Decagonal Quasicrystals Research Articles

Alumina nanowire growth by water decomposition and the peritectic reaction of decagonal Al65Cu15Co20 quasicrystals

In this paper, the results of the Al2O3 nanowires' growth through a chemical reaction between Al and water vapor at 1050°C are presented. Our approach is based on two primary considerations. First, at room temperature, the Al65Cu15Co20 alloy is affected by the following mechanism: 2Al (s)+3H2O (g)→Al2O3 (s)+H2 (g). In this reaction, the released hydrogen induces cleavage fracture of the material to form small particles. Second, the Al65Cu15Co20 quasicrystalline phase is transformed on heating to liquid+Al (Cu, Co) cubic phase through a peritectic reaction at 1050°C. The Al-rich liquid then reacts with water vapor, forming Al2O3 nanowires. X-ray diffraction (XRD) analysis shows that the formed nanowires have a hexagonal structure, and infrared analysis further confirms the presence of α-Al2O3 phase in the final products. Transmission electron microscopy observations show that nanoparticles are present at the end of nanowires, suggesting the VLS growth mechanism. Elemental analysis by energy dispersive spectroscopy (EDS) indicates that the particles at the tip of the nanowires are mainly formed by Co and Cu alloying elements and small amounts of Al. Electron microscopy observations showed nanowires with diameters ranging from 20 to 70nm; the average diameter was 37nm and the nanowire lengths were up to several micrometers.

A Partial Isothermal Section at 1000 °C of Al-Mn-Fe Phase Diagram in Vicinity of Taylor Phase and Decagonal Quasicrystal

Altogether 19 alloys of an Al-Mn-Fe system with compositions near to the Taylor phase and/or the decagonal quasicrystal were characterised by the x-ray diffraction and the energy-dispersive x-ray spectroscopy coupled with the scanning electron microscopy, after annealing at 1000 °C for 330 h. The obtained experimental results were used to propose a partial isothermal section at 1000 °C of the Al-Mn-Fe phase diagram. The ternary T-phase area of an untypical saddle shape was found to touch the Al-Mn binary one. The γ2-phase was found to be stable between 2 and 30 at.% of Fe at 1000 °C and boundaries between γ1- and γ2-areas are expected to be located very close to the Al-Mn binary.

Stability of two-dimensional soft quasicrystals in systems with two length scales.

The relative stability of two-dimensional soft quasicrystals in systems with two length scales is examined using a recently developed projection method, which provides a unified numerical framework to compute the free energy of periodic crystal and quasicrystals. Accurate free energies of numerous ordered phases, including dodecagonal, decagonal, and octagonal quasicrystals, are obtained for a simple model, i.e., the Lifshitz-Petrich free-energy functional, of soft quasicrystals with two length scales. The availability of the free energy allows us to construct phase diagrams of the system, demonstrating that, for the Lifshitz-Petrich model, the dodecagonal and decagonal quasicrystals can become stable phases, whereas the octagonal quasicrystal stays as a metastable phase.

Cluster-Based Solidification and Growth Algorithm for Decagonal Quasicrystals.

A novel approach is used for the simulation of decagonal quasicrystal (DQC) solidification and growth. It is based on the observation that in well-ordered DQCs the atoms are largely arranged along quasiperiodically spaced planes parallel to the tenfold axis, running throughout the whole structure in five different directions. The structures themselves can be described as quasiperiodic arrangements of decagonal columnar clusters (cluster covering) that partially overlap in a systematic way. Based on these findings, we define a cluster interaction model within the mean field approximation, with effectively asymmetric interactions ranging beyond the nearest neighbors. In our MonteCarlo simulations, this leads to a long-range ordered quasiperiodic ground state. Indications of two finite-temperature unlocking phase transitions are observed, and are related to the two fundamental length scales that are characteristic for the system.

Experimental Observation of Quasicrystal Growth.

The growth of an Al-Ni-Co decagonal quasicrystal was observed by in situ, high-temperature, high-resolution transmission electron microscopy. The tiling patterns extracted from a series of high-resolution transmission electron microscopy images were analyzed on the basis of the high-dimensional description of quasicrystalline structures. The analyses indicated that the growth proceeded with frequent error-and-repair processes. The final, grown structure showed nearly perfect quasicrystalline order. Our observations suggest that the repair process by phason relaxation, rather than local growth rule, plays an essential role in the construction of ideal quasicrystalline order in real materials.

