Short-range order of quasicrystals after ball milling

Thermodynamically stable icosahedral Al₆₅Cu₂₀Fe₁₅ alloy is studied using⁵⁷Fe Mössbauer experiments. Its quasicrystalline structure is subjected to a low energy process of mechanical grinding up to 800 hours. The influence of ball milling on the electric field gradient magnitudes is discussed using an analysis of the Mössbauer spectra to different fitting models. The presence of an amorphous phase which co-exists with the quasicrystalline one is revealed in the early stage of mechanical grinding.     

High-temperature electronic and thermal properties of icosahedral quasicrystals

We discuss the high-temperature electronic and thermal properties of an icosahedral quasicrystal within the framework of the fractional multicomponent Fermi-surface model. When intervalley electron-phonon scattering sets in above a characteristic temperature T^∗ of the order of the Debye temperature ΘD the quasicrystal becomes more “metallic”. In this regime the electrical conductivity and the electronic contribution to the thermal conductivity vary as T and T², respectively. We predict that at elevated temperatures the electronic specific heat will vary faster than γT and the low-frequency Drude-type component of the optical conductivity σ₁(ω) will gain weight.     

Planar and cluster structure of icosahedral quasicrystals

Twofold-, threefold-, and fivefold-symmetry elements are observed in the near-surface region of the quasicrystal Al₇₀Pd₂₀Mn₁₀ using a real-space imaging technique based on secondary-electron emission. The observed icosahedral point-group symmetry implies the presence of atomic clusters within the analyzed region of the solid. The same surface produces perfect low-energy electron diffraction patterns typical for well-defined crystallographic planes. We present a model which reconciles this dual structural nature of quasicrystals. Our model is constructed from an icosahedral seed followed by concentric symmetry-preserving “growth” to form the macroscopic solid. Presented at the VIII-th Symposium on Surface Physics, Třešt’ Castle, Czech Republic, June 28 – July 2, 1999. This work was supported in part by the Schweizerischer Nationalfonds.     

Bravais quasilattices of icosahedral quasicrystals

A classification of icosahedral quasicrystals based the mutual-local-derivability (MLD) concept is performed. There are eighteen MLD classes within the reservation that the faces of the hyperatoms (windows) are perpendicular to the two-, three-, or fivefold axes. Each MLD class has a representative member to be called the Bravais quasilattice from which the structure of each member of the class is derived by decorating it according to a local rule depending on the member.     

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     

Nonicosahedral equilibrium overlayers of icosahedral quasicrystals

We demonstrate that icosahedral Al-Pd-Mn quasicrystals can have nonicosahedrally ordered thermodynamic equilibrium overlayers. The formation of orthorhombic or decagonal equilibrium surface structures is determined by the phase equilibrium of the ternary alloy at given composition and temperature as well as by the surface acting as nucleation site. Nonequilibrium steady-state orthorhombic and hexagonal structures can also be derived with the same methodology when taking preferential evaporation into account. The results describe consistently all presently observed surface structures.     

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.     

Solitons and coreless defects in icosahedral quasicrystals

New types of spatially non-uniform excitations in icosahedral quasicrystalline lattices — solitons and coreless defects — are studied by the projection and topology techniques. The topological charges of particle-like solitons are revealed, each represents the set (z ₁,z ₂) of integers. The coreless defects are found to be topologically unstable excitations.     

Internal field emission nature of the fine structure of tunnel spectra in icosahedral quasicrystals

Calorimetric and tunnel data for the icosahedral phases of the Al–Cu–Fe system have been jointly analyzed. It has been found that the field-dependent part of the tunnel conductance can be represented as the sum of elementary terms similar in nature to thermal Schottky anomalies. As a result, the features of the fine structure of tunnel spectra in the form of zero-bias anomalies, peaks, and humps can be due to the internal field emission and can indicate a wide distribution of two-level electron traps in the electronic structure of quasicrystals. It was previously assumed that these features constitute a direct image of the density of single-electron states of the conduction band.     

Electron spectrum and wave functions of icosahedral quasicrystals

Electron spectra and wave functions of icosahedral quasicrystals have been investigated in the tight-binding approximation using the two-fragment structural model (the Amman-MacKay network) with “central” decoration. A quasicrystal has been considered as a limiting structure in a set of optimal cubic approximants with increasing lattice constants. The method of level statistics indicates that the energy spectrum of an icosahedral quasicrystal contains a singular (nonsmooth) component. The density of electron states has been calculated for the first four optimal cubic approximants of the icosahedral quasicrystal, and the respective Lebesgue measures of energy spectra of these approximants have been obtained. Unlike the case of a one-dimensional quasiperiodic structure, the energy spectrum of an icosahedral quasicrystal does not contain a hierarchical gap structure typical of the Cantor set of measure zero in a one-dimensional quasicrystal. Localization of wave functions in an icosahedral quasicrystal has been studied, and their “critical” behavior has been detected. The effect of disorder due to substitutional impurities on electron properties of icosahedral quasicrystals has been investigated. This disorder makes the electron spectrum “smoother” and leads to a tendency to localization of wave functions. Zh. éksp. Teor. Fiz. 113, 1009–1025 (March 1998)     

Hierarchy of vertices in imperfect icosahedral quasicrystals

Imperfect icosahedral quasicrystals are assumed to grow obeying a local rule which imposes the twin orientation of like building blocks. The vertex configurations and their representations are briefly discussed. The vertices are classified by their abundances and energies determined according to a simple model taking account of nearest-neighbour interactions and calculating the corresponding overlap volumes in dual space.     

Critical behavior of the wave functions of icosahedral quasicrystals

The character of the localization of the wave functions of an icosahedral quasicrystal is investigated in the tight-binding approximation. It is found that the wave functions exhibit “critical behavior”: they are neither localized, as in the case of Anderson localization, nor delocalized, as in the case of Bloch states. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 559–563 (25 October 1996)