Decagonal Approximant Research Articles

One-step synthesis of non-equilibrium Pd-Ru alloys from Al-Pd-Ru quasicrystals and approximants

Non-equilibrium Pd–Ru alloys were synthesized by leaching quasicrystal (icosahedral quasicrystal, IQC: Al71Pd19Ru10) and approximants (3/2 approximant, P40: Al72Pd16.4Ru11.6, 1/1 approximant, C1: Al70.4Pd14.7Ru14.9) of Al–Pd–Ru alloys with 20 wt% NaOH aqueous solution. The Pd-Ru alloys were investigated using XRD and HAADF-STEM, which showed that Pd and Ru were mixed and formed a non-equilibrium state (atomic ratio: 0.9 < Pd/Ru < 2). The Pd–Ru alloy obtained by leaching of P40 phase was found to exhibit high catalytic performance toward CO oxidation than Pd and Ru catalysts obtained by leaching of Al3Pd (decagonal quasicrystal) and Al13Ru4 (decagonal approximant), respectively (i.e., the alloying effect). Consequently, Al-Pd-Ru quasicrystals and approximant alloys are found to be useful precursors to obtain the non-equilibrium Pd-Ru alloys.

Shear based gap control in 2D photonic quasicrystals of dielectric cylinders.

2D dielectric photonic quasicrystals can be designed to show isotropic band gaps. In this work we study a quasiperiodic lattice made of silicon dielectric cylinders (ɛ = 12) arranged as periodic unit cell based on a decagonal approximant of a quasiperiodic Penrose lattice. We analyze the bulk properties of the resulting lattice as well as the bright states excited in the gap, which correspond to localized resonances of the electromagnetic field in specific cylinder clusters of the lattice. Then we introduce a controlled shear deformation γ which breaks the decagonal symmetry and evaluate the width reduction of the gap together with the evolution of the resonances, for all shear values compatible with physical constraints (cylinder contact). The gap width reduction reaches 18.5% while different states change their frequency in several ways. Realistic analysis of the actual transmission of the electromagnetic radiation, often missing in the literature, has been performed for a finite "slice" of the proposed quasicrystals structure. Two calculation procedures based on MIT Photonic Bands (MPB) and Finite Integration Technique (FIT) are used for the bulk and the finite structures showing an excellent agreement between them.

Atomic-scale configurations of variant twin boundaries of a pseudo-decagonal quasicrystal approximant in Al60Cr20Fe10Si10 alloy

Twin boundaries (TBs) of decagonal quasicrystal approximants generally exhibit structural characteristics that are peculiar compared with traditional crystals with small lattice parameters. Herein, the TBs of the orthorhombic (3/2, 2/1)2 decagonal approximant in the quaternary Al60Cr20Fe10Si10 alloy were investigated, and four types of (101) TBs were found using atomic-resolution high-angle annular dark-field scanning transmission electron microscopy. The structural features of these TBs at the atomic level were revealed and the corresponding projected structural models along the pseudo-tenfold axis were proposed and discussed. These results demonstrate that the diversifications of the TBs of decagonal approximants are closely related to the rich combinations of substructural blocks, and this may trigger further interest in the planar defects present in other decagonal approximants.

Atomic-scale mapping of twins and relevant defective structures in Al20Cu2Mn3 decagonal approximant

Twins or multiple twins occur frequently in the orthorhombic Al20Cu2Mn3 approximant of decagonal quasi crystal (DQC). Due to the specific structural units, the twins in the Al20Cu2Mn3 approximant usually exhibit the glide-reflection characteristics. Using aberration-corrected transmission electron microscope at the atomic scale, we have observed not only glide-reflection twins but also simple mirror-reflection twins in the Al20Cu2Mn3 approximant. The two twinning modes are found to coexist in the present sample. These twins exhibit variant configurations at the twin boundaries where the tessellations of local subunits are imaged at an atomic scale. At the twin boundaries, diversified tiles such as star-like (S), bowtie-shaped and boat-shaped (B) are observed. The diversified tiles stacking with various manners allow the coexistence of the DQC and the approximant. Furthermore, the variants of B and S tiles are also found.

Multiple twins of a decagonal approximant embedded in S-Al2CuMg phase resulting in pitting initiation of a 2024Al alloy

The pitting of Al–Cu–Mg alloy is believed to originate from the local dissolution of S-Al2CuMg particles, and the dissolution activity differs from one particle to another. Nevertheless, the initial site where the dissolution of the S phase preferentially occurs and the cause of the heterogeneity in the electrochemical dissolution activity remain unknown, hindering our understanding of pitting initiation of Al–Cu–Mg alloys. In this work, we have applied in situ ex-environmental transmission electron microscopy and identified a large number of nanosized Al20Cu2Mn3 approximants of the decagonal quasicrystal embedded in the S phase. We find that the S phase with Al20Cu2Mn3 inclusions is more active than those free of the approximants. Such a preference is clarified to result from the decomposition of Al20Cu2Mn3 approximant prior to the dissolution of the S phase. In addition, we also find that the electrochemical behavior of Al20Cu2Mn3 approximants is different. The approximants with multiple twins are more active than those with few planar defects.

