Jumps in icosahedral quasicrystals

Atomic jumps in icosahedral (AlCu)Li quasicrystals and related structures have been studied by molecular dynamics simulations. In quasicrystalline structures jumps exists with jump vectors much shorter than an average nearest neighbor distance. This is a consequence of the phasonic degree of freedom. The jumps therefore are called flips and the sites connected by the jump vector are denoted alternative positions. We find that the atoms in the quasicrystal structures studied here do not flip to alternative positions as proposed and observed in decagonal or dodecagonal quasicrystals but jump to sites which are at least an ordinary interatomic distance apart. Furthermore we observe two diffusion regimes: below about 55% of the melting temperature only small (AlCu) atoms carry out ring processes whereas at higher temperatures both kinds of atoms contribute to long-range diffusion. Received 21 July 1999     

Elastic Green's function of icosahedral quasicrystals

The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom. We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling between the phonons and phasons is small. Received: 18 December 1997 / Accepted: 6 March 1998     

Decagonal quasicrystals

Following the discovery of two dimensional quasicrystals in rapidly solidified Al-Mn alloys by us and L. Bendersky in 1985, a number of fascinating studies has been conducted to unravel the atomic configuration of quasicrystals with decagonal symmetry. A comprehensive mapping of the reciprocal space of decagonal quasicrystals is now available. The interpretation of the diffraction patterns brings out the comparative advantages of various indexing schemes. In addition, the nature of the variable periodicity can be addressed as a form of polytypism. The relation between decagonal quasicrystals and their crystalline homologues will be explored with emphasis on Al₆₀Mn₁₁Ni₄ and ‘Al₃Mn’. It will also be shown that decagonal quasicrystals are closely related to icosahedral quasicrystals, icosahedral twins and vacancy ordered phases.     

Disorder diffuse scattering from quasicrystals

Very sharp Bragg reflections accompanied by diffuse scattering phenomena are typical for most stable quasicrystals. The correlation length of the quasiperiodic average structure can reach several micrometers as proved by high-resolution X-ray diffraction experiments. This corresponds to a structural perfection of some quasicrystals similar to that of silicon. Nevertheless, the omnipresent diffuse scattering indicates significant deviations from a strictly ordered quasiperiodic structure especially in the case of decagonal phases. These structural deviations may be caused by phason fluctuations, by disorder in the packing of the basic atomic clusters, by the formation of nanodomains, by chemical disorder, or by superstructure formation on a short-range scale. Characteristic examples of different types of structural disorder present in icosahedral and decagonal quasicrystals are reported. The diffuse scattering phenomena in decagonal Al-Co-Ni as a function of composition and temperature are discussed in more detail.     

Local structure of Co and Ni in decagonal AlNiCo investigated by polarized EXAFS

The local structure of cobalt and nickel in single crystals of decagonal quasicrystals with composition Al_71.5Ni_15.5Co₁₃ and Al₇₅Ni_14.5Co_10.5 have been studied by polarized EXAFS. Significant differences between the Ni and Co local environments have been detected. The effective absence of the 4 ? periodicity along the decagonal axis in these QCs is confirmed and indications about its reasons are presented. Received 26 July 2000 and Received in final form 20 October 2000     

Isotropic and anisotropic physical properties of quasicrystals

Since quasicrystals have positional and orientational long-range order, they are essentially anisotropic. However, the researches show that some physical properties of quasicrystals are isotropic. On the other hand, quasicrystals have additional phason degrees of freedom which can influence on their physical behaviours. To reveal the quasicrystal anisotropy, we investigate the quasicrystal elasticity and other physical properties, such as thermal expansion, piezoelectric and piezoresistance, for which one must consider the contributions of the phason field. The results indicate that: for the elastic properties, within linear phonon domain all quasicrystals are isotropic, and within nonlinear phonon domain the planar quasicrystals are still isotropic but the icosahedral quasicrystals are anisotropic. Moreover, the nonlinear elastic properties due to the coupling between phonons and phasons may reveal the anisotropic structure of QCs. For the other physical properties all quasicrystals behave like isotropic media except for piezoresistance properties of icosahedral quasicrystals due to the phason field.     

