Study of the electronic properties of a double-chain model for Al-rich-transition-metal quasicrystals,amorphous, and crystalline phases

The electronic properties of quasicrystals containing transition-metals are studied employing a simple double-chain model within the tight-binding approximation. We show that, under determined conditions, spectral fine structures are the result of competing localized- and extended-like states, which are not observed in traditional one-dimensional aperiodic models. These spectral features can explain the experimentally observed transport properties. From this point of view this double-chain model mimics the behavior of electrons in realistic icosahedral quasicrystals. Moreover, in view of the electronic transport, the relationship between quasicrystals and related amorphous phases is explained in a natural way.     

Wave function behavior in a Fibonacci lattice with electronic correlation

The electronic correlation and the spatial symmetry in quasicrystals are by themselves two very complicated research topics since we cannot use the reciprocal space to study quasicrystals and the electronic correlation in many-body system has been solved exactly only for one and for infinite dimension. We should note that even in one-dimensional quasiperiodic structures, the interactions between electrons have often been neglected and only few results have been obtained. In this work, we solved the case of two interacting particles in a Fibonacci lattice using a real-space method and the Hubbard model. The real-space method is based on mapping the correlated many-body problem onto an equivalent site- and bond-impurity tight-binding one in a higher dimensional space. Within the Hubbard Hamiltonian we obtained the behavior of the wave function and the analysis of these eigen-functions in the Fibonacci lattice when correlation is off shows a critical behavior.     

光子准晶研究进展

准晶是具有长程有序但不具有周期性的奇特结构。光子准晶以其优越的调控电磁波的能力和广阔的应用前景受到国内外学者的广泛关注。光子准晶不仅具有全带隙、局域态、负折射、近零折射率等一般特性,还因其独特的旋转对称性在激光和非线性频率转换等方面具有优势。本文简要回顾近年来光子准晶的发展历程,从理论研究与应用研究两方面介绍光子准晶研究的主要方向,并对其未来发展趋势进行了展望。     

Gorsky-Bragg-Williams theory of phase transitions in the approximants of icosahedral quasicrystals

The Gorsky-Bragg-Williams (GBW) theory has been modified to describe phase transitions caused by the ordering of two kinds of atoms in the even and the odd sublattices of the structures of icosahedral quasicrystals with the dodecahedral local order (DLO) and their approximants. The modified method is exemplified by numerical calculations of such phase transitions in the structures of several simplest approximants.     

Tetrahedral structures with icosahedral order and their relation to quasicrystals

The possible existence of quasicrystals in tetrahedral phases is considered. It is shown that one of the well-known crystalline silicon phases (the BC8 phase or silicon III) is characterized by the icosahedral local order with three-quarters of the interatomic bonds being directed along the fivefold axes of an icosahedron. This crystal is considered as an approximant of an icosahedral quasicrystal. Higher order approximants and other tetrahedral structures related to quasicrystals are also constructed. It is shown that in these structures, the formation of the intrinsic phason disorder with the preservation of the energetically favorable coordination number four is possible. The ab initio quantum-mechanical calculations for carbon and silicon show that, although all the considered phases are metastable, their energies only slightly differ from the energies of the corresponding stable phases.     

Continuous periodic to quasiperiodic structural transformations in crystalline and superlattice structures

Attention is focussed on the fact that the β—Mn, the σ—phase and the Al₅Ti₃ and the Al₁₁Ti₇ superlattice derivatives of the δ—AlTi phase all belong to a category of structures which comprises an identical periodic arrangement of square and rhombic tiles — the shapes of the rhombic tiles being different in each of these cases. While the first and the second structures constitute periodic approximants of the octagonal and the dodecagonal quasicrystals respectively, the last two (superlattice) structures are the approximants of a hypothetical quasiperiodic superlattice structure. The strip projection method has been used here to model the intermediate structures which arise during the continuous periodic to quasiperiodic transitions between the relevant structures and was found to be quite successful in explaining many of the related experimental findings.     

Formation of quasicrystals and metallic glasses in relation to icosahedral clusters

It has been widely accepted that quasicrystals and at least some metallic glasses are built up with icosahedral clusters. Information about the cluster structures can be obtained from crystalline counterparts. In this paper, we will describe the formation rules of bulk metallic glasses, originally developed for quasicrystals, by combining cluster structures with phase diagram features. We will introduce the e/a-constant and e/a-variant criteria for ternary systems, and e/a-constant and atomic size constant criteria for quaternary systems. We will show how the glass forming composition optimization is realized by applying these rules in the Zr–Al–Ni and Zr–Al–Ni–Cu systems. In both systems the optimized glass-forming composition is related to a common binary icosahedral cluster Zr₉Ni₄ derived from the fcc Zr₂Ni phase. A novel route to reach amorphous forming composition is also attempted by mixing Al-based quasicrystal-forming compositions with Zr.     

Hydrodynamics of layered and cubic quasicrystals

The dissipative processes associated with sound absorption in layered and cubic quasicrystals have been studied within the framework of the hydrodynamic approach. The decagonal, octagonal, and dodecagonal quasicrystals are considered as layered quasicrystals. Proceeding from the general theory, the complex law of dispersion is calculated for various directions of the propagation and polarization of sonic waves in layered and cubic quasicrystals. The effect of the phason modes on the process of sound absorption and the role of symmetry constraints are analyzed. The validity of the macroscopic consideration is discussed in terms of the theory of the generalized color symmetry.     

Search for possible structures of cubic approximants of icosahedral quasicrystals

Admissible structures of the approximants are obtained within the model of the dodecahedral local order (DLO) with due regard for the constraints imposed by the space symmetry. It is shown that the number of cubic approximants of icosahedral quasicrystals having a certain order and dodecahedral local order is finite and that the number of positions that can be occupied by the atoms from the unit cells of an approximant of each order is also finite. The corresponding estimates from above are made. In particular, it is shown that there exists only one structure for the 1/?1 approximant. It is also shown that it is possible to determine all the structures for any approximant of any order. The corresponding algorithm of the exhaustive search for these structures is suggested. The implementation of this algorithm provided the determination of all the structures of the 0/1 approximants and also some possible structures of the 0/1 and 1/1 approximants. The tables of possible approximant structures can be useful in the studies of new phases having approximant structures.     

Stable Al-Cu-Co decagonal quasicrystals

Stable Al₆₅Cu₂₀Co₁₅ and Al₆₅Cu₁₅Co₂₀ decagonal quasicrystals, sometimes using a few percent of Si to replace Al, can be grown directly from the melt as single grain decaprisms of up to 1 cm in length. Some salient features of their solidification processes, growth morphologies, surface structures, high resolution electron microscopic images, two dimensional quasicrystalline structure, relationship to one-dimensional quasicrystals, crystalline approximants, and dislocations are presented.     

Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals

The atomic dynamics of an Al-Ni-Fe decagonal quasicrystal and an Al-Cu-Fe icosahedral quasicrystal are investigated experimentally using the isotopic contrast method in inelastic neutron scattering. The partial spectra of thermal vibrations of copper, nickel, iron, and aluminum atoms in the decagonal and icosahedral quasicrystals are reconstructed directly from the experimental data without recourse to model concepts. The limiting energies and positions of the main features in the partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals are determined. It is established that, in the quasicrystals under investigation, the copper and nickel atoms are bound more weakly than the iron atoms and that the partial vibrational spectrum of aluminum atoms in the quasicrystals is considerably harder than the spectrum of pure metallic aluminum.     

Computer-aided evaluation of kossel patterns obtained from quasicrystals

For the evaluation of Kossel experiments on quasicrystals such as the decagonal phase of Al Co Ni or Al Co Cu Si a computer program called KOQUA has been written, which allows to simulate Kossel patterns of two- and three-dimensional quasicrystals as well as of every conventional crystal system. In some examples the application of the program is demonstrated.     

Growth of single crystals of quasicrystalline phases

To study the mechanical and physical properties of quasicrystals, single-crystal samples of large size (several centimeters) are necessary. However, obtainment of such single crystals meets a number of difficulties related to the peritectic character of melting of quasicrystalline compounds, high volatility and oxidizability of the initial components, low growth rate in aperiodic directions, and metastability of the most quasicrystalline structures. In this study, criteria for stable growth of quasicrystalline phases have been determined. The growth mechanisms of icosahedral and decahedral single crystals are described and experimental techniques of single-crystal growth are reviewed.     

Intensity and width of bragg reflections from imperfect icosahedral quasicrystals obtained by simulating atomic growth

The Bragg reflections from icosahedral quasicrystals obtained in the course of a computer experiment on the simulation of crystal growth have been studied. The computer experiments based on the theory developed earlier allow one to “grow” in a computer the imperfect quasicrystals of nanometer dimensions. It is shown that the absolute value of the structure factor can be close to the maximum possible one for crystals, i.e., to the structure factor in the case where all the atoms scatter in phase. The spectral width of Bragg reflections is studied, and it is shown that the reflection width depends not only on the quasicrystal dimensions in the physical space but, also, on the perpendicular component of the reciprocal-lattice vectors. The data obtained are compared with the known experimental data.     

Indexing of diffraction patterns and indentification of fault vector in decagonal Al65Cu20Co15 phase

Characterisations of defect structures such as pencil disorder, faulting in quasiperiodic layers and dislocation in decagonal quasicrystals has assumed importance currently. The first step towards a complete understanding of these defects requires easy and unambiguous method of indexing the diffraction patterns. The present study is devoted to this task. New rules have been framed for an unambiguous indexing of the diffraction patterns following the model of Mandal and Lele. The scheme is applied to the indexing of important electron diffraction patterns from a decagonal Al₆₅ Cu₂₀ Co₁₅ alloy and the indices for the direction of streaking in some of the diffraction patterns have been found and are of the type .     

Quasicrystals: Structure and properties

The structure and properties of quasicrystals are discussed. The short-and long-range atomic orders and the effect of these factors on the physical characteristics are considered. It is noted that investigations of the physical properties of quasicrystals at temperatures above room temperature should be performed. Promising applications are briefly outlined.     

Structural and energetic aspects of the differences between real and predicted polymorphs

In crystal structure prediction simulations based on lattice energy minimization, usually hundreds of structures within a reasonable range of lattice energy and density are found, whereas in practice, it is very rare to find more than a few polymorphs of the same compound. In the work presented here, this discrepancy is investigated from a structural and energetic point of view. 56 crystal structures of 26 polymorphic mono‐ and disubstituted aromatic compounds, extracted from the Cambridge Structural Database, have been analysed with respect to inter‐polymorphic structural similarity. For comparison, potential crystal packing arrangements of the substances have been predicted with molecular mechanics simulations using a generic force field. The predicted structures are analysed with respect to structural features and similarity, and with respect to the number of structures and their lattice energy. It is found that the real polymorphs studied in this work tend to be structurally quite dissimilar with regard to hydrogen bonding and spatial packing of structural motifs, while many of the predicted structures of a given compound are very similar to each other. The results suggest that structure and lattice energy alone cannot explain why so few polymorphs are found in practice compared to the very large numbers predicted in simulations. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gamma-resonance study of nanopowders with different dispersion and quasicrystalline phases in the Al-Cu-Fe system

⁵⁷Fe Mössbauer spectroscopy has been used to monitor synthesis of quasicrystals in the Al-Cu-Fe system and study the influence of the size of quasicrystalline particles in powder samples of the Al_63.1Cu_25.6Fe_11.3 alloy on the properties of synthesized materials. Quasicrystalline samples of different dispersion with particle sizes from 0.3 to 15 μm have been studied in the temperature range 80–295 K. It is established that iron atoms in an Al_63.1Cu_25.6Fe_11.3 quasicrystals occupy four types of structural positions, which differ in the atomic composition of the nearest environment. The results of the analysis suggest the dependence of the hyperfine-interaction parameters on the degree of sample dispersion. The components corresponding to iron atoms in both the surface layer and bulk of microparticles are isolated in the Mössbauer spectra. No magnetic hyperfine splitting has been found in the Mössbauer spectra in the entire temperature range. This fact suggests that a localized magnetic moment is absent in iron atoms.     

Regularities of plastic deformation in indentation on the (111) plane of NaCl single crystals

Dislocation structures arising in indentation on the (111) face of NaCl single crystals are studied by etch-pit technique. The deformation temperature varied in the interval from 77 to 520 °K. The effect of radiation defects introduced by γ-irradiation on the shape of dislocation rosette was investigated. Three types of dislocation rosettes depending on the experimental conditions were observed. A possible explanation of this phenomenon is proposed. It is shown that the polarity of plastic deformation observed under indentation is an universal phenomenon which is revealed in the temperature range from 77 to 470 °K. The phenomenon of dislocation rosette inversion was first observed.