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

AbstractCrystallographic 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.

Ab initio investigations on the stability of seven-fold approximants

The stability of theoretical heptagonal approximants was investigated. No approximant phase has yet been confirmed consisting of all three heptagonal rhomb prototiles. To solve this problem, two new approximant structures were constructed from supertiles taken from the ThB4 and YCrB4 structure types. In order to compare structural stability, the total energy convex hulls were calculated for the ternary systems B–Cr–RE (RE = Dy, Er, Ho, Y), as well as B–Mn–Dy and B–Mn–Y, by means of ab initio calculations, using density functional theory. This included all known stable monary, binary and ternary phases. Additionally, several layered boride structure types, which are not stable in the respective ternary systems but show four-, five-, six- or seven-fold local environments, were included by chemical substitution. In all ternary systems, the theoretical approximants were found to be mechanically stable, but chemically unstable by an amount of energy larger than the margin of error. A tendency towards the stabilization of structures showing five- or 10-fold local environments was observed. This is consistent with the findings of decagonal approximants in the systems B–Ti–Ru and B–Mg–Ru.

M-Al-Mgroups trapped in cages ofAl13M4(M=Co, Fe, Ni, Ru)complex intermetallic phases as seen via NMR

The crystallographic structures of decagonal quasicrystals and their periodic approximants are traditionally described as a periodic stacking of atomic planes. By performing a $^{27}\text{A}\text{l}$ NMR spectroscopic study of the ${\text{Al}}_{13}{M}_{4}$ ($M=\text{transition}$ metal) family of four-layer decagonal approximants, including the orthorhombic ${\text{o-Al}}_{13}{\text{Co}}_{4}$, the monoclinic ${\text{Al}}_{13}{\text{Fe}}_{4}$, its ternary derivative ${\text{Al}}_{13}{(\text{Fe},\text{Ni})}_{4}$, and the monoclinic ${\text{Al}}_{13}{\text{Ru}}_{4}$, we show that all these phases contain structural detail of a nearly linear $M\text{-Al-}M$ atomic group trapped inside an elongated cage, resembling the three-dimensional (3D) ``cage-compound'' structure of the intermetallic clathrates. We determined the electric-field-gradient- (EFG) and the magnetic-shielding tensors at the Al site of the $M\text{-Al-}M$ groups. The asymmetry parameter of the EFG tensor was estimated theoretically by a point-charge model, taking into account the charges of both the $M\text{-Al-}M$ atoms and the surrounding cage atoms. The calculations support ionic bonding of the $M\text{-Al-}M$ group to the cage atoms and the existence of a 3D chemical bonding network in the ${\text{Al}}_{13}{M}_{4}$ phases. The above results show that the traditional description of the ${\text{Al}}_{13}{M}_{4}$ decagonal approximant phases in terms of two-dimensional (2D) atomic layers stacked along the pseudotenfold crystallographic direction is a convenient geometrical approach to describe their complex structures but is not appropriate for the description of their physical properties, which should be analyzed by taking into account the full 3D nature of the chemical bonding framework. This favors the 3D cage-compound structural description of the ${\text{Al}}_{13}{M}_{4}$ phases over the pseudo-2D stacked-layer description.

Hall effect in the Y-Al-Ni-Co and o-Al13Co4 decagonal approximants

The Hall effect in Y-Al-Ni-Co and o-Al13Co4 single crystals has been investigated for all combinations of the electrical current and magnetic field directions and in the temperature interval from 90 to 380 K. In these intermetallics the Hall coefficient RH exhibits well defined anisotropy and only weak temperature dependence. RH is negative electron-like or zero for the magnetic field perpendicular to the plane that corresponds to the quasiperiodic plane in decagonal quasicrystals, and is positive hole-like or zero for the magnetic field parallel to this plane. The results for the anisotropy of RH are well correlated to the anisotropy of RH in d-Al-Ni-Co and d-Al-Cu-Co quasicrystals. Therefore, the anisotropy in both crystalline and quasicrystaline samples originates from the specific stacked-layer structure and the chemical decoration of the lattice. The investigated anisotropic RH in Y-Al-Ni-Co was reproduced theoretically by calculation using Boltzmann transport theory, ab-initio calculated anisotropic Fermi surface, and isotropic relaxation time approximation.

