Dodecagonal Phase Research Articles

Computing interface with quasiperiodicity

We propose a method suitable for the computation of quasiperiodic interface, and apply it to simulate the interface between ordered phases in Lifschitz–Petrich model. The function space, initial and boundary conditions are carefully chosen so that it fixes the relative orientation and displacement, and we follow a gradient flow to let the interface find its optimal structure. The gradient flow is discretized by the scalar auxiliary variable (SAV) approach in time, and a spectral method in space using quasiperiodic Fourier series and generalized Jacobi polynomials. We use the method to study interface between striped, hexagonal and dodecagonal phases, especially when the interface is quasiperiodic. The numerical examples show that our method is efficient, accurate, and can successfully capture the interfacial structure.

A five-dimensional model of dodecagonal Ta-Te quasicrystals with fractal occupation domains.

The consideration of two approximants of the first stable dodecagonal Ta-Te quasicrystal shows that the five-dimensional (5D) space group of the dodecagonal phase is P12m2(12(5)mm) and the structure consists of five layers within a 10 A period. A 5D quasicrystal model leading to the two approximate structures by the introduction of appropriate linear phason strains is derived by the section method. The model shows 20 A dodecagonal clusters (DDC) arranged at each vertex of the square-triangle dodecagonal pattern and has fractal occupation domains, suggesting that the quasicrystal has either a deterministic or a random square-triangle packing of the DDC.

Microstructural characterisation of thermally sprayed quasicrystalline Al–Co–Fe–Cr coatings

A microstructural characterisation was carried out for Al–Co–Fe–Cr feed powder and the coatings sprayed with a high velocity oxy-fuel method using different operation conditions. The aims of the study were to explore the structural development of thick Al–Co–Fe–Cr coatings and the influence of the spraying parameters on the microstructure of produced Al–Co–Fe–Cr coatings. X-ray diffractometry, scanning electron microscopy and analytical transmission electron microscopy were the techniques used in the phase identification and in the microstructural exploration of the study. The results show that Al–Co–Fe–Cr feed powder and the coatings sprayed with low and high operation temperature are composed of a dodecagonal quasicrystalline phase. The composition of this new dodecagonal phase approximately corresponds to that of the feed powder, being A1 70.6Co 12.5Fe 9.4Cr 7.5. The dodecagonal phase does not decompose during the spraying process. Instead, it orientates to form a lamellar coating structure. When a lower spraying temperature is used, the incomplete melting of powder particles introduces a partly orientated coating structure. Due to this incomplete melting of powder particles, porosity is also involved in these coatings. Higher spraying temperature, in turn, promotes oxidation, leading to the incorporation of an oxygen-containing film on the splat boundaries. While the feed powder and the coating deposited with a lower spraying temperature are one-phase quasicrystalline structures, the coating sprayed with a higher operation temperature is comprised of a dodecagonal phase and an oxygen-containing phase. This oxygen-containing phase is not pure aluminium oxide but contains all the elements present in the alloy.

Structural Phase Evolution in the Equilibrium Immiscible Co–Cu System Studied by Solid-State Reaction/Ion Beam Mixing of Nano-Sized Multilayers

Unique structural phase evolution was observed in the nano-sized Co–Cu multilayers upon solid-state reaction/ion beam mixing and resulted in the formation of several metastable phases in the equilibrium immiscible Co–Cu system. Despite of a positive heat of formation of the Co–Cu system, a superlattice was obtained in the nano-sized Co 34 Cu 66 multilayered films upon 600 K thermal annealing, and it later evolved into a dodecagonal phase when the annealing temperature was risen up to 800 K. Comparatively, by ion beam mixing, other metastable phases were obtained, e.g. , an amorphous phase and a dodecagonal phase were obtained in the Co 15 Cu 85 films. The same dodecagonal phase was also formed in the Co 50 Cu 50 films and the ion mixed dodecagons tended to assemble themselves into a fourfold rotational symmetry at relatively high irradiation dose. In the present paper, thermodynamic modeling and the formation mechanism of the metastable phases were also discussed based on Miedima's model and consideration of the physical process driven far-from-equilibrium by ion beam mixing.

