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Decagonal Quasicrystals and Approximants: Two-Dimensional or Three-Dimensional Solids?

Authors

  • Janez Dolinšek ,

    Corresponding author
    1. J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia phone:+386 (0)1 4773 740 fax:+386 (0)1 4773 191
    2. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
    3. EN-FIST Centre of Excellence, Dunajska 156, SI-1000 Ljubljana, Slovenia
    • J. Stefan Institute, Jamova 39, SI-1000 Ljubljana, Slovenia phone:+386 (0)1 4773 740 fax:+386 (0)1 4773 191
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  • Ana Smontara

    1. Institute of Physics, Laboratory for the Study of Transport Phenomena, Bijenička 46, POB 304, HR-10001 Zagreb, Croatia
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Abstract

Crystallographic structures of decagonal quasicrystals (d-QCs) are traditionally described as a periodic stacking of atomic planes with quasiperiodic in-plane atomic order, so that d-QCs are considered to be two-dimensional (2D) quasicrystals, whereas they are periodic crystals in the third dimension. Similar stacked-layer structures are observed also in the periodic decagonal approximant phases. In this review paper, we consider the dimensionality of the chemical bonding network in the d-QCs and their approximants on the basis of electrical resistivity. By comparing the anisotropic resistivity along the stacking- and the in-plane directions of a series of decagonal approximants with different numbers of atomic layers within one periodicity unit (the two-layer Y-Al-Co-Ni, the four-layer o-Al13Co4, Al13Fe4 and Al13(Fe,Ni)4, and the six-layer Al4(Cr,Fe) and T-Al3(Mn,Fe)) and of a two-layer d-Al-Co-Ni decagonal quasicrystal, we show that universally, the stacking direction perpendicular to the atomic planes is always the most conducting one. Since the in-plane electrical resistivities are of the same order of magnitude as the resistivity along the stacking direction, this confirms the 3D character of the investigated solids. The stacked-layer description in terms of 2D atomic planes should therefore be regarded as a convenient geometrical approach to describe the complex structures of the d-QCs and their approximants, whereas their physical properties are those of true 3D solids.

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