Phonon-enhanced thermoelectric power of Y–Al–Ni–Co decagonal approximant

Abstract We have investigated anisotropic electrical resistivity and thermoelectric power of the ypsilon-phase Al–Ni–Co (Y–Al–Ni–Co) decagonal approximant with composition Al76Co22Ni2. The crystalline-direction-dependent measurements were performed along three orthogonal directions a*, b and c of the Y–Al–Ni–Co unit cell, where (a, c) monoclinic atomic planes are stacked along the perpendicular b direction. Anisotropic electrical resistivity is low in all crystalline directions, appearing in the order ρ a* &gt; ρ c &gt; ρ b and showing positive temperature coefficient typical of electron-phonon scattering mechanism. Thermopower shows electron-phonon enhancement effect. Anisotropic bare thermopower (in the absence of electron-phonon interactions) was extracted, appearing in the same order as the resistivity, ΙS a* bare/TΙ &gt; Ι S c bare/T Ι &gt; Ι S b bare/T Ι.

Anisotropic electrical and thermal conductivities of the Al76Co22Ni2 decagonal approximant

Abstract The electrical (σ) and thermal conductivity (λ) of Al76Co22Ni2 decagonal approximant has been measured along three orthogonal directions a *, b and cof the Al76Co22Ni2 unit cell, where (a, c) monoclinic atomic planes are stacked along the perpendicular b direction. Electrical conductivity is relatively high in all crystalline directions, appearing in the order σb &gt;&gt; σc &gt; σa* . Thermal conductivity appears in the same order λb &gt; λc &gt; λa*, so that b is the most conducting direction for both electricity and heat. The results are compared to the reported anisotropic electrical and thermal conductivity of the d-Al–Ni–Co decagonal quasicrystal.

Anisotropic magnetic, electrical, and thermal transport properties of the Y-Al-Ni-Co decagonal approximant

We have investigated anisotropic physical properties (magnetic susceptibility, electrical resistivity, thermoelectric power, Hall coefficient, and thermal conductivity) of Y-Al-Ni-Co decagonal approximant with composition ${\text{Al}}_{76}{\text{Co}}_{22}{\text{Ni}}_{2}$. The crystalline-direction-dependent measurements were performed along three orthogonal directions ${a}^{\ensuremath{\ast}}$, $b$, and $c$ of the Y-Al-Ni-Co unit cell, where $(a,c)$ monoclinic atomic planes are stacked along the perpendicular $b$ direction. Anisotropic magnetic susceptibility of conduction electrons is paramagnetic for the field lying within the $(a,c)$ atomic planes and diamagnetic for the field along the $b$ direction. Anisotropic electrical resistivity is low in all crystalline directions, appearing in the order ${\ensuremath{\rho}}_{{a}^{\ensuremath{\ast}}}g{\ensuremath{\rho}}_{c}⪢{\ensuremath{\rho}}_{b}$. Thermopower shows electron-phonon enhancement effect. Anisotropic bare thermopower (in the absence of electron-phonon interactions) was extracted, appearing in the same order as the resistivity, $|{S}_{{a}^{\ensuremath{\ast}}}^{\text{bare}}/T|g|{S}_{c}^{\text{bare}}/T|g|{S}_{b}^{\text{bare}}/T|$. Anisotropic thermal conductivity appears in the order ${\ensuremath{\kappa}}^{b}g{\ensuremath{\kappa}}^{c}g{\ensuremath{\kappa}}^{{a}^{\ensuremath{\ast}}}$, so that $b$ is the most conducting direction for both electricity and heat. Hall coefficient ${R}_{H}$ exhibits pronounced anisotropy, where the magnetic field in a given crystalline direction yields the same ${R}_{H}$ for the current along the other two crystalline directions in the perpendicular plane. These anisotropies are analyzed in terms of the anisotropic structure of the Y-Al-Ni-Co phase and the ab initio calculated anisotropic Fermi surface. The results are compared with the literature-reported anisotropy of the physical properties of the $d$-Al-Ni-Co decagonal quasicrystal.

New boron-based decagonal approximants

New boron-based decagonal approximants

Anisotropic electrical, magnetic and thermal transport properties of the Al80Cr15Fe5 decagonal approximant

The anisotropic magnetic, electrical and thermal transport properties were studied of a single-crystalline Al80Cr15Fe5 approximant to the decagonal quasicrystal. The temperature-dependent electrical resistivity along the b and c crystalline directions shows non-metallic behaviour with a broad maximum, whereas it exhibits a metallic positive temperature coefficient along the a direction perpendicular to the (b, c) atomic planes. The resistivity can be treated with the model of slow charge carriers, where the increased electron–phonon scattering upon raising the temperature induces a transition from dominant Boltzmann (metallic) to dominant non-Boltzmann (insulating-like) regime. The magnetic susceptibility and thermal conductivity also reveal a small anisotropy.

Origin of anisotropic nonmetallic transport in theAl80Cr15Fe5decagonal 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)].

