DOI: 10.1002/ijch.201100132 Decagonal Quasicrystals and Approximants: Two- Dimensional or Three-Dimensional Solids? Janez Dolins ˇek * [a, b, c] and Ana Smontara [d] 1. Introduction The crystallographic structures of decagonal quasicrystals (d-QCs) and their periodic approximants are traditionally described as a periodic stacking of atomic planes with either quasiperiodic in-plane atomic order, in the case of d-QCs, or translationally periodic order, in the case of the approximants. [1] Consequently, d-QCs are considered to be two-dimensional (2D) quasicrystals, whereas they are periodic crystals in the third dimension. Examples of the stacked-layer d-QC structures are d-Al-Co-Ni and d-Al- Co-Cu with two atomic layers within the periodicity length of about 0.4 nm along the stacking (10-fold) direc- tion, d-Al-Co, d-Al-Ni and d-Al-Si-Cu-Co with four layers within the periodicity length of about 0.8 nm, d-Al- Mn, d-Al-Cr and d-Al-Mn-Pd with six layers within the periodicity length of about 1.2 nm, and d-Al-Pd and d-Al- Cu-Fe with eight layers within the periodicity length of 1.6 nm. Decagonal approximant phases are characterized by large unit cells but preserve the stacked-layer struc- ture, with the periodicity lengths along the stacking direc- tion almost identical to those of the d-QCs. The mono- clinic Al 13x (Co 1y Ni y ) 4 decagonal approximant, [2] known as the Y-phase of Al-Co-Ni (denoted as Y-Al-Co-Ni), comprises two atomic layers within one periodic unit. The Al 13 TM 4 (TM = transition metal) family with TM = Co, Fe, Ru, Rh, Os represents four-layer approximant phases, [3–7] whereas the orthorhombic Al 4 TM phases, de- scribed by Deng et al., [8] and the orthorhombic Taylor- phase [9, 10] T-Al 3 Mn represent six-layer approximant struc- tures. However, recent analysis of the chemical bonding in the orthorhombic o-Al 13 Co 4 four-layer approximant by means of the electron localizability indicator (ELI) [11, 12] has led to a highly unexpected result that has put the tra- ditional view of the Al 13 TM 4 crystallographic structures in terms of atomic layers in question. Numerous covalent- like Co-Al and Al-Al bonds were found within the atomic layers as well as between the layers, revealing the Abstract : Crystallographic structures of decagonal quasicrys- tals (d-QCs) are traditionally described as a periodic stack- ing 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 ob- served 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 approxim- ants 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 differ- ent numbers of atomic layers within one periodicity unit (the two-layer Y-Al-Co-Ni, the four-layer o-Al 13 Co 4 , Al 13 Fe 4 and Al 13 (Fe,Ni) 4 , and the six-layer Al 4 (Cr,Fe) and T-Al 3 - (Mn,Fe)) and of a two-layer d-Al-Co-Ni decagonal quasicrys- tal, we show that universally, the stacking direction perpen- dicular 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 di- rection, 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 geo- metrical approach to describe the complex structures of the d-QCs and their approximants, whereas their physical prop- erties are those of true 3D solids. Keywords: conducting materials · decagonal quasicrystals · electrical transport · intermetallic phases · quasicrystalline approximants [a] J. Dolins ˇek J. Stefan Institute Jamova 39, SI-1000 Ljubljana, Slovenia phone: + 386 (0)1 4773 740 fax: + 386 (0)1 4773 191 e-mail: jani.dolinsek@ijs.si [b] J. Dolins ˇek Faculty of Mathematics and Physics, University of Ljubljana Jadranska 19, SI-1000 Ljubljana, Slovenia [c] J. Dolins ˇek EN-FIST Centre of Excellence Dunajska 156, SI-1000 Ljubljana, Slovenia [d] A. Smontara Institute of Physics Laboratory for the Study of Transport Phenomena Bijenic ˇka 46, POB 304, HR-10001 Zagreb, Croatia Isr. J. Chem. 2011, 51, 1 – 11 # 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim &1& These are not the final page numbers! ÞÞ Review