Approximants of Al–Cr–Fe–Si decagonal quasicrystals described by single structural block

The orthorhombic (3/2, 2/1) approximant with a = 3.06 nm, b = 1.23 nm, c = 2.24 nm, and the coexisting (2/1, 3/2) approximant of decagonal quasicrystals with a = 1.90 nm, c = 3.64 nm, and β ≅ 90° are found in Al–Cr–Fe–Si alloys by aberration-corrected transmission electron microscope. The structural relationships of these two approximants are analyzed and discussed based on the high-angle annular dark-field scanning transmission electron microscopy images at atomic resolution. We find that both of their structural tiling along the [010] direction can be described by one shield-like tile, with the superiority over the previous HBS tiling model due to the clarity. Combining the shield-like tile and HBS tiling model, the domains of approximants are clearly demonstrated.

The study of Al3(Mn, Pd) crystal and Al–Mn–Pd decagonal quasicrystal by spherical aberration-corrected scanning transmission microscopy and atomic-resolution energy dispersive X-ray spectroscopy

An Al3Mn-type Al3(Mn, Pd) crystal and an Al–Mn–Pd decagonal quasicrystal (DQC) in an Al70Mn20Pd10 alloy are studied using a spherical aberration (Cs)-corrected scanning transmission electron microscope (STEM) with high-angle annular dark-field (HAADF) and annular bright-field (ABF) techniques, together with atomic-resolution energy dispersive X-ray spectroscopy (EDS). Mn and Pd atomic positions in the Al3(Mn, Pd) structure projected along the b-axis (pseudo-tenfold rotational axis) are represented by separate bright dots in observed HAADF-STEM images. Besides, Al as well as Mn and Pd atomic positions are represented as dark dots in ABF-STEM images. Most Mn and Pd atomic positions in the Al3(Mn, Pd) structure can be observed on atomic-resolution EDS maps. On the basis of the good correlation between the STEM images and the EDS maps, and also considering the structure of the Al3(Mn, Pd) crystal, which was determined by X-ray diffraction using a single crystal, observed HAADF and ABF-STEM images of the Al–Mn–Pd DQC have been interpreted. Pd and Mn atomic positions in the Al–Mn–Pd DQC can be detected on the observed EDS maps. It can be seen that Pd is enriched around the centre of the columnar clusters, having a decagonal section with 2 nm in diameter. It can therefore be concluded that Pd plays an important role in the stabilization of the decagonal clusters, which form the Al–Mn–Pd DQC structure.

Chemical ordering of Co and Ni in a W-(AlCoNi) crystalline approximant related to Al–Co–Ni decagonal quasicrystals studied by atomic resolution energy-dispersive X-ray spectroscopy

A W-(AlCoNi) crystalline approximant, which is closely related to Al–Co–Ni decagonal quasicrystals, in an Al72.5Co20Ni7.5 alloy has been studied by atomic resolution energy-dispersive X-ray spectroscopy (EDS), in an instrument attached to a spherical aberration (Cs)-corrected scanning transmission electron microscope. On high-resolution EDS maps of Co and Ni elements, obtained by integrating many sets of EDS data taken from undamaged areas, chemical ordering of Co and Ni is clearly detected. In the structure of the W-(AlCoNi) phase, consisting of arrangements of transition-metal (TM) atoms located at vertices of pentagonal tilings and pentagonal arrangements of mixed sites (MSs) of TM and Al atoms, Co atoms occupy the TM atom positions with the pentagonal tiling and Ni is enriched in part of the pentagonal arrangements of MSs.

Atomic structure solution of the complex quasicrystal approximant Al77Rh15Ru8 from electron diffraction data.

The crystal structure of the novel Al77Rh15Ru8 phase (which is an approximant of decagonal quasicrystals) was determined using modern direct methods (MDM) applied to automated electron diffraction tomography (ADT) data. The Al77Rh15Ru8 E-phase is orthorhombic [Pbma, a = 23.40 (5), b = 16.20 (4) and c = 20.00 (5) Å] and has one of the most complicated intermetallic structures solved solely by electron diffraction methods. Its structural model consists of 78 unique atomic positions in the unit cell (19 Rh/Ru and 59 Al). Precession electron diffraction (PED) patterns and high-resolution electron microscopy (HRTEM) images were used for the validation of the proposed atomic model. The structure of the E-phase is described using hierarchical packing of polyhedra and a single type of tiling in the form of a parallelogram. Based on this description, the structure of the E-phase is compared with that of the ε6-phase formed in Al-Rh-Ru at close compositions.

