Dynamic behaviour of the icosahedral Al-Pd-Mn quasicrystal with a Griffith crack

The dynamic response of an icosahedral Al-Pd Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon-phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.

Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.

MICROSTRUCTURE FORMATION AND MECHANICAL PROPERTY INVOLVING ICOSAHEDRAL QUASICRYSTAL PHASE OF Y RICH Mg-Zn-Y QUASICRYSTAL ALLOY

The microstructure formation and mechanical property involving icosahedral quasicrystal （I-phase） in the Y-rich Mg-Zn-Y alloy have been studied. The equilibrium formation of I-phase from the Y-rich Mg-Zn-Y melt is through a peritectic reaction between the Y-rich melt and the primary W-phase, which is discussed in detail. The independent nucleation and coupling growth mechanism between the W-phase and the I-phase, from the melt, are revealed, which is significant for understanding the peritectic reaction process involving icosahedral quasicrystal in the Mg-Zn-Y alloy. The mechanism of the quasicrystal phase strengthened magnesium alloys is also discussed here.

Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow

The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.

Effect of heat treatment on the microstructure and micromechanical properties of the rapidly solidified Mg61.7Zn34Gd4.3 alloy containing icosahedral phase

In this paper, the microstructure evolution of the rapidly solidified (RS) Mg61.7Zn34Gd4.3 (at%, atomic ratio) alloy at high temperatures was investigated. The hardness and elastic modulus of the main precipitated phases were also analyzed and compared with those of the α-Mg matrix on the basis of nanoindentation tests. The results show that the RS alloy consists of either a petal-like icosahedral quasicrystal (IQC) phase (~20 μm) and block-shaped H1 phase (~15 μm) or IQC particles with an average grain size of ~107 nm as well as a small proportion of amorphous phase, which mainly depends on the holding time at the liquid temperature and the thickness of the ribbons. The IQC phase gradually transforms at 400?C to a short-rod-shaped μ-phase (Mg28.6Zn63.8Gd7.7) with a hexagonal structure. The hardness of the IQC phase is higher than that of H1 phase, and both phases exhibit a higher hardness than the α-Mg matrix and the μ-phase. The elasticity of the H1 phase is superior to that of the α-Mg matrix. The IQC phase possesses a higher elastic modulus than H1 phase. The easily formed H1 phase exhibits the poorest plastic deformation capacity among these phases but a higher elastic modulus than the α-Mg matrix.

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended Stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.

Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole

The generalized 2D problem of icosahedral quasicrystals containing an elliptic hole is considered by using the ex- tended Stroh formalism. The closed-form solutions for the displacements and stresses are obtained under general loading conditions. The solution of the Griffith crack problem as a special case of the results is also observed. The stress intensity factor and strain energy release rate are given. The effect of the phonon-phason coupling elastic constant on the mechanical behavior is also discussed.

Analysis and Evaluation of the Global Aerosol Optical Properties Simulated by an Online Aerosol-coupled Non-hydrostatic Icosahedral Atmospheric Model

Aerosol optical properties are simulated using the Spectral Radiation Transport Model I~）r Aerosol Species （SPRINTARS） coupled with the Non-hydrostatic ICosahedral Atmospheric Model （NICAM）. The 3-year global mean all-sky aerosol optical thickness （AOT） at 550 nm, theAngstr/Sm Exponent （AE） based on AOTs at 440 and 870 nm, and the single scattering albedo （SSA） at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer （MODIS） and the Aerosol Robotic Network （AERONET）. The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the＇opposite is found over regions dominated by hydrophobic aerosol.

Finite size specimens with cracks of icosahedral Al Pd Mn quasicrystals

Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.

Exact analytic solutions for an elliptic hole with asymmetric collinear cracks in a one-dimensional hexagonal quasi-crystal

Using the complex variable function method and the technique of conformal mapping, the anti-plane shear problem of an elliptic hole with asymmetric colfinear cracks in a one-dimensional hexagonal quasi-crystal is solved, and the exact analytic solutions of the stress intensity factors （SIFs） for mode Ⅲ problem are obtained. Under the limiting conditions, the present results reduce to the Griffith crack and many new results obtained as well, such as the circular hole with asymmetric collinear cracks, the elliptic hole with a straight crack, the mode T crack, the cross crack and so on. As far as the phonon field is concerned, these results, which play an important role in many practical and theoretical applications, are shown to be in good agreement with the classical results.

