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

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.

Bonding network and stability of clusters: the case study of Al13TM4pseudo-tenfold surfaces

“…The ratio S in =ðS in þ S out Þ is calculated to be 24.5%, 26.8%, 24.4% and 28.4% for TM = Fe, Co, Ru, Rh, respectively. These results are consistent with the conclusions of Dolinšek & Smontara (2011), based on anisotropic resistivity measurements, stating that the stacked-layer description in terms of 2D atomic planes should only be regarded as a convenient geometrical approach to describe structures of the Al 13 TM 4 quasicrystalline approximants, whereas their physical properties are those of true 3D solids. Cluster stability is evaluated through the bonding capacity of TM atoms located in the P-type planes (TM P-type ).…”

“…Whether or not clusters are preserved at the surface must be linked to the strength of their intrinsic bonds and, as such, is expected to strongly depend on the atomic and electronic structures of the considered compounds. While the dimensionality of the chemical bonding network in o-Al 13 Co 4 and Al 13 Fe 4 has been investigated on the basis of electrical transport measurements (Dolinšek & Smontara, 2011), no theoretical extensive and systematic comparison of the compounds in the Al 13 TM 4 (TM = Co, Fe, Ru, Rh) series has been carried out so far. Our work is based on a wide range of ab initio tools, based on DFT, in order to investigate the influence of the chemical composition on the pertinence of a bulk structure description based on clusters.…”

Enhanced thermoelectric properties of the n-type Magnéli phase WO2.90: reduced thermal conductivity through microstructure engineering

“…Large unit cells are attractive, as it is known that a large number of atoms in the unit cell lead to low lattice thermal conductivities k lat in oxides and intermetallic compounds because of the low velocity of optical phonon modes. [26][27][28][29][30][31] This relationship between a large atom number and low k lat can be qualitatively understood within the periodic boundary conditions of a monoatomic chain described elsewhere. 30,32 Most complex metal oxides are electrical insulators, such as Y 3 Al 5 O 12 , 33 La 2 Mo 2 O 9 , 34 and W 3 Nb 14 O 44 , 35 the latter being structurally related to the Magnéli-type oxides.…”

A tight-binding atomistic approach for point defects and surfaces applied to the o-Al13Co4 quasicrystalline approximant

“…The validity of the 2D versus 3D picture has been discussed in ref. 45. According to electrical resistivity measurements, the physical properties of the compound are those of a 3D solid.…”