Modeling quasi-lattice with octagonal symmetry

We prove the possibility to use the method of modeling of a quasi-lattice with octagonal symmetry similar to that proposed earlier for the decagonal quasicrystal. The method is based on the multiplication of the groups of basis sites according to specified rules. This model is shown to be equivalent to the method of the periodic lattice projection, but is simpler because it considers merely two-dimensional site groups. The application of the proposed modeling procedure to the reciprocal lattice of octagonal quasicrystals shows a fairly good matching with the electron diffraction pattern. Similarly to the decagonal quasicrystals, the possibility of three-index labeling of the diffraction reflections is exhibited in this case. Moreover, the ascertained ratio of indices provides information on the intensity of diffraction reflections.

Structure of a crystalline approximant related to Al–Co–Ni decagonal quasicrystals studied by spherical aberration (Cs)-corrected scanning transmission electron microscopy and atomic-resolution energy dispersive X-ray spectroscopy

Six types of decagonal quasicrystals (DQCs) found in Al–Co–Ni alloys with a wide compositional ratio of Co/Ni are considered to be stabilized by chemical ordering of Co and Ni, but the elucidation of this ordering has never been performed on alloys containing neighbouring elements Co and Ni. In order to examine the chemical ordering, an Al–Co–Ni crystalline phase, the PD3c phase, which is an important approximant for understanding the structures of ordered Al–Co–Ni DQCs, in an Al71.5Co16Ni12.5 alloy has been studied by spherical aberration (Cs)-corrected scanning transmission electron microscopy (STEM) and atomic-resolution energy dispersive X-ray spectroscopy (EDXS). From the combination of observed high-angle annular dark-field and annular bright-field STEM observations, an atomic arrangement of the crystalline approximant can be directly derived. The chemical ordering of Co and Ni in the arrangement of transition-metal (TM) atoms and mixed sites (MSs) of TM and Al atoms can be clearly detected on atomic-resolution EDXS maps obtained with the special technique. Co atoms are located at the TM atom positions arranged in pentagonal tiling with a bond length of 0.76 nm, whereas Ni is enriched in the MSs located in pentagonal tiles of Co atoms. It can be concluded that the change of an area ratio of Co-rich clusters to Ni-rich MSs produces various types of DQCs with different compositional Ni/Co ratios.

Controlled self-assembly of periodic and aperiodic cluster crystals.

Soft particles are known to overlap and form stable clusters that self-assemble into periodic crystalline phases with density-independent lattice constants. We use molecular dynamics simulations in two dimensions to demonstrate that, through a judicious design of an isotropic pair potential, one can control the ordering of the clusters and generate a variety of phases, including decagonal and dodecagonal quasicrystals. Our results confirm analytical predictions based on a mean-field approximation, providing insight into the stabilization of quasicrystals in soft macromolecular systems, and suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles.

Elastic fields around a nanosized elliptic hole in decagonal quasicrystals

Based on the variational principle, a continuum theory of surface elasticity and new boundary conditions for quasicrystals is proposed. The effect of the residual surface stress on a decagonal quasicrystal that is weakened by a nanoscale elliptical hole is considered. The explicit expressions for the hoop stress along the edge of the hole are obtained using the Stroh formalism. The results show that the residual surface stress and the shape of the hole have a significant effect on the elastic state around the hole.