Microstructures and Morphology Evolution of Icosahedral Phase of As-cast Mg_(67.4)Zn_(28.9)Y_(3.7) Ternary Alloy Subjected to the Pouring Temperature

The microstructure, chemical composition and morphology evolution of icosahedral quasicrystalline phase of Mg67.4Zn28.9Y3.7 ternary alloy were investigated in detail at different pouring temperatures by X-ray diffraction （XRD）, scanning electron microscopy （SEM） and energy-dispersive spectrum （EDS）. Low interracial energy favors the formation of l-phase. The experimental results show that the primary l-phase reveals petal-shaped with five and six branches, where each branch has facetted growth morphology with the size ranging from 50 to 100μm. As the temperature decreases, the polygon-shaped l-phase forms, attributed to the decomposition of branch of petal-shaped l-phase, and then it grows bigger and some of the fine polygons join together to form large polygons. Besides these, （α-Mg＋l-phase） eutectic structures disappear and the relative amount of Mg7Zn3 phase increases as the pouring temperature decreases. The chemical composition and morphology evolution of l-phase were also discussed.

Investigation on the icosahedral quasicrystal phase in Mg_(70.8)Zn_(28)Nd_(1.2) alloy

Mg70.8Zn28Nd1.2（mole fraction） alloy containing icosahedral quasicrystal phase （I-phase） was prepared under conventional metal casting conditions. The microstructure, phase constitution and phase structure of the alloy were investigated by means of scanning electron microscopy （SEM）, X-ray diffraction （XRD）, energy dispersive spectrometer （EDS） and transmission electron microscopy （TEM）. The resuits showed that the spherical phase in Mg70.8Zn28Nd1.2 alloy was a simple icosahedral quasicrystal with stoichiometric composition of Mg40Zn55Nd5 and quasi-lattice of 0.525 nm. In this research, the as-cast microstructure of Mg70.8Zn28Nd1.2 alloy mainly consisted of Mg40Zn55Nd5 icosahedral quasicrystal phase and Mg7Zn3 columnar crystal matrix. In the growing process of Mg40Zn55Nd5 icosahedral quasicrystal phase, the growth morphology mainly depended on interface energy, adsorption effect of Nd and cooling rate.

Implementation of a Conservative Two-step Shape-Preserving Advection Scheme on a Spherical Icosahedral Hexagonal Geodesic Grid

An Eulerian flux-form advection scheme, called the Two-step Shape-Preserving Advection Scheme （TSPAS）, was generalized and implemented on a spherical icosahedral hexagonal grid （also referred to as a geodesic grid） to solve the transport equation. The C grid discretization was used for the spatial discretization. To implement TSPAS on an unstructured grid, the original finite-difference scheme was further generalized. The two-step integration utilizes a combination of two separate schemes （a low-order monotone scheme and a high-order scheme that typically cannot ensure monotonicity） to calculate the fluxes at the cell walls （one scheme corresponds to one cell wall）. The choice between these two schemes for each edge depends on a pre-updated scalar value using slightly increased fluxes. After the determination of an appropriate scheme, the final integration at a target cell is achieved by summing the fluxes that are computed by the different schemes. The conservative and shape-preserving properties of the generalized scheme are demonstrated. Numerical experiments are conducted at several horizontal resolutions. TSPAS is compared with the Flux Corrected Transport （FCT） approach to demonstrate the differences between the two methods, and several transport tests are performed to examine the accuracy, efficiency and robustness of the two schemes.

