Decagonal Quasicrystals Research Articles

Nucleation and phase transition of decagonal quasicrystals.

In this work, we study the nucleation of quasicrystals from liquid or periodic crystals by developing an efficient order-order phase transition algorithm, namely, the nullspace-preserving saddle search method. In particular, we focus on nucleation and phase transitions of the decagonal quasicrystal (DQC) based on the Lifshitz-Petrich model. We present the nucleation path of DQC from the liquid and demonstrate one- and two-stage transition paths between DQC and periodic crystals. We provide a perspective of the group-subgroup phase transition and nucleation rates to understand the nucleation and phase transition mechanisms involving DQC. These results reveal the one-step and multi-step modes of symmetry breaking or recovery in the phase transition from DQC, where the multi-step modes are more probable.

Simulated structure and thermodynamics of decagonal Al-Co-Cu quasicrystals

Atomic structures of Al-Co-Cu decagonal quasicrystals (dQCs) are investigated using empirical oscillating pair potentials (EOPP) in molecular dynamic (MD) simulations that we enhance by Monte Carlo (MC) swapping of chemical species and replica exchange. Predicted structures exhibit planar decagonal tiling patterns and are periodic along the perpendicular direction. We then recalculate the energies of promising structures using first-principles density functional theory (DFT), along with energies of competing phases. We find that our τ-inflated sequence of QC approximants (QCAs) are energetically unstable at low temperature by at least 3 meV/atom. Extending our study to finite temperatures by calculating harmonic vibrational entropy, as well as anharmonic contributions that include chemical species swaps and tile flips, our results suggest that the quasicrystal phase is entropically stabilized at temperatures in the range 600-800 K and above. It decomposes into ordinary (though complex) crystal phases at low temperatures, including a partially disordered B2-type phase. We discuss the influence of density and composition on QC phase stability; we compare the structural differences between Co-rich and Cu-rich quasicrystals; and we analyze the role of entropy in stabilizing the quasicrystal, concluding with a discussion of the possible existence of “high entropy” quasicrystals. Published by the American Physical Society 2024

Hamiltonian System for Three-Dimensional Problem of Two-Dimensional Decagonal Piezoelectric Quasicrystals and Its Symplectic Analytical Solutions

Hamiltonian System for Three-Dimensional Problem of Two-Dimensional Decagonal Piezoelectric Quasicrystals and Its Symplectic Analytical Solutions

Postbuckling behavior of two-dimensional decagonal quasicrystal plates under biaxial compression

Two-dimensional (2D) decagonal quasicrystal (QC) plates are analyzed for their postbuckling behaviors when subjected to biaxial compressive loads in this research. The analysis using a combination of the first-order shear deformation theory (FSDT) along with von Kármán’s nonlinear equations of motion, while also accounting for the initial geometric imperfections. The governing equations for the QC plate are obtained through the application of the Hamiltonian variational principle, and the postbuckling equilibrium path for the four-sided plate with simply support is calculated using a two-step perturbation technique. The quasiperiodic structure and phonon-phason coupling in 2D decagonal QCs play a crucial role in determining their mechanical behavior. The numerical analysis explores the effects of geometric shape, phonon-phason coupling constants, initial geometric imperfections, and compressive forces on the postbuckling characteristics of the plates. Numerical simulations validate the theoretical model, demonstrating its accuracy. The application of FSDT, von Kármán theory, and the two-step perturbation method to QC plates, considering the complex interactions involving the phason field unique to quasicrystals, provides new insights into the intricate mechanical responses of QC plates under postbuckling conditions.

25 Years of Quasiperiodic Crystallography in Physical Space using the Average Unit Cell Approach

AbstractSince the discovery of quasicrystals 40 years ago, many new paradigms and methods have been introduced to crystallography. 25 years ago, a statistical method of structure and diffraction analysis of aperiodic materials was proposed and, over these years, developed to describe model and real systems. This short review paper briefly invokes the basic concepts of the method: a reference lattice and an average unit cell, but also gives an overview of its application to atomic structure and diffraction analysis of various systems. Results are briefly discussed for mathematical sequences (Fibonacci and Thue‐Morse), model quasilattices in 2D and 3D (Penrose and Ammann tiling), refinements of real decagonal and icosahedral quasicrystals, analysis of structure disorder in quasicrystals, description of modulated systems, including macromolecular biological systems, and beyond usual application in crystallography.