Recent advances in the study of quasicrystals

Some recent advances in the study of quasicrystals at Ames Laboratory are reviewed. In particular, growth from the melt of large, high-quality, single-grain quasicrystals is described in detail for icosahedral R-Mg-Zn and decagonal Al-Ni-Co. In addition, the magnetic properties of the rare-earth-containing icosahedral R-Mg-Zn quasicrystals are discussed.     

Structure and composition of cleaved and heat-treated tenfold surfaces of decagonal Al-Ni-Co quasicrystals

We investigated cleavage surfaces perpendicular to the tenfold direction of as-grown decagonal Al-Ni-Co quasicrystals by scanning tunneling microscopy, Auger electron spectroscopy, and scanning electron microscopy. The cleavage surface is determined by a cluster-subcluster structure. The image contrast of the smallest features, 1-2 nm in diameter, is related to the columnar atom arrangements extending perpendicular to the cleavage plane, which are predicted by current models of the decagonal quasicrystal structure. No voltage dependence of the STM images is observed. The presence of surface states and an enhanced density of states are discussed. Heat-treatments of the cleaved Al-Ni-Co quasicrystal surfaces show nearly no changes in chemical composition and structure up to about 750 °C. This is correlated with a much lower concentration of vacancies in as-grown decagonal Al-Ni-Co quasicrystals as compared to that in as-grown icosahedral Al-Pd-Mn quasicrystals.     

Dynamics of phason fluctuations in the i-AlPdMn quasicrystal

We report on the study of the dynamics of long wavelength phason fluctuations in the i-AlPdMn icosahedral phase using coherent x-ray scattering. When measured with a coherent x-ray beam, the diffuse intensity due to phasons presents strong fluctuations or speckles pattern. From room temperature to 500 degrees C the speckle pattern is time independent. At 650 degrees C the time correlation of the speckle pattern exhibits an exponential time decay, from which a characteristic time tau is extracted. We find that tau is proportional to the square of the phason wavelength, which demonstrates that phasons are collective diffusive modes in quasicrystals, in agreement with theoretical predictions.     

Basics of NMR line shape in quasicrystals

The measurement and analysis of broad nuclear magnetic resonance (NMR) spectra of quasicrystals require experimental methods and theoretical interpretations different from NMR investigations of regular periodic crystals. Frequency- and field-sweep methods for recording quasicrystalline NMR spectra are described and compared with the measurement of²⁷Al NMR spectra of icosahedral AlPdMn and decagonal AlNiCo quasicrystals. The nuclear spin interactions that determine the NMR line shape are the same for both types of the above Al-based quasicrystals, where the electric quadrupolar interaction with the broad distribution of its electric field gradient parameters predominantly determines the shape of the broad satellite “background” intensity. The essential observations are an almost isotropic²⁷Al NMR spectrum of the icosahedral quasicrystals and a strong angular dependence of the spectrum of decagonal quasicrystals.     

Anisotropy of the phonon-phason dynamics and the pinning effect in icosahedral AlPdMn quasicrystals

A minimal model of the phonon-phason dynamics in icosahedral quasicrystals with inclusion of the pinning effect is suggested. Resonant attenuation of low-frequency acoustic waves in the temperature range corresponding to thermal activation of phasons is considered. In the long-wave length limit, the velocity of acoustic phonons is isotropic; however, the phonon-phason coupling causes anisotropy of the velocity and of the attenuation of acoustic waves with small wave vectors. These effects manifest themselves most strongly at an acoustic wave frequency close to the inverse relaxation time of phasons with the same wave vector. The pinning effect can cause a significant decrease in the anisotropy of the velocity and of attenuation of acoustic waves.     

The effect of phason defects on the radiation-induced swelling of quasicrystalline materials

The radiation-induced vacancy swelling of quasicrystals is considered. In quasicrystals, the dislocation kinetics involves the formation of phasons: vacancy- and interstitial-like localized topological defects. Phasons interact with radiation-induced point defects (PD; vacancies and interstitials) and influence the swelling behavior of quasicrystals. After absorption of vacancies, phasons of the interstitial type transform into phasons of the vacancy type and vice versa. In other words, phasons are the recombination centers of alternating polarity for PD. Assuming that (i) the production rate of phasons is proportional to the dislocation climbing rate and (ii) voids are the sinks for mobile phasons, the set of rate equations for PD and phasons is formulated and analyzed both analytically and numerically. It is shown that the swelling rate is lower in quasicrystals compared with crystals. Growth rates of loops and voids, as well as the swelling rate, strongly depend on the phason concentration which is controlled by phason diffusion to sinks.     

