Structure analysis of two-dimensional quasicrystals

Aperiodic materials, such as two-dimensional quasicrystalline structures, show characteristic elements in transmission electron microscopy images that are closely related to structure elements in the corresponding material. Although the arrangement of these structure elements fundamentally influences the properties of the two-dimensional quasicrystalline structures, it cannot be determined in a satisfactory way by conventional diffraction-based methods. We have developed an automated procedure for analysing images obtained by high-resolution transmission electron microscopy. The method, which is based on image processing, determines the two-dimensional arrangement of the characteristic features and enables subsequent statistical data analysis. It is illustrated with new tiling analyses of highly perfect decagonal Al-Co-Ni quasicrystals.     

X-ray study of phason strain in Al-based quasicrystals

Abstract

X-ray powder diffraction spectra have been measured for melt-spun Al-Si–Mn, Al-Cu–Fe and Al-Li–Cu and Bridgman-grown Al-Li-Cu quasicrystals to investigate the phason strain frozen during the solidification process. For the melt-spun samples, most of the peaks have a shoulder or a tail which is attributed to the anisotropic linear phason strain. The peak shapes for the three melt-spun samples are essentially the same, which indicate that the same type of linear phason is quenched in these samples. In contrast, symmetric peak shapes without shoulders nor tails are seen for the Bridgman-grown Al-Li–Cu, indicating that it contains little linear phason strain.

Our findings are discussed with respect to the three linear phason models which can be derived by degradation of the symmetry from ideal icosahedral group m35 to its maximal subgroups 3m, m3 and 5m. Of these three, the model for 3m reproduces best the observed shapes and widths of the peaks.     

Twinning of quasicrystals and related structures

Abstract

We consider for the first time twinning in quasicrystals and related structures in a systematic manner. The twinning operations are considered in the framework of six-dimensional crystallography. The number of twin variants and the symmetry of twinned aggregates are also discussed. It is shown that essentially two different types of interface can arise between any two twin variants.     

Dislocations in quasicrystals and their interaction with cluster-like obstacles

A dislocation moving through a quasicrystal leaves in its wake a fault denoted a phason wall. For a two-dimensional model quasicrystal the disregistry energy of this phason wall is studied to determine possible Burgers vectors of the quasicrystalline structure. Unlike periodic crystals, the disregistry energy is an average quantity with large fluctuations on the atomic scale. Therefore the dislocation core structure and mobility cannot be linked to this quantity, e.g. by a Peierls-Nabarro model. Atomistic simulations show that dislocation motion is controlled by local obstacles inherent to the atomic structure of the quasicrystal.     

A general solution of elasto-hydrodynamics of two-dimensional quasicrystals

Dynamic problems of quasicrystals are analysed within the framework of continuum mechanics. Phonon excitations yield wave propagation while phason excitations yield atomic diffusion. Phonon fields obey the equations of motion and phason fields obey the diffusion equations. Governing equations of elasto-hydrodynamics of decagonal quasicrystals combine characteristics of the equations of motion and diffusion. A general solution is derived in terms of two introduced auxiliary functions. It provides an easy-to-use approach to solve initial-boundary value problems encountered in elasticity problems for quasicrystals. Explicit expressions for displacements and stresses in the phonon and phason fields can be directly obtained. A derived general solution is also applicable to some planar quasicrystals such as pentagonal quasicrystals with fivefold symmetry.     

On the short-range order in Al-Mn quasicrystals during low-temperature ageing

Abstract

We report the evolution of diffuse intensity during the low-temperature ageing of Al-Mn quasicrystals. This is taken as evidence of short-range order in the icosahedral phase prior to its decomposition. The implication of these diffuse intensities is discussed     

Four-phonon model of soft-matter quasicrystals for studying thermodynamics

Four-phonon model of soft-matter quasicrystals is proposed, in which there are three solid phonons and one fluid phonon. With this model, the vibration spectrum of soft-matter quasicrystals can be obtained. The generalized Debye frequency, generalized Debye temperature and the thermodynamic functions of soft-matter quasicrystals are observed. The results on the specific heat of soft-matter quasicrystals demonstrate the contributions of both solid phonons and fluid phonon, respectively.     

Elasto-hydrodynamics of quasicrystals with a crack under sudden impacts

ABSTRACT

In this paper, a mode-III crack in one-dimensional (1D) hexagonal quasicrystals subjected to anti-plane impact loading is analyzed. The elasto-hydrodynamics of quasicrystals is adopted, where the phonon field obeys wave equation, and the phason field obeys diffusion equation. By introducing a new auxiliary function, the coupled wave-diffusion equations are converted to a single higher-order partial differential equation. With the aid of the Laplace transform, an associated mixed initial-boundary value problem is reduced to two sets of dual integral equations, and then transformed into two coupled Fredholm integral equations of the second kind. Numerical results of transient phonon and phason stress intensity factors and crack-centre displacement jump are obtained through the numerical inversion of the Laplace transform and are presented graphically to show the influences of the phason.     

