$In${}_{42}$Yb${}_{16}$ is either small enough to be considered within the range of the experimental uncertainty (the electrical resistivity and the thermal conductivity) or negligible (the Seebeck and the Hall coefficients). The anisotropy of the magnetization and magnetic susceptibility was also found small, originating from different Yb${}^{3+}$ magnetic fractions (of the order 10${}^{\ensuremath{-}3}$ of all Yb atoms) determined along the three symmetry directions. Our experimental results support the consideration that perfect icosahedral quasicrystals should be isotropic solids regarding their physical properties, unlike decagonal quasicrystals that are strongly anisotropic. Theoretical reproduction of the temperature-dependent electron transport coefficients of $i$-Ag${}_{42}$In${}_{42}$Yb${}_{16}$ by a spectral conductivity model was another aim of this paper.
Published Version
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