Chemical ordering in Al-Co-Ni approximants studied by Cs-corrected STEM with EDS

Six-types of decagonal quasicrystals (DQCs) and some crystalline approximants have been found in Al-Co-Ni alloys with a wide compositional range from 8 to 25.5 at.% Co and from 20 to 5 at.% Ni with a nearly constant Al content of around 70 at.%, and so the stability of the six DQCs is considered to depend on a ratio of Co/Ni associated with chemical ordering of Co and Ni. However, the study of the chemical ordering of Co and Ni in the Al-Co-Ni DQCs is difficult because of next atomic numbers of Co and Ni, though arrangements of transition-metal (TM) atoms have been determined by Cs-corrected HAADF-STEM observations [1-2]. Besides, it was impossible to distinguish between Co and Ni in a W-(AlNiCo) crystalline approximant by single-crystal X-ray diffraction [3]. Our intention in the present paper is two-fold; the first is to study the structure of the Al-Co-Ni crystalline approximant by Cs-corrected HAADF- and ABF- STEM observations, and the second is to investigate the chemical ordering of Co and Ni in the structure. Using a Cs-corrected scanning transmission electron microscope (JEM-ARM200F), HAADF and ABF images were simultaneously acquired with an incident beam parallel to the b-axis. And atomic-resolution elemental maps were taken with a newly developed silicon drift detector (SDD). The chemical ordering of Co and Ni is clearly seen in the acquired elemental maps. Co atoms are enriched in atomic columns with a decagonal section of 1.2 nm in diameter, and Ni atoms are located in gaps between two-dimensional arrangements of the 1.2 nm atom clusters. It can be concluded that the area ratio of the Co-rich 1.2 nm atom clusters to the Ni-rich gaps results in various types of Al-Co-Ni DQCs with different arrangements of the 1.2 nm clusters.

Single crystals of Al-rich complex metallic alloys grown by Czochralski method

In quasicrystal-forming systems very often complex metallic phases exist which show similar structure motifs as the neighbouring quasicrystals but are periodic in all three directions. Therefore these phases are called approximants. They have similar chemical compositions as their parent quasicrystalline phases and can show the same periodicity of stacking of planes as for example found in decagonal quasicrystals. Using the Czochralski method cm3-size single-grain approximants of the Al4TM type, as orthorhombic Al4(Cr,Fe) and hexagonal Al4Cr and of the Al13TM4type, as monoclinic Al13(Co,Ni)4, orthorhombic Al13Co4, monoclinic Al13Fe4and its ternary extensions Al13(Fe,Cr)4and Al13(Fe,Ni)4have been grown from Al-rich solutions [1,2]. The Czochralski method has proven to be a suitable technique for growing single crystals from off-stoichiometric melts due to easy seeding, good mixing of the melt and by allowing good observation of the growth process. To meet the special needs of Al-rich melts a fully metal-sealed growth chamber is used to prevent almost any contact to traces of oxygen. Simultaneously to pulling the change of the liquidus temperature during the growth process has to be compensated by slightly decreasing the temperature using ramps of -(0.1 - 0.8) K/h. For seeding native seeds in different orientations were used. Pulling rates as low as (0.05 - 0.15) mm/h were necessary for growing because of matter transport limits in solution growth and kinetic reasons. Growing the approximant phases the same slow growth kinetics as known from the decagonal quasicrystals was found. Therefore, it might be concluded that the growth of quasicrystalline phases is primarily not limited by the absence of periodicity but by the large clusters that are a common feature in the crystal structures of both, quasicrystals and their approximants.

Phase Evolution of Al/Cu/Co Thin Films into Decagonal Quasicrystalline Phases

Quasicrystals have drawn increased scientific attention during the past decade not only for the purpose of fundamental research, but also due to their possible applications as bulk materials or thin films [1]. In particular, decagonal (d) quasicrystals could be very attractive because of their anisotropic structure being quasiperiodic in two dimensions and periodic in the third. Recently it has been shown that icosahedral quasicrystalline Al-Cu-Fe and approximant Al-Si-Cu-Fe thin films can be prepared by annealing a multilayer thin film on a sapphire or Si substrate, respectively [2]. In this work, multilayered Al/Cu/Co thin films have been deposited by magnetron sputtering onto Al2O3 (0001) and Si (001) substrates. The multilayers were produced with a multilayer period of 100 nm, repeated 3 times to a total thickness of 300 nm. The Al:Cu:Co layer thickness ratios were adjusted to obtain films with global compositions around the ideal decagonal quasicrystalline phase d-Al65Cu17.5Co17.5. The phase evolution during annealing, and the concurrent changes in film microstructure and crystal quality was investigated. The decagonal d-Al-Cu-Co and d-Al-Cu-Co-Si phases were both found by X-ray diffraction, electron diffraction, and high-resolution (scanning) electron microscopy to form at 5000C on Al2O3 and Si, respectively, and at 6000C these were the only phases present. Figure 1 shows the HRTEM micrograph of the Al-Cu-Co-Si phase after annealing to 7000C. At increasing temperatures, the quasicrystal grains grew larger in size, up to 500 nm, and the Al-Cu-Co obtained a preferred orientation with the 10-fold periodic axis aligned with the Al2O3 substrate normal. The d-Al-Cu-Co phase persisted to more than 8500C, with a complete 00001-texturing, while the d-Al-Cu-Co-Si phase was replaced by other crystalline phases at 8000C. The d-Al-Cu-Co-Si phase was also observed to grow into the Si substrate by a solid-state diffusion reaction.