Thermal expansion of icosahedral Al-Pd-Mn and decagonal Al-Cu-Co quasicrystals

Thermal expansion measurements have been performed by X-ray diffractometry on icosahedral Al-Pd-Mn (i-(Al-Pd-Mn)) in the temperature range between 10 and 700K and on decagonal Al-Cu-Co (d-(Al-Cu-Co)) in the range between 100 and 750K. The linear thermal expansion coefficient alpha(T) of i-(Al-Pd-Mn) is about half of that for the pure aluminium phase at room temperature and does not show a negative thermal expansion at low temperatures. The degree of anisotropy in the thermal expansion of d-(Al-Cu-Co) is small; the ratio of the average alpha between the tenfold periodic direction and a quasiperiodic direction perpendicular to it is 0:93 +/- 0:05. The Gruneisen parameter gamma(T) has been evaluated from the measured alpha(T). gamma for d-(Al-CuCo) is almost isotropic, similar to alpha. The gamma values for the two phases lie in the range between 1.5 and 1.8, which are comparable with those for conventional metallic crystals. They are almost constant over the temperature range studied.     

Interaction of a dislocation with an elliptical hole in icosahedral quasicrystals

The interaction between a dislocation and an elliptical hole in icosahedral quasicrystals is considered. An explicit expression for the complex potential is derived using the extended Stroh formalism. Based on the conformal mapping method and a perturbation technique, closed-form solutions are obtained. The field intensity factors at a crack tip and the image forces on the dislocation arising from the crack are calculated. The effects of phonon–phason elastic coupling on the mechanical behavior are also observed.     

Production of single quasicrystals and their electrical resistivity in the Al-Pd-Re system

Single Al-Pd-Re icosahedral quasicrystals with a maximum diameter of 5mm have been grown by a slow cooling method on the basis of a partial phase diagram determined in the present study. Laue X-ray and electron diffraction verified the highly ordered structure of the single icosahedral quasicrystals. The electrical resistivity rho of the single quasicrystals was measured to be 2000- 4000muOmegacm at 300K and 3000-6000muOmegacm at 2K, revealing a negative temperature dependence with a rho_4.2K/rho_300K value smaller than 2.     

Dislocation density evolution upon plastic deformation of Al-Pd-Mn single quasicrystals

Dislocation density studies have been performed on icosahedral Al-Pd-Mn single quasicrystals after plastic deformation and after subsequent heat treatment. The deformation tests were carried out at a constant strain rate of 10- 5 s-1 at temperatures between 695 and 820 C. The heat treatments were performed at 730 C, corresponding to one of the deformation temperatures. The development of the dislocation density during heat treatment and that during plastic deformation are compared. The experimental data are interpreted using a kinetic equation, which describes the evolution of the dislocation density during deformation. Numerical values for the dislocation multiplication constant and the annihilation rate for icosahedral Al-Pd-Mn are presented.     

Stable icosahedral quasicrystals in the Ag-In-Ca,Ag-In-Yb,Ag-In-Ca-Mg and Ag-In-Yb-Mg systems

On the basis of the idea that a quasicrystal is a compound in which the average number of valence electrons per atom is around 2.0 and that its formation is dominated by atom size, stable icosahedral quasicrystals have been successfully synthesized in Ag-In-Ca, Ag-In-Yb, Ag-In-Ca-Mg and Ag- In-Yb-Mg systems. The Ag-In-Ca and Ag-In-Yb icosahedral quasicrystals have stoichiometry around Ag 42 In 42 Ca 16 and Ag 42 In 42 Yb 16 . The Ag-In-Ca-Mg and Ag-In-Yb-Mg quasicrystals form in the composition ranges Ag42 x /2 In 42 x /2 Ca 16 Mg x ( x =0-7.5 at.%) and Ag 42 x /2 In 42 x /2 Yb 16 Mg x ( x =0-10 at.%). Electron diffraction studies confirmed that the icosahedral quasicrystals have a primitive lattice. The average number of valence electrons per atom in all these quasicrystals is 2.0.     

