Calculation of vibrational spectra of an icosahedral quasicrystal AlCuFe

Vibrational spectra of an icosahedral quasicrystal AlCuFe have been calculated on the basis of a crystalline 1/1 approximant by the recurrence method. To describe the interaction of atoms in a quasicrystal, the semiempirical EAM model was used. It is shown that the calculated spectra are in satisfactory agreement with the experimental neutron inelastic scattering data.     

Interatomic force interaction in an i-AlCuFe quasicrystal

Partial spectra of thermal vibrations of Al, Cu, and Fe atoms in an icosahedral quasicrystal have been obtained by the isotopic-contrast method in inelastic neutron scattering. Joint analysis of these results and the published data on the atomic and electronic structures of the icosahedral i-AlCuFe quasicrystal has been performed. A physical model of the quasicrystal structure is proposed that is in agreement with the existing experimental data and qualitatively describes the peculiarities of interatomic interaction.     

Raman study of lattice dynamics in quasicrystals

We present the first Raman investigation of icosahedral quasicrystals. Broad structured bands in the energy range up to ~500 cm^− 1 have been observed in a series of AlCuFe, AlPdMn and AlPdRe systems. Original information on the vibrational density of states g(ω) was obtained for AlPdRe; for AlCuFe and AlPdMn estimated g(ω) shows a good agreement with the previous neutron results, but demonstrates finer structure. Strong increase in the parameter of electron-vibrational coupling for the low-energy vibrations and its correlation with changes in electronic conductivity has been observed in the series from AlCuFe to AlPdRe. This suggests the increase of the degree of localization for these vibrational excitations and involved electronic states.     

Twinning of quasicrystals and related crystals

Electron microscopy and electron diffraction have been employed to bring out the intimate relationship between icosahedral quasicrystal and various types of crystalline phases with emphasis on aluminium transition metal alloys. The relationship between quasicrystal and twinned rational approximant structures will be treated in the context of irrational twinning. The twinned aggregates show an icosahedral like symmetry in electron diffraction patterns. The crystallography of irrational twins has been discussed in terms of various ways of representing a twin relationship in a cubic lattice.     

A single-crystal X-ray diffraction study of an Al70.5Pd21Mn8.5 icosahedral quasicrystal

X-ray diffraction data were measured on a single grain of a stable Al_70.5Pd₂₁Mn_8.5 perfect quasicrystal, in order to complement the neutron diffraction data obtained previously. The F-type lattice structure of the six-dimensional periodic arrangement was confirmed along with the very strong chemical order, due basically to an uneven distribution of the Pd atoms among the lattice sites. This distribution might be the origin of the high stability of the icosahedral structure in this system.     

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.     

Structural modelling of icosahedral and simple cubic approximant phase in Al-Mn(Fe)-Si system

In spite of various models being available for the icosahedral quasicrystal structure in Al-Mn(Fe)-Si system, a consistent model for describing the simple cubic approximant and icosahahedral structure in terms of rational and irrational sections of the same six dimensional cubic crystal seems to be lacking. Such a model is presented and the subtle difference between the present model and the previous ones is discussed. The necessity of such considerations is spelt out while accomplishing the partitioning of the tricontahedral motif (with extension in three dimensional pseudo direct space) based on the chemistry of the alloy. An algorithm for generating the required polyhedra for partitioning is also presented.     

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.     

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.     

Microstructures of Mg–Zn–Nd alloy including small quasicrystalline grains

Two kinds of Mg-rich and low neodymium Mg–Zn–Nd alloys including icosahedral quasicrystal phase (I-phase) were prepared under conventional casting conditions. The microstructures and phases of Mg–Zn–Nd quasicrystal alloys were investigated by means of X-ray diffraction (XRD), scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), and transmission electron microscopy (TEM). The results indicate that the I-phase in Mg–Zn–Nd quasicrystal alloy is a simple icosahedral quasicrystal with quasi-lattice of a_R = 0.525 nm. It has been proved that the as-cast Mg_70.8Zn₂₈Nd_1.2 quasicrystal alloy mainly consisted of I-phase and Mg₇Zn₃ matrix phase. While the as-cast Mg_70.5Zn_28.5Nd₁ alloy mainly consisted of I-phase, Mg₇Zn₃ matrix phase, dendrite α-Mg phase and a new rod-like hexagonal phase.     

Icosahedral and dense random cluster packing in metallic glass structures

It has recently been shown that metallic glass structures can be idealized as inter-penetrating solute-centered atomic clusters that are packed with essentially periodic symmetry. The present work applies the same methodology to explore whether experimental observations can be matched by inter-connected solute-centered clusters that are organized in space via dense random cluster packing, Bergman icosahedral cluster packing or Mackay icosahedral cluster packing. Idealized partial pair distribution functions are developed where the symmetry of the solute positions in the structure is derived from the cluster-packing symmetry and the solute concentration, which establishes occupation of inter-cluster sites, especially β structural sites enclosed by an octahedron of solute-centered clusters. While each of the three models matches major features of the measured solute-solute partial pair distribution functions, the arrangement of clusters with Mackay icosahedral ordering provides the best fit. However, this model is not able to match an essential feature in solute-lean glasses and does not provide the same overall agreement as does periodic cluster packing for solute-rich glasses. Strong similarities between the structure factors in the Mackay icosahedral and periodic cluster-packing models, along with expected deviations from the idealized solute positions studied here, are likely to hinder an unambiguous distinction between these two models.     

