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.     

Quasicrystal as a locally deformed crystal structure

Lattice models for a two-dimensional octagonal quasicrystal and a three-dimensional icosahedral quasicrystal with the icosahedral-dodecahedral local order are introduced. It is shown that an octagonal quasicrystal may be obtained as a result of the local deformation of an ideal square atomic lattice. Possible paths of structural transformations between various phases of an AlPd crystal are determined. It is shown that icosahedral quasicrystals of aluminum alloys with transition metals can be considered to be a result of the local distortions of an ideal fcc lattice of elemental aluminum induced by a transition metal impurity.     

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.     

Approximants of icosahedral quasicrystals: Atomic structure, inherent defects, and superstructural ordering

The structural features of approximants of icosahedral and decagonal quasicrystals and new unusual approximants (rhombohedral AlPd and cubic Al₆₈Pd₂₀Ru₁₂) are considered. It is shown that most approximants can be described in terms of universal local ordering of atoms, in which the nearest neighbors of each atom occupy the vertices of an almost ideal dodecahedron: the so-called dodecahedral local ordering. A set of general atomic motifs in the approximants of different orders is found for quasicrystals of different types. It is shown that the dodecahedral local ordering can be easily described by the project method, in which the basis vectors directed along icosahedral threefold axes are used. Different types of defects inherent in dodecahedral local ordering are analyzed.     

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.     

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.     

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.     

Distortions of the atomic structure of 2/1 approximants of icosahedral quasicrystals

Ideal structures of several 2/1 approximants of icosahedral quasicrystals with the sp. gr. Pm \(\overline 3 \) and Pa \(\overline 3 \) have been constructed. It is shown that most atoms have dodecadhedral local coordination. The structural features of the crystals studied have been analyzed. It is found that displacements of atoms from ideal positions in real crystals tend to increase with an increase in the distance to the center of the approximant projection on the perpendicular space. Large displacements are generally related to the presence of very close neighbors in the ideal structure of the approximant. The importance of the investigation of approximants as a source of information about the structure of polyatomic nanoclusters is indicated.     

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.     

Quasicrystalline and related phases in titanium based alloy systems

Amongst the non-aluminium based quasicrystalline alloys, investigations of titanium containing alloys in regard to the occurrence and stability of quasicrystalline phases have aroused considerable interest in recent years. Employing X-ray and TEM techniques a systematic investigation of the influence of substitution for Fe by Si and Ni on the stability of icosahedral phase in rapidly quenched Fe-Ti alloy has been carried out. The occurrence of metastable phases including commensurately modulated phase and the decagonal phase in Fe-Ti-Si system have been found. In addition, the occurrence ofstructural disorder manifested by arcs of diffuse scattering in diffraction patterns and anisotropy in the shape of idffraction spots has also been pointed out. It has been observed that 6 at.% of Si in Fe-Ti-Si system results in the formation of single-phase icosahedral quasicrystals. We have shown that contrary to some earlier reported results on Ti₂Ni, Ti₂Ni(Si) and Ti₅₆Ni₂₃Fe₅Si₁₆ alloys do not possess the icosahedral phase. In Ti₆₈Fe_26−xNi_xSi₆ alloy system, icosahedral phase formation ability is limited to the value of x < 9. The occurrence of icosahedral phase in these alloy systems has been analysed in terms of e/a ratio.     

Rosette patterns – a common description for both crystalline and quasicrystalline structures

Crystalline structures are generally considered to be the normal case and quasicrystals a rare peculiarity. An attempt has been made to find a generalized view for both of these long range ordered atomic arrangements. It has been shown that they can be understood in terms of an angle‐periodic rosette pattern. The three‐dimensional wall paper design patterns, normally used to describe crystalline structures, are a large subgroup of this rosette pattern supergroup, which have the additional characteristics of translational periodicity. The topic is dealt with from a combined crystallographic and solid state physics point of view. The covalent bonding in the quasicrystals is an important prerequisite for their appearance.     

Experimental study of the dynamics of Zn2Mg Laves phase

A way to address the problem of phonons in quasicrystals (QCs) is to compare their dynamical response with that of approximant crystalline structures. Although the Zn₂Mg Laves phase is not a periodic approximant of a QC phase, its structure is a periodic packing of Friauf polyhedra which are basic units involved in the construction of larger icosahedral atomic clusters found in Frank–Kasper type quasicrystals. We report on the experimental study of the lattice dynamics of the Zn₂Mg hexagonal phase using inelastic neutron scattering with a particular attention devoted to the behavior of transverse acoustic (TA) modes. For TA modes propagating along the (T) direction, polarized along the c axis, there is a strong bending of the dispersion curve. Whereas the broadening rate is rather slow, going like q², a strong coupling of the acoustic mode with an higher energy optical mode takes place. For TA modes propagating along the (Δ) direction, polarized in the hexagonal plane, the dispersion relation reaches much higher energy: the broadening rate is however steeper, going like q⁴, most likely due to a mixing of several excitations in the spectral response. In any case, the width of acoustic and optical excitations is found much smaller than in quasicrystals.     