Inelastic neutron scattering study of the dynamics of the AlNiCo decagonal phase

The dynamics of the decagonal AlNiCo phase has been investigated on a single-grain quasicrystalline sample using inelastic neutron scattering. The decagonal structure can be viewed as a periodic stacking of quasiperiodic planes. The anisotropy between the modes propagating in the periodic and quasiperiodic directions is found to be much weaker than theoretically predicted. A strong resonance splitting is observed at an energy transfer of 15 meV for transverse modes polarized in the quasiperiodic plane. Received: 18 November 1998 / Accepted: 27 November 1998     

Quasicrystal surfaces: structure and growth of atomic overlayers

We review recent developments in surface studies of single-grain quasicrystals under ultra high-vacuum conditions, focusing on two different topics: surface structure and growth of atomic overlayers on surfaces. Quasicrystalline phases are currently used for investigation of the first topic are icosahedral (i) Al-Pd-Mn, i-Al-Cu-Fe, i-Al-Cu-Ru, i-Ag-In-Yb and decagonal (d) Al-Ni-Co, and d-Al-Cu-Co. We report the progress made with all of these phases. The second topic covers the study of single-element overlayer growth by vapor deposition.     

Shear modulus and compliance in the range of the dynamic glass transition for metallic glasses

High-resolution synchrotron-radiation powder diffraction experiments were performed to observe structural changes induced by hydrogen loading in rapidly-quenched Ti-Zr-Ni alloy ribbons with dominant icosahedral character. Lattice expansion effects due to hydrogen storage in Ti-Zr-Ni quasicrystals as well as phonon and phason disorder coefficients are obtained from an analysis of diffraction linewidths. Received: 26 August 1997 / Revised: 8 January 1998 / Accepted: 10 February 1998     

How do quasicrystals grow?

Using molecular simulations, we show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal nucleus to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In the system under investigation, which forms a dodecagonal quasicrystal, we show that this process occurs through the assimilation of stable icosahedral clusters by the growing quasicrystal. Our results demonstrate how local atomic interactions give rise to the long-range aperiodicity of quasicrystals.     

Thermodynamics of equilibrium properties of quasicrystals

Thermodynamics of equilibrium properties of crystals has been generalized to the case of quasicrystals. Based on it, relations between direct and converse effects, and some relations between the coefficients measured under different conditions have been derived. By group representation theory, physical property tensors have been derived for two-dimensional pentagonal, octagonal, decagonal and dodecagonal, and three-dimensional icosahedral and cubic quasicrystals.     

Dislocations and mechanical properties of icosahedral quasicrystals

In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals.     

Composition rule for Al–transition metal binary quasicrystals

Compositions of Al–transition metal (TM) binary quasicrystals are revisited using the cluster-plus-glue-atom model. These compositions all conform to a unified cluster formula [icosahedron](glue)₁, where the icosahedron is taken from a crystalline approximant. In a given binary system, icosahedral and decagonal quasicrystals are expressed by the same icosahedron but glued, respectively, by one Al and one TM, and their e/a ratios fall close to 1.86 and 1.71–1.79, respectively. Their relative stabilities are discussed by referring to compositions satisfying the fully filled TM-3d states according to Häussler's resonance model.     

Two-dimensional quasicrystals of decagonal order in one-component monolayer films

By using Monte Carlo simulations we demonstrate that atomic monolayers formed on a crystalline surface may exhibit quasicrystalline decagonal order. It is shown that the stability of two-dimensional quasicrystals (QCs) is determined by the misfit between the adsorbate and the surface lattice and by the corrugation of the surface potential. QCs may be stable at the ground state or develop from the compressed commensurate c(2 x 2) structure, via the first-order phase transition at finite temperatures. The decagonally ordered phase melts into a partially ordered liquidlike phase, which then disorders via a continuous Ising-like transition.