A Closed-Form Solution to the Mechanism of Interface Crack Formation with One Contact Area in Decagonal Quasicrystal Bi-Materials

Cracks and crack-like defects in engineering structures have greatly reduced the structural strength. An interface crack with one contact area in a combined tension–shear field of decagonal quasicrystal bi-material is investigated. Based on the deformation compatibility equation and displacement potential function, the complex representation of stress and displacement is given. Using the mixed boundary conditions, the closed-form expressions for the stresses and the displacement jumps in the phonon field and phason field on the material interface are obtained. The results show that the stress intensity factor at the crack tip is zero for the phason field. The variation in the stress intensity factor and the length of the contact zone in the phonon field is given, and the result is consistent with the properties of the crystal. The design of safe engineering structures and the formulation of reasonable quality acceptance standards may benefit from the theoretical research carried out here.

Molecular dynamics simulation of mechanical properties of decagonal quasicrystal approximate phase Al2Fe

By using the molecular dynamics method, the tensile and elastic mechanical properties of Al2Fe (tI6 and oF24) alloys for decagonal quasicrystals approximation are simulated. Structural models for tI6 and oF24 are first established and then the appropriate embedded atom method (EAM) potential function is selected to analyze the effects of temperature and strain rate on the stress-strain relation, atomic structure and deformation mechanism. Furthermore, all the elastic constants Cij of tI6 and oF24 are calculated by the molecular dynamics explicit deformation method, and the crystal structure and stability of tI6 and oF24 are also judged. Besides, the elastic mechanical properties of tI6 and oF24 including bulk modulus, shear modulus, elastic modulus, and Poisson's ratio, are derived by means of both the general formula and the independent crystal system formula. The results show that the elastic modulus and tensile strength of tI6 and oF24 almost decrease linearly with increasing temperature. An increase of strain rate has little effect on the elastic modulus of tI6 and oF24, but it can result in an obvious increase of the tensile strength and ultimate strain. By calculating, tI6 possesses a stable tetragonal crystal structure and oF24 has a stable orthorhombic crystal structure, which are consistent with the previous results derived by the first-principle. The Young's modulus, shear modulus and Poisson's ratio display high anisotropy except for the bulk modulus. The anisotropic of oF24 is higher than that of tI6, while the stiffness and hardness of tI6 are greater than those of oF24. The present work can provide a theoretical reference for analyzing the mechanical properties of the approximate phase of decagonal quasicrystal as well as a novel numerical calculation method for determining the mechanical properties of related materials.

Hamiltonian System for Two-Dimensional Decagonal Quasicrystal Plates and Its Analytical Solutions

Hamiltonian System for Two-Dimensional Decagonal Quasicrystal Plates and Its Analytical Solutions

Ultra-short pulsed laser ablation of decagonal AlCoNi and AlCoCuNi quasicrystals

Al70Co20Ni10 and Al70Co15Cu10Ni5 (at%) decagonal quasicrystals (DQCs) were subjected to femtosecond laser ablation at a laser wavelength of 800 nm, in deionized water (DI). The generated nanoparticles (NPs) confined within the liquid medium were studied for optical and structural properties. The structural analysis revealed the retention of the targets phase in the NPs. In case of Al70Co20Ni10, formation of Al3Ni2 phase was confirmed through the SAED patterns and HRTEM micrographs. Contrary to this, the formation of Al-Ni phase was not observed in Al70Co15Cu10Ni5. This is attributed to the presence of Cu in the latter sample, which restricts the mixing of Ni with Al. The HRTEM micrographs in both cases showed that Al2O3 was present at the edges of the NPs. The optical analysis confirmed the formation of Al2O3 in both cases. However, in the case of Al70Co15Cu10Ni5, a very weak signal corresponding to CuO was detected. This is attributed to the diffusion of Cu along with Al at the edge. The ablated region of the target’s surface was studied for the formation of laser-induced periodic surface structures (LIPSS) also known as ripples, and the type of ripples formed was identified.

Microstructures and microtextures of melt-spun decagonal Al–Co–Ni and Al–Co

The fabrication and applications of quasicrystals often involve multigrain aggregates. Microstructures and textures of polycrystals can be conveniently studied by orientation mapping. Such studies of quasicrystals have been rare because the widely used electron backscatter diffraction (EBSD) mapping systems do not index patterns from materials with non-crystallographic symmetries. This complication can be circumvented by using a commercial system to detect individual EBSD bands and an in-house software to index the bands and determine the orientations. This approach was applied to decagonal Al–Co–Ni and Al–Co quasicrystals obtained by the melt-spinning technique. The investigated samples showed similar textures and microstructures on the wheel sides of the ribbons. Maps of cross-sections and free sides revealed microstructural differences implying differences in solidification mechanisms. The growth in Al–Co was columnar, whereas ribbons of Al–Co–Ni showed columnar-to-equiaxed transition. The study demonstrates applicability of the conventional orientation mapping based on detection of diffraction reflections to decagonal quasicrystals.