Controlled Self-Assembly of Soft-Matter Quasicrystals

A large number of soft-matter systems, whose building blocks range in size from several nanometers to almost a micron, have been shown in recent years to form ordered phases with dodecagonal (12-fold) symmetry (for recent reviews see [1]). Contrary to metallurgic quasicrystals, whose source of stability remains a question of great debate to this day, we show that the stability of certain soft-matter quasicrystals–interacting via pair potentials with repulsive cores, which are either bounded or only slowly diverging–can directly be explained. Their stability is attributed to the existence of two natural length scales in their isotropic pair potentials, along with an effective three-body interaction arising from entropy. We establish the validity of this mechanism at the level of a mean-field theory [2], and then use molecular dynamics simulations in two dimensions to confirm it beyond mean field, and to show that it leads to the formation of cluster crystals [3]. We demonstrate that our understanding of the stability mechanism allows us to generate a variety of desired structures, including decagonal and dodecagonal quasicrystals [3], suggesting a practical approach for their controlled self-assembly in laboratory realizations using synthesized soft-matter particles.

In-situ HRTEM observations of growth process of decagonal quasicrystals

Quasicrystals possess quasiperiodicity, where the structure cannot be described simply by the repetition of unit cell like conventional crystals. This fact raises the question of how quasicrystals grow, i.e., what physical mechanism makes the growth of quasicrystals possible. While crystals can grow by copying a unit cell via local atomic interactions, nonlocal structural information seems to be required in the growth of quasicrystals. This problem has attracted much attention ever since the first discovery of a quasicrystal in 1984, and several theoretical growth models [1] have been proposed. However, no experimental studies have so far been reported, and it is still unclear whether these theoretical growth models apply to real quasicrystals. In the present study, we have conducted in-situ high-temperature electron microscopic (HRTEM: High-Resolution Transmission Electron Microscopy) observations of the growth process of decagonal quasicrystals to elucidate the growth mechanism. The growth processes of a decagonal quasicrystal of Al70.8Ni19.7Co9.5were observed by HRTEM in the temperature range 1073-1173K. Tiling patterns with edge length of about 2nm were constructed from a series of HRTEM images. They were analysed in the framework of the projection method. Here, we followed the procedures in our previous work [2]. We have already reported the results of some observations and analyses elsewhere [3]. However, the growth processes of them were on a small scale, and the results were indefinite. Recently, we have succeeded in observing a growth process on a massive scale. In this paper, we present the results of this observation and subsequent analyses, and discuss the growth mechanism of the quasicrystal.

Surface Decorations of Al-Cu-Fe and Al-Cu-Co Single Quasicrystals

We studied surface decorations of faceted icosahedral Al Cu Fe and decagonal Al Cu Co single quasicrystals by the scanning electron microscopy using primary and secondary electrons. Both types of single quasicrystals exhibited decorations on their facets, however the character of the decorations was totally di erent. Three kinds of decorations has been developed. On icosahedral Al60Cu26Fe14 quasicrystals we found three kinds of decorations: cellular, cavity type and fractal-like. There was no evident di erence in chemical composition between the inner dodecahedra and the decorations of all types. Surface decorations found on decagonal Al73.5Cu17.5Co9 quasicrystals formed a kind of irregular dendritic stars on the separate bright islands.

Structure of an Al-Fe-Ni Decagonal Quasicrystal Studied by Cs-Corrected STEM

Structure of an Al-Fe-Ni Decagonal Quasicrystal Studied by Cs-Corrected STEM