Formation and hydrogen adsorption properties of Ti-Hf-Ni quasicrystals and crystal approximants

The formation of a high-order rational approximant (RA) phase in rapidly quenched Ti-Hf-Ni alloys and the hydrogen absorption properties of that phase are reported. Electron diffraction patterns show systematic shifts of the diffraction spots from their expected positions for the icosahedral phase (i-phase); the diffraction patterns are consistent with those expected for a 3/2 RA phase RA-(Ti-Hf-Ni). Based on differential scanning calorimetry studies, RA-(Ti-Hf-Ni) is metastable, transforming between 350 and 500°C to a quasicrystal with strong phason disorder. This crystallizes at 620°C to a Ti 2 Nitype phase. RA-(Ti-Hf-Ni) readily absorbs hydrogen, up to 1.2 hydrogen atoms per metal atom ([H][M] =1.2). Pressure-composition isotherm studies for gasphase loading show that the pressure plateau for RA-(Ti-Hf-Ni) is similar to that observed for the i-(Ti-Zr-Ni) phase, although it occurs at as lightly higher pressure and extends over a smaller range of hydrogen concentrations. Unlike i-(Ti-Zr-Ni), no irreversible hydride phase forms with hydrogen loading at 250°C, suggesting that RA-(Ti-Hf-Ni) may have superior cycling properties, of interest for hydrogen storage applications.     

Microstructure of icosahedral Al-Pd-Mn quasicrystals deformed at room temperature in an anisotropic confining medium

Plastic deformation of Al-Pd-Mn icosahedral quasicrystals has been achieved at room temperature using a high-confining-pressure medium. The deformation microstructure, investigated by transmission electron microscopy, is characterized by long straight bands of dislocations. A detailed analysis of the dislocation configurations indicates that the plastic deformation is controlled by dislocation glide.     

Sign determination of the 57 Fe electric-field gradient in Al-based crystals and icosahedral quasicrystals

Abstract

The icosahedral quasicrystals i-AIMn, isomorphically substituted by 28 at.% Fe or by a mixture of (CrFe) atoms, have been studied for the first time by in-field Mössbauer spectroscopy in order to determine the sign and asymmetry parameter of the dominant electric-field gradient (EFG) term. In addition, the orthorhombic o-Al(MnFe) and cubic α- and hexagonal β-Al(MnFe)Si crystalline phases have been studied. We show that the previous Mössbauer results are inadequate for determining whether there are two sites in the quasicrystalline structure in the ratio of the golden number. Our results for i-Al(MnFe) show that the dominant EFG is negative, with an asymmetry parameter of about 0·6. For i-Al(CrFe), essentially no deviations are found from the model of Czjzek or the Gaussian isotropic model. One crystalline phase, the hexagonal β phase, is found to have a very similar quadrupole effect to that found in i-Al(MnFe). In addition it is found that this phase undergoes a change which is at least partly of magnetic origin.     

Determination of the Burgers vector of dislocations in icosahedral quasicrystals by a high-resolution lattice-fringe technique

A technique for the determination of the full six-dimensional Burgers vector characterizing a dislocation in an icosahedral quasicrystal is presented. It is based on the lattice-fringe analysis of two high-resolution transmission electron microscopy images taken at two different sample orientations. As an example we present the analysis of a dislocation in a bent icosahedral Al-Pd-Mn quasicrystal. We obtained a Burgers vector B = A₀[-2,0,3,-2,3,0] where A₀ = 0.645nm is the six-dimensional hyperlattice constant. This result is consistent with previous results obtained by diffraction contrast analysis and convergent-beam electron diffraction techniques.     

An analytic solution of initial boundary value problem for 3D quasicrystals in half space

In this article, initial boundary value problem for 3D quasicrystals in half space is considered. An analytic method is proposed for special form of initial conditions and nonhomogeneous term. It is explained that a weak solution of the problem can be constructed in the similar form of data by using symbolic calculations.     

Plastic deformation behaviour of decagonal Al70Ni15Co15 single quasicrystals

High-temperature deformation experiments have been performed on decagonal Al₇₀Ni₁₅Co₁₅ single quasicrystals at a constant strain rate of 10^-5s^-1 in the temperature range between 700 and 860°C. The samples were deformed in compression with the compression axis in different orientations, parallel to, inclined by 45° and perpendicular to the tenfold symmetry axis. Stress relaxation tests and temperature changes were carried out to determine thermodynamic activation parameters. The flow stress and the activation enthalpy were found to depend on the sample orientation whereas dependences of the activation volume and the stress exponent on the orientation were not observed. Additionally, deformation tests were performed on samples of the basic Co-rich modification of the decagonal phase at the temperature of 860°C in the same three orientations. The deformation behaviours of the two different modifications of the decagonal phase are discussed.     

Conduction-electron mediated 1H nuclear spin-lattice relaxation in Ti45Zr38Ni17H x icosahedral quasicrystals

Nuclear magnetic resonance spin-lattice relaxation rates for ¹H in quasicrystalline Ti₄₅Zr₃₈Ni₁₇H _x are presented as a function of temperature and hydrogen concentration x. The temperature dependence demonstrates that the relaxation is via interaction with conduction electrons. The relaxation rate is extremely sensitive to hydrogen content, with the rate changing by a factor of as much as two for samples that differ in x