Molecular dynamics simulations for quasicrystals under the Born-Gauss potentials

Molecular dynamics simulations are a tool for the study of the microscopic dynamics in quasicrystals. By choosing suitable potentials, such as the Dzugutov potential and the Lennard-Jones-Gauss potential, two-dimensional quasicrystals with 8-, 10- and 12-fold symmetries have been formed. In this work, we propose a Born-Gauss type potential with more adjusting parameters to do simulations in two dimensions. Decagonal and dodecagonal quasicrystals are successfully obtained. The structural properties are analyzed and the phase transitions between different structures are discussed.

Mode-I Plane Elasticity Problem of Two Asymmetrical Edge Cracks Emanating from an Elliptical Hole in Two-Dimensional Decagonal Quasicrystals

We consider the plane elasticity problem of two asymmetrical edge cracks emanating from an elliptical hole in two-dimensional decagonal quasicrystals (QCs) under remotely uniform tensile stress. A complex variation method of two-dimensional QCs is developed to solve the plane elasticity problem of two-dimensional decagonal QCs containing complex defects. The analytical solutions for the stress field and the stress intensity factors near the crack tip are expressed by using a conformal mapping technique and complex potential theory. Some special cases of the results are also obtained, such as the T-type crack, cross crack, and Griffith crack. The effects of geometrical parameters of crack configuration on the stress intensity factors are presented graphically.

A phase-field model for thermo-elastic fracture in quasicrystals

In this paper, a thermo-elastic phase-field model for brittle fracture in quasicrystals is developed. The kind of quasicrystals is not preset, so this model is suitable for almost all thermo-elastic quasicrystal solids. The phonon force and thermal load trigger the variation of the phonon elastic energy, and then drive crack initiation and propagation. The thermal conductivity in the cracked region is assumed to be degraded, which means cracks are adiabatic. For the static penny-shaped crack problem, the results based on the present model agree well with the existing analytical solution. For the quasi-static crack problems, both the tensile/shear fracture in a thermal environment and the thermal shock cracking failure can be dealt with by the present model. Several examples of 1D hexagonal and 2D decagonal quasicrystals are performed to evaluate the effects of thermal load and phason elastic field. The simulation results show that the thermal load can influence the peak force and fracture displacement. For the single-edge notched tension test, the effect of the thermal load on the peak force is small, but it on the fracture displacement is obvious. For the single-edge notched shear test, the thermal load has an obvious influence on both the peak force and fracture displacement. For the thermal shock cracking problem, the phason elastic field has a significant effect on the cracking time and crack number. The present model can serve as a powerful tool to simulate various thermo-elastic fracture problems in quasicrystals.

A phase-field framework for brittle fracture in quasi-crystals

Most of quasi-crystals are brittle at room temperature due to their specific cluster structures. Phase-field fracture models have demonstrated a powerful ability to predict brittle crack evolution. This paper develops a phase-field framework for modeling macroscopic brittle fracture in quasi-crystal solids. The kind of quasi-crystals is not preset in the phase-field model; therefore, this model is valid for almost all quasi-crystal solids. The phase-field model for the first time introduces a volume fraction parameter into the fracture toughness to reflect the effect of phason wall. Furthermore, a new numerical implementation approach of phase-field fracture models in Comsol Multiphysics is presented. Several examples of 1D hexagonal and 2D decagonal quasi-crystals are performed. The developed model is validated against the reported results of benchmark problems. Further investigations indicate that the phason field peculiar to quasi-crystals has a certain influence on the crack paths in asymmetric fracture problems and on the force–displacement curves in both symmetric and asymmetric fracture problems. When the fracture toughness is fixed, the increase of the volume fraction parameter results in the decrease of the peak force and the increase of the failure displacement. When the influence of the phason field on the fracture toughness is considered, both the peak force and failure displacement would sharply decrease, which indicates that the degradation of fracture toughness due to the phason field plays a more important role than the phason elastic energy in the fracture of quasi-crystals. Furthermore, the relation between the phonon-phason energy transformation and the elastic constants of QCs has been qualitatively analyzed. The developed phase-field modeling framework provides a guidance for understanding the fracture mechanism of quasi-crystals and assessing the safety of quasi-crystal structures in engineering practice.

A Phase Field Approach to Two-Dimensional Quasicrystals with Mixed Mode Cracks.