Microstructure and Chemistry of Annealed Al–Cu–Fe–Cr Quasicrystalline Approximant Coatings

An as-deposited Al–Cu–Fe–Cr film was annealed in flowing argon to study development of a quasicrystalline approximant microstructure. Sputter profile x-ray photoemission spectroscopy analysis showed oxygen incorporation reached approximately 70 at.% at the surface of the film, declined monotonically, and stabilized at ∼10 at.% at a depth of 160 nm. Synchrotron grazing incidence x-ray scattering was used to probe the structure of the coating at various penetration depths by altering the angle of the incident x-ray beam. An amorphous structure was observed near the termination surface, which coexisted with a compressively strained crystalline aluminum. These phases were the dominant microstructure to a depth of 110 nm. Below 150 nm, the film was primarily O1 decagonal approximant. Cross-section transmission electron microscopy elucidated a columnar growth morphology with associated porosity in the interstices between the columns. The resulting development of the Al–Cu–Fe–Cr decagonal approximant coatings from the precursor is reported.

Physical vapor deposition route for production of Al–Cu–Fe–Cr and Al–Cu–Fe quasicrystalline and approximant coatings

A novel route for production of Al–Cu–Fe–Cr and Al–Cu–Fe quasicrystalline and approximant coatings by physical vapor deposition (PVD) methods is described. Powdered elemental stoichiometric mixtures were formed and vacuum pressed at 400 °C in a graphite die to produce ≈50% dense sputtering targets. X-ray diffraction analysis performed on the expended targets revealed elemental Al and Cu phases with significant quantities of intermetallic θ (Al 2Cu) and/or λ (Al 13Fe 4) phases also present. These targets were used to sputter thick (10 μm) precursor coatings onto alumina substrates. Predominantly O 1 approximant decagonal approximant coatings were produced by sputtering from the Al–Cu–Fe–Cr target and subsequent annealing in vacuum in flowing argon at 500 °C for 4 h. Icosohedral and rhombohedral approximant phases are produced by sputtering from the Al–Cu–Fe target and annealing in argon at 850 or 450 °C, respectively.

Study of decagonal approximant and γ-brass-type compounds in Al–Cr–Fe thin films

This paper reports the preparation conditions and structure characteristics of Al–Cr–Fe very thin films (10–30 nm) obtained by the flash evaporation technique. The films are either amorphous or crystallized, depending on the thickness of the sample and temperature of the substrate. Annealing of amorphous films leads to crystallization of intermetallic phases that are all linked with quasicrystals. In particular, we have identified by transmission electron microscopy the following structures: body-centered-cubic (bcc) γ-brass phase, monoclinic λ–Al13(Cr,Fe)4phase, and orthorhombic O1-phase, all of them already observed in this system, together with four new structures, i.e., a face-centered-cubic (fcc) γ-brass phase (superstructure of the bcc phase), monoclinic λ′-phase (related to the λ-phase) and two orthorhombic phases (1/1/; 1/1) and (1/0; 2/1) approximants of the decagonal phase). In this study, we point out the occurrence of twin defects of the λ–Al13(Cr,Fe)4phase. Films prepared directly in the crystalline state comprise the O1approximant. Electron energy loss spectroscopy measurements show that all films are not oxidized except for the presence of a native oxide layer that forms in ambient atmosphere with a thickness that cannot exceed 0.3 nm. Optical properties were investigated and show that films need to be large enough (&gt;30 nm) to reproduce the properties of bulk alloys. Finally, contact angle wetting measurements reveal that the presence of such films on a substrate, even at very low thickness, considerably decreases the wetting behavior by water.

Orthorhombic rational approximants for decagonal quasicrystals

An important exercise in the study of rational approximants is to derive their metric, especially in relation to the corresponding quasicrystal or the underlying clusters. Kuo’s model has been the widely accepted model to calculate the metric of the decagonal approximants. Using an alternate model, the metric of the approximants and other complex structures with the icosahedral cluster are explained elsewhere. In this work a comparison is made between the two models bringing out their equivalence. Further, using the concept of average lattices, a modified model is proposed.

Intermediate stages of a transformation between a quasicrystal and an approximant including nanodomain structures in the Al-Ni-Co system

Transition states between decagonal quasicrystal and periodic approximants are studied in the Al-Ni-Co system at a measured composition of Al71.3Ni11.3Co 17.4 by high-resolution transmission electron microscopy and electron diffraction. The nanodomain structures appearing after annealing at 1270 K show periodic fluctuations coherently embedded in domains with the coarse order of a one-dimensional quasicrystal. Further annealing at lower temperatures changes the features of nanodomain structures and results in an increase in more periodic structures. These can be strongly disordered and full of defects but tiling analysis and electron diffraction patterns show that they correspond to locked phason strain values of two closely related periodic approximants. We conclude that the periodic approximants do not result from a continuous increase in phason strain but from the growth of seeds with a locked phason strain.