Atomic dynamics and interatomic interaction in quasicrystals

The previous experimental data on the partial spectra of thermal atomic vibrations in icosahedral (Al₆₂Cu_25.5Fe_12.5) and decagonal (Al_71.3Ni₂₄Fe_4.7) quasicrystals have been used to perform a comparative analysis of the atomic dynamics features and determine the role that Al, Cu, Ni, and Fe atoms play in the formation of interatomic interaction in the alloys studied. A physical model of the decagonal quasicrystal structure is proposed.     

Phason strains on growth, stability and structure of icosahedral phases

Growth, stability and structure of icosahedral (i-) phases have been studied by electron diffraction and X-ray diffraction in relation with the phason strains. Three alloy systems; AlPdCr, AlPdMn and AlCuV were chosen in this study. An i- Al₇₂Pd₂₅Cr₃ grain has been analysed to have a phason matrix toward to a tetragonal or orthorhombic structure. Stability of the i-phases correlated with the phason relaxation was discussed in Al-Pd-Mn system. A quenched i-Al₇₄Pd₁₇Mn₉ close to but containing significant phason strains, revealed that the phason relaxation induced by precipitation of crystalline phases upon annealing. Phason disorder dominated by the chemical composition was evidenced in a composition study in Al-Pd-Mn system. A high density random phasons characterized the icosahedral glass phase was observed in AlCuV alloys.     

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.     

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.     

Icosahedral symmetry in clusters

First principles calculations and simulations based on interatomic potentials together with experimental studies of abundance spectrum suggest icosahedral structures to be common for some magic clusters of diverse systems such as rare gases, metals, covalently bonded systems and water. Close packing models obtained from pair potentials are shown to be good representations of the structure of rare gas clusters. However, the electronic structure is found to play the important role in the atomic structure and related properties of other clusters. Results of recent studies of fullerenes, their derivatives as well as some large icosahedral metal clusters containing several thousand atoms are also presented. Further results on doped icosahedral clusters are discussed which hold promise for the development of new materials and for understanding the occurrence of icosahedral order in several aluminum alloys.     

Quasi-two-dimensional crystalline clusters on a sphere: Method of topological description

The formation of a “quasicrystal” on a closed surface has been considered for the Thomson problem on the arrangement with the lowest energy of N Coulomb charges on a sphere. The stable and metastable states of the system of charges with the charge number N = 2–100 and the symmetry groups of the corresponding configurations have been determined. The structure and possible structural transitions between the system states are described in terms of the introduced notion of a closed quasi-two-dimensional triangular lattice with topological defects. The graph of lattice defects is defined. A method for classifying the system in terms of the charge and the arrangement of topological defects in the lattice is suggested and extended to the case of an arbitrary lattice. The use of the model is considered on various physical examples, in particular, on a closed hexagonal lattice with disclinations in fullerenes.     

Hydrogen embrittlement assisted by ball-milling to obtain AlCuFe nanoparticles

In this work, we show that the synthesis of AlCuFe nanoparticles can be achieved by a wet ball-milling process. The AlCuFe intermetallic system is highly sensitive to the environmental embrittlement mechanism. Taking advantage of this, the wet ball-milling was used to increase the rate of grinding and accelerate the characteristic cleavage fracture of these phases. This research was carried out by subjecting Al₆₄Cu₂₄Fe₁₂ pre-alloyed ribbons to high-energy ball-milling under different powder–humidity relationships. The pre-alloyed and milled powders were characterized using scanning electron microscopy (SEM), X-ray diffraction (XRD), and scanning transmission electron microscopy (STEM). High resolution electron microscopy (HREM) measurements and energy-dispersive X-ray spectroscopy (EDXS) elemental chemical mapping confirm that the nanoparticles have a BCC structure with Al–Cu–Fe chemical composition. During the wet ball-milling, the aluminum content in the ψ-phase diminishes due to embrittlement mechanism which provokes its aperiodic disarrangement. This aluminum loss could be related with a ψ–β transformation.     

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.     

Magnetic properties of Al-based icosahedral alloys

One of the fundamental questions which has not been answered sufficiently well till today is whether a nonclassical symmetry such as an icosahedral one would induce any special and distinctive features in the physical properties of the systems. Most theoretical investigations indicate that there are unique features in the electronic structure on account of icosahedral symmetry which could for example, influence the magnetic properties significantly. Experimental studies, particularly, on Al-based icosahedral alloys, have shown a large variation in magnetic properties ranging from diamagnetic to Curie like and Pauli paramagnetism on one hand and ferromagnetic and spin glass like behaviour on the other. In the present article, we will concentrate on some aspects of moment formation and variation in magnetic properties in Al-Mn based icosahedral systems and their dependence on the method of preparation which presumably controls and introduces the variable disorder. We will also try to answer some pertinent questions related to magnetism in icosahedral systems such as extent and origin of moment formation existence of magnetic and nonmagnetic Mn sites and distribution of interatomic distances reponsible for variation in magnetic properties.