Quasicrystals (QCs) are representatives of a novel kind of material exhibiting a large number of remarkable specific properties. However, QCs are usually brittle, and crack propagation inevitably occurs in such materials. Therefore, it is of great significance to study the crack growth behaviors in QCs. In this work, the crack propagation of two-dimensional (2D) decagonal QCs is investigated by a fracture phase field method. In this method, a phase field variable is introduced to evaluate the damage of QCs near the crack. Thus, the crack topology is described by the phase field variable and its gradient. In this manner, it is unnecessary to track the crack tip, and therefore remeshing is avoided during the crack propagation. In the numerical examples, the crack propagation paths of 2D QCs are simulated by the proposed method, and the effects of the phason field on the crack growth behaviors of QCs are studied in detail. Furthermore, the interaction of the double cracks in QCs is also discussed.

Structural Features of the Rapidly Quenched Al–Cu–Fe Alloy with Decagonal Quasicrystals

Structural Features of the Rapidly Quenched Al–Cu–Fe Alloy with Decagonal Quasicrystals

STRUCTURAL FEATURES OF THE RAPIDLY QUENCHED Al–Cu–Fe ALLOY WITH DECAGONAL QUASICRYSTALS

The multiphase alloys with a high Al content and the presence of quasicrystalline phases are promising for aviation and space industry due to their low specific weight, high specific strength, corrosion resistance, and high tribological properties. An Al82Cu7Fe11 alloy ribbon has been obtained by spinning. It is shown by X-ray diffraction analysis that the alloy contains Al (sp. gr. Fm m), Al13Fe4 (sp. gr. С2/m), Al2Cu (sp. gr. I4/mcm), Al23CuFe4 (sp. gr. Cmc21), and decagonal quasicrystals (sp. gr. P105mc). The inhomogeneity of the ribbon surface is revealed by scanning electron microscopy. The presence of Al, Al13Fe4, and decagonal quasicrystals in the ribbon is found by transmission electron microscopy.

Precipitation of multi-type nano-quasicrystals in a Mg-Zn-Y alloy

Mg-6Zn-1Y (at.%) ribbons with strengthening precipitates of multi-type nanoquasicrystals were prepared by melt-spinning followed by aging treatments. Microstructural evolution of the rapidly solidified ribbons during isothermal aging was comprehensively studied using various electron microscopy techniques. Two new kinds of decagonal quasicrystals were formed in aged ribbons, in addition to precipitation of nanometer icosahedral quasicrystals. Atomic-resolution observations reveal that both decagonal quasicrystals can be modeled by quasi-periodic tiling with decagonal clusters of 2.5 nm in diameter, but overlap of neighboring clusters in both decagonal quasicrystals is different from the Gummelt model observed in other quasicrystals. A shell composed of complex Laves Mg-Zn domains was formed surrounding each decagonal quasicrystal precipitate upon prolonged aging. In addition, all kinds of nanoprecipitates exhibit excellent structure and size stability at 573 K. Our findings may have implications for not only fundamental studies about quasicrystals, but also microstructural manipulation of high-performance Mg alloys.

An Analysis Method of Symplectic Dual System for Decagonal Quasicrystal Plane Elasticity and Application

The symplectic solution system of decagonal quasicrystal elastic mechanics is considered. Hamiltonian dual equations together with the boundary conditions are investigated by utilizing the principle of minimum potential energy. Then the symplectic eigenvectors are given on the basis of the variable separation method. As application, analytical solution for decagonal quasicrystal cantilever beam with concentrated load is discussed. The analytical expressions of the stresses and displacements of the phonon field and phason field are obtained. The present method allows for the exploration of new analytic solutions of quasicrystal elasticity that are difficult to obtain by other analytic methods

Expanding quasiperiodicity in soft matter: Supramolecular decagonal quasicrystals by binary giant molecule blends

The quasiperiodic structures in metal alloys have been known to depend on the existence of icosahedral order in the melt. Among different phases observed in intermetallics, decagonal quasicrystal (DQC) structures have been identified in many glass-forming alloys yet remain inaccessible in bulk-state condensed soft matters. Via annealing the mixture of two giant molecules, the binary system assemblies into an axial DQC superlattice, which is identified comprehensively with meso-atomic accuracy. Analysis indicates that the DQC superlattice is composed of mesoatoms with an unusually broad volume distribution. The interplays of submesoatomic (molecular) and mesoatomic (supramolecular) local packings are found to play a crucial role in not only the formation of the metastable DQC superlattice but also its transition to dodecagonal quasicrystal and Frank-Kasper σ superlattices.