CONSTITUTION OF Al-BASE MULTI-COMPONENT QUASI-CRYSTALLINE ALLOYS

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Icosahedral quasicrystal structure of the Mg_(40)Zn_(55)Nd_(5) phase and its thermodynamic stability

The quasicrystal phase is beneficial to increasing the strength of magnesium alloys.However,its complicated structure and unclear phase relations impede the design of alloys with good mechanical properties.In this paper,the Mg_(40)Zn_(55)Nd_(5) icosahedral quasicrystal(I-phase)structure is discovered in an as-cast Mg-58Zn-4Nd alloy by atomic resolution high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM).A cloud-like morphology is observed with Mg_(41.6)Zn_(55.0)Nd_(3.4) composition.The selected area electronic diffrac-tion(SAED)analysis shows that the icosahedral quasicrystal structure has 5-fold,4-fold,3-fold,and 2-fold symmetry zone axes.The thermo-dynamic stability of the icosahedral quasicrystal is investigated by differential scanning calorimetry(DSC)in the annealed alloys.When an-nealed above 300℃,the Mg_(40)Zn_(55)Nd_(5) quasicrystal is found to decompose into a stable ternary phase Mg_(35)Zn_(60)Nd_(5),a binary phase MgZn,andα-Mg,suggesting that the quasicrystal is a metastable phase in the Mg-Zn-Nd system.

Solidification of Mg-28%Zn-2%Y alloy involving icosahedral quasicrystal phase

Applying XRD, DTA, SEM and TEM techniques, an investigation on the solidification microstructure and solidification sequence of Mg-rich Mg-28%Zn-2%Y (mole fraction) alloy was carried out. It is found that, α-Mg dendrites, Mg7Zn3 phase and icosahedral quasicrystal phase coexist in the as-solidified alloy, where the icosahedral quasicrystal, whose structure is indentified to be a face-centered type, originates from a peritectic reaction occurring at 416 ℃. The primary phase of this peritectic reaction has the composition of Mg20Zn66Y14, which is coincident with the H phase reported by TSAI as (Zn, Mg)5Y. Furthermore, the single I-phase grain morphology was observed and its growth evolution was also discussed.

Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure

The interface crack problems in the two-dimensional(2D)decagonal quasicrystal(QC)coating are theoretically and numerically investigated with a displacement discontinuity method.The 2D general solution is obtained based on the potential theory.An analogy method is proposed based on the relationship between the general solutions for 2D decagonal and one-dimensional(1D)hexagonal QCs.According to the analogy method,the fundamental solutions of concentrated point phonon displacement discontinuities are obtained on the interface.By using the superposition principle,the hypersingular boundary integral-differential equations in terms of displacement discontinuities are determined for a line interface crack.Further,Green’s functions are found for uniform displacement discontinuities on a line element.The oscillatory singularity near a crack tip is eliminated by adopting the Gaussian distribution to approximate the delta function.The stress intensity factors(SIFs)with ordinary singularity and the energy release rate(ERR)are derived.Finally,a boundary element method is put forward to investigate the effects of different factors on the fracture.

Effect of icosahedral clusters on β-relaxations in metallic glasses

The most pronounced β-relaxation was found in the Y-based binary metallic glasses（MGs）. The correlation betweenβ-relaxation and local atomic structure was studied. The dynamic mechanical measurements were performed for three chosen binary systems： Zr-, Ti-, and Y-based MGs. The experimental results show that, in each system,the larger negative enthalpy of mixing（？Hm） between the component elements makes β-relaxation become more pronounced. The less negative value of ？Hm facilitates the formation of icosahedral clusters, which have a pinning effect on the excitation of β-relaxations and correspondingly make the β-relaxation become less pronounced. These chemical effects on β-relaxations can only be compared in the same MG system, and it is not suitable for the comparison between different systems due to the different features of the major metallic elements.

Computing methods for icosahedral and symmetry-mismatch reconstruction of viruses by cryo-electron microscopy

Three-dimensional（3 D） reconstruction of icosahedral viruses has played a crucial role in the development of cryoelectron microscopy single-particle reconstruction, with many cryo-electron microscopy techniques first established for structural studies of icosahedral viruses, owing to their high symmetry and large mass. This review summarizes the computational methods for icosahedral and symmetry-mismatch reconstruction of viruses, as well as the likely challenges and bottlenecks in virus reconstruction, such as symmetry mismatch reconstruction, contrast transformation function（CTF）correction, and particle distortion.