Formation of adodecagonal phase in the nano-sized Ag-Pt multilayers uponsolid-state reaction

A dodecagonal quasicrystalline phase was grown in nano-sized Ag-Pt multilayers upon solid-state reaction and the existence of the respective metastable state in the Ag-Pt system was also confirmed by ion-beam mixing experiments. The major driving force for intermixing between the nano-sized Ag and Pt layers, as well as for the crystal-to-quasicrystal transition, was thought to be the interfacial free energy, which elevated the initial Ag-Pt multilayers up to an energetic state corresponding to the dodecagonal phase.

Irradiation-induced amorphization and growth of dodecagonal phase in an immiscible Co–Cu system

Anomalous structural evolution was observed in an equilibrium immiscible Co–Cu system while the Co–Cu multilayers were irradiated by Xenon ions at 77 K. In the as-deposited Co 15Cu 85 multilayers consisting of polycrystalline Co and Cu of fcc structure, 100 keV Xenon ion irradiation to a dose of 7×10 15 Xe +/ cm 2 resulted in amorphization and the formation of a new dodecagonal phase embedded in the amorphous matrix. In another sample with an overall composition of Co 35Cu 65, the same dodecagonal phase was also obtained by 200 keV Xenon ion irradiation within a dose range of 5×10 15–9×10 15 Xe +/ cm 2 and interestingly, the formed dodecagons assembled themselves in a superlattice with an in-plane four-fold rotational symmetry. According to the non-equilibrium characteristics involved in ion irradiation process, the mechanism of the above structural evolution is discussed in terms of the similarity in the atomic configuration between the quasicrystal and amorphous short-range orders as well as the effect of interfacial free energy stored in the Co–Cu multilayers.

Formation of Quasicrystalline Phases in the Equilibrium Immiscible Co-Cu and Fe-Cu Systems by Ion Mixing/Solid-State Reaction

AbstractAnomalous structural evolution was induced in the equilibrium immiscible Co-Cu and Fe-Cu systems by 100 or 200 keV xenon ion irradiation at 77 K or room temperature. In the Co15Cu85 and Fe70Cu30 multilayered films, nanosized quasicrystals were formed in an amorphous matrix, through a two-step transition of crystal-to-amorphous-to-quasicrystal. The obtained quasicrystals are Co-Cu dodecagonal and Fe-Cu icosahedral phases with twelve-fold and five-fold rotational symmetries, respectively. The real compositions of the amorphous matrix were determined to be close to Co10Cu90 and Fe70Cu30, while those for quasicrystals are nearly Co20Cu80 and Fe50Cu50, respectively. Moreover, the same dodecagonal and icosahedral phases were also obtained in the specifically designed Co50Cu50 and Fe50Cu50 multilayered samples upon thermal annealing at 500°C and 850°C, respectively, confirming the existence of these new metastable states in the respective systems. Besides, our molecular dynamics study showed that either Co or Fe could be mixed with Cu at an atomic scale in forming some metastable alloy phases. The amorphous-to-quasicrystal transition was discussed in terms of the similarity in the atomic configuration between the quasicrystal and amorphous short-range orders.

The mesoscopic structure of disordered dodecagonal tantalum telluride: A high-resolution transmission electron microscopy study

A disordered dodecagonal quasicrystalline tantalum-rich telluride was prepared at the upper thermal stability limit of the related quasicrystalline phase by application of conventional high-temperature synthesis techniques. The structure of the disordered telluride was studied on a mesoscopic scale by means of high-resolution transmission electron microscopy (HRTEM). A selective imaging technique was employed in order to produce HRTEM images which allow a square-triangle tiling underlying the structure on a length scale of about 2 nm to be recognized The tiling was analysed with regard to specific deviations from a perfectly ordered quasicrystalline dodecagonal telluride and various crystalline approximants. The application of a general construction principle derived from the structures of two well characterized approximants allows the reconstruction of a realistic structural model for the disordered dodecagonal phase and the calculation of its composition. The disordered phase is interpreted as an intergrowth of nuclei of various crystalline approximants with interspersed relics of the dodecagonal phase. The tantalum mole fraction of the disordered phase deviates by about 5 ppm from that of a truly dodecagonal telluride Ta3+2x31/2Te4 containing the two components in an irrational ratio.

A Dodecagonal Quasicrystalline Chalcogenide.

Diffractograms with twelvefold rotational symmetry (depicted on the right) were obtained from the first quasicrystalline chalcogenide Ta1.6 Te. This compound was prepared on a preparative scale by the reduction of TaTe2 with tantalum below 1870 K. This tantalum-rich telluride, which is the first stable dodecagonal phase, has enabled an in-depth investigation of this unusual state of ordering.

Reply to "Comment on 'Understanding twelvefold symmetry in electron-diffraction patterns' "

A Frank-Kaspar phase-related periodic model of V-Ni is set up. It explains well the experimental data of the dodecagonal phase [see Phys. Rev. Lett. 60, 1645 (1988)] but not the corresponding unclear high-resolution electron-microscopic image. The dodecagonal phase can be understood to be that of a perturbed nonclassical crystal.

Nucleation and formation of quasicrystalline phases in undercooled AlMn melts

The nucleation and the formation of metastable quasicrystalline icosahedral and dodecagonal phases, as well as of the stable crystalline Al 6Mn intermetallic phase, have been analysed for undercooled Al 88Mn 12 metls on the basis of classical nucleation theory. In detail, the difference of free energy between the undercooled liquid and the solid state, the activation energy for the formation of postcritical nuclei, the nucleation frequency and the crystal growth velocities have been calculated as a function of temperature for the various phases using experimentally determined thermodynamic parameters. These calculations lead to temperature-time-transformation curves capable of describing experimental findings on containerless processes droplets, provided homogeneous nucleation of the quasicrystalline phases is assumed.

Quasicrystal–crystal transition in the dodecagonal phase

Abstract The quasicrystal-crystal transition in dodecagonal structures is studied in the case of a two-dimensional quasiperiodic tiling obtained by projecting a six-dimensional cubic lattice. By following the already proposed technique which consists of tilting the projection plane, we propose a decoration of the quasilattice which satisfies the hard-core condition and explains qualitatively some features of the electron diffraction patterns of the dodecagonal phase recently reported in a Bi-Mn alloy. It suggests that the quasicrystal-crystal transition in the dodecagonal phase occurs in a continuous fashion.

Displacive transformations for the octagonal and dodecagonal phases

Abstract In this Letter we present a new geometric transformation to connect in a continuous way the octagonal phase with the related crystalline ones. This transformation avoids the tiles vanishing and hence it allows us to define a simple atomic decoration which preserves the ‘hard core’ condition. In the model presented here, the quasicrystal-related crystal density ratio is so close to 1 that it implies very short atomic displacementa and allows phase transitions to be physically possible in large enough clusters. A Shannon entropy is defined to estimate physically this evolutionary model. The strategy is extended to study the connection of the dodecagonal phase with two hexagonal phases rotated 30° from one to another.

Pseudoquasicrystals: Quasicrystal-like crystals with thirteen to eighteen strong electron scatterers per unit cell.

We present examples of two-dimensional crystals with thirteen to eighteen strong electron scatterers per unit cell which have almost perfect twelvefold, tenfold, and eightfold diffraction patterns in the regions in $k$ space where current experiments are performed. These examples show that it is at present premature to identify the recently discovered octagonal and dodecagonal phases as quasicrystals.