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.     

Study on as-cast microstructures and solidification process of Mg-Zn-Y Alloys

The microstructures and phases of as-cast Mg-Zn-Y alloys were investigated by means of scanning electron microscopy (SEM), energy-dispersive spectrum (EDS), X-ray diffraction (XRD), and transmission electron microscopy (TEM) in this study. Stable icosahedral Mg₃₀Zn₆₀Y₁₀ quasicrystals were obtained using common casting technique. With increasing Y content, the contents of quasicrystals increased, the distribution of quasicrystals was improved, and the morphologies of quasicrystal and other microstructures of Mg-Zn-Y alloys showed different characteristics. In addition, the solidification process of Mg-Zn-Y alloys was analyzed. Icosahedral Mg₃₀Zn₆₀Y₁₀ quasicrystalline phase is easy to nucleate in slow cooling.     

Combined atomic ordering in the A and B sublattices of perovskite structure

The simultaneous ordering of cations in the A and B sublattices of cubic perovskite structure has been investigated by the group-theoretical method. It is found that 147 ordered phases may exist. Among them, there may be 121 phases with simultaneous cation ordering in the 1(a)- and 1(c) positions of perovskite structure. It is shown that 53 phases are described by improper order parameters related to cation ordering, the formation of 56 phases is related to improper rotations of octahedra, and 15 phases are improper ferroelectrics. Calculated structures of some types of ordered low-symmetry perovskite modifications are presented.     

Efficient ITO–Si solar cells and power modules fabricated with a low temperature technology: Results and perspectives

ITO–SiO_x–nSi semiconductor–insulator–semiconductor (SIS) structures have been produced with a simple spraying technique. It is shown that the structures obtained in such a way may be considered as an induced p–n diode, in which the polycrystalline tin–doped indium oxide (ITO) layer spray deposited on the preliminary treated silicon surface leads to an inversion p-layer at the interface. Solar cells with an active area of 1–4 cm² have been fabricated based on ITO–SiO_x–nSi structures and studied. Under AM0 illumination conditions, the efficiency is nearly 11%, whereas it exceeds 12% for AM1.5 illumination conditions. The theoretical analysis provided in this work shows a good agreement with experimental results and allows for predicting the efficiency of the cells depending on the silicon electro-physical properties.     

Crystal chemistry of germanates: Characteristic structural features of Li,Ge-germanates

Crystallochemical classification of eleven compounds from the Li-germanate family is suggested. Depending on the set of the primary building units (PBU) (M-octahedra of the composition [GeO₆] and T-tetrahedra of the composition [GeO₄]) and the type of their “condensation,” these germanates are divided into three crystallochemical groups: framework MT-structures (four phases), condensed MT-structures (two phases), and tetrahedral T-condensed structures (five phases). The structural characteristics of the framework Li,Ge-germanates are considered, i.e., their symmetry, crystallographically independent sets of the primary building units, framework architecture, and the types of chains and layers of the (Ge,O)-radicals.     

Zn–Mg–(Y,RE) Quasicrystals: Growth Experiments and Phase Diagrams

We report about our work on the preparation and characterization of icosahedral Zn–Mg–(Y, RE) (RE = rare earth element) quasicrystals. We obtained single grains of the icosahedral (i-) phase via slow cooling experiments and with the Bridgman technique. We revealed a composition range of the i-phase, within which the structure changes. Additionally a systematic investigation of the Zn–Mg–Y phase diagram, including the determination of the primary solidification area of the icosahedral phase is presented. It was found that for a growth from the melt a starting composition with a low Y-content is needed.     

Remote plasma deposition of microcrystalline silicon thin-films: Film structure and the role of atomic hydrogen

Microcrystalline silicon films grown in an expanding thermal plasma, i.e. in the absence of ion bombardment, are found to be porous and rich in nano-sized voids. By carrying out an extensive investigation on the material quality of films deposited in the amorphous-to-microcrystalline transition regime, on the microcrystalline silicon growth development, and on the influence of the substrate temperature, it is concluded that the inferior material quality is related to the lack of a sufficient amount of amorphous silicon tissue. As possible cause for the insufficient amount of amorphous silicon tissue, the interaction of atomic hydrogen with amorphous silicon films has been studied in order to highlight a possible competition between film growth and H-induced etching of amorphous silicon, and between film growth and H-induced surface/film modification. The etch rates obtained are too low to compete with film growth. Furthermore, atomic H cannot be considered responsible for the poor quality of amorphous tissue present in the microcrystalline silicon films, as the H up-take mainly takes place in divacancies. These results suggest that ion bombardment may be a necessary condition to provide good